Civil Engineering Research Papers

A discrete numerical model for granular assemblies

1979, Geotechnique

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Five Misunderstandings about Case-Study Research

2006, Qualitative Inquiry, vol. 12, no. 2, pp. 219-245

This article examines five common misunderstandings about case-study research: (a) theoretical knowledge is more valuable than practical knowledge; (b) one cannot generalize from a single case, therefore, the single-case study cannot... more

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Large Area Hydrologic Modeling and Assessment Part II: Model APPLICATION1

by Tharacad Ramanarayanan

1998, Jawra Journal of the American Water Resources Association

A conceptual, continuous time model called SWAT (Soil and Water Assessment Tool) was developed to assist water resource managers in assessing the impact of management on water supplies and nonpoint source pollution in watersheds and large... more

Figure 2. Components of the Hydrologic Balance Simulated Within a SWAT Subbasin.

$Figure 4. Nitrogen Forms and Transformations Simulated with a SWAT Subbasin. Fertilization. Fertilizer applications can also be scheduled by the user or automatically applied by the model. The user-scheduled option requires the user to input the application date, total amount of N and P, fraction of organic and inorganic N and P, and the soil layer of application. The model adds the amount of fertilizer to the proper nutrient pool (organic and inorganic) and to the specified soil layer. The auto- matic fertilization option requires the user to input the plant nitrogen stress level (0-1) to trigger fertil- ization, the amount of NOs in the soil profile after fer- tilization, the soil layer of the application, the maximum amount of NO3 that can be applied in one year, and the minimum time between fertilizer appli- cations.$

Figure 5. Pesticide Transformations Simulated Within a SWAT Subbasin.

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Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology

by Hygreeva Namburi

The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original... more

FIG. 1. Schematic illustration of indentation load—displacement data showing important measured parameters (after Ref. 1).

FIG. 2. Schematic illustration of the unloading process showing pa- rameters characterizing the contact geometry (after Ref. 1). Using Eq. (2) to approximate the vertical displacement of the contact periphery, it follows from the geometry of where € is a constant that depends on the geometry of the indenter. Important values are: € = 0.72 for a conical punch, € = 0.75 for a paraboloid of revolution (which approximates to a sphere at small depths), and e = 1.00 for a flat punch.** Based on the empirical observation that the unloading curves are best approximated by an indenter that behaves like a paraboloid of revolution (m = 1.5), the value € = 0.75 was recommended and has since become the standard value used for analysis. Recent analytical work has provided a more complete picture of why ¢ takes on this value.***? This is also addressed in Sec. III. A.

FIG. 3. Concepts used to understand and define the effective indenter shape (from Ref. 35). The ideas underlying the effective indenter shape are outlined in Fig. 3. The basic principles are derived from observations gleaned from finite element simulations of indentation of elastic—plastic materials by a rigid conical indenter with a half included angle of 70.3°.*° During the initial loading of the indenter [Fig. 3(a)], both elastic and plastic deformation processes occur, and the indenter conforms perfectly to the shape of the hardness impres-

FIG. 4. Topographic image of a Berkovich indentation in fused silica obtained using a quantitative imaging system that uses the indenter itself as the imaging tip: (a) complete 3D image showing the curvature of the faces; (b) cross section through an edge and the opposing face with straight lines included to accentuate the curvature. Experimental evidence for the curvature in the un- loaded hardness impressions is given in Fig. 4, where topographical images of a Berkovich indentation in fused silica are presented. The images were obtained by scan- ning the specimen laterally under the indenter tip with a very light load applied to the indenter to keep it in con- tact. The three-dimensional (3D) image in Fig. 4(a)

FIG. 5. The relation between € and m given by Eq. (17) (from Ref. 35).

FIG. 7. Dependence of normalized contact areas on the experimental parameter h,/h,,,,. The areas are normalized with respect to Aj, the area given by the area function of the indenter assuming no pile-up or sink-in (after Ref. 25).

FIG. 8. Finite element simulation of normalized contact profiles under load for spherical indentation of an elastic—perfectly-plastic material with E/oy = 200 showing the influence of the normalized penetration depth, //R, on the pile-up/sink-in behavior (after Ref. 34).

Recent studies have shown that even for perfectly elas- tic contact by a rigid cone, 8 may deviate from unity due to departures from the small strain approximation. Hay et al.*° used both finite element simulation and analytical techniques to examine indentation of an elastic half- space by a rigid conical indenter. They showed that the derivation used to obtain Eq. (6) with B = 1 is not strictly valid for the conical indenter geometry because it improperly accounts for radial material displacements in the region of contact (note: Hay et al. originally desig- nated this correction factor as y). They developed an approximate correction for the effect that gives

FIG. 10. Typical load versus displacement curve for a calibratior experiment in fused silica. FIG. 9. An indentation in fused silica made by raster scanning with a nanopositioning stage. Data obtained from this indentation were used to calibrate the load frame compliance and area function. (a) The image on the left shows the borders defining the two contact areas discussed in the text. (b) The image on the right is included for clarity.

FIG. 12. An expanded view of the load versus displacement curve at the point of contact. Although the harmonic stiffness is the preferred loca- tor of the surface in this particular situation, it should be noted that which of the measurements in Figs. 12-15 provides the best surface definition depends on the prop- erties of the material and the characteristics of the testing system. The resonant frequency of the testing system is particularly important (12 Hz for the system used here). As the stiffness of the contact increases, the resonant frequency of the combined instrument and contact sweeps toward higher values. The exact nature of the changes observed in the dynamic measurements in Figs. 13-15 then depends on whether the system moves toward resonance (as in our experiments) or away from it as contact is made. In fact, it is because the system moves toward and through resonance that the harmonic dis- placement in Fig. 13 actually increases rather than de- creasing when contact is made. Often, the most sensitive frequency for surface detection is the resonant frequency of the testing system just prior to contact; however, this is generally also the frequency at which the system is most vulnerable to noise (vibration, and so forth).

FIG. 11. A typical stiffness versus displacement curve for the cali- bration experiment. Stiffnesses were determined using the continuous stiffness measurement technique.

FIG. 14. An expanded view of the phase angle versus displacement curve at the point of contact. FIG. 13. An expanded view of the harmonic displacement amplitude versus displacement curve at the point of contact.

FIG. 16. A typical load over stiffness squared versus displacement for the calibration experiment. Note the constant value beyond 1000 nm. In Fig. 17, we demonstrate the load frame compliance measurement procedure for three different assumed val- ues of C;. The correct value, C; = 9.62 x 10° m/N, results in a flat curve for the data between 1000 nm and 2300 nm where the tip rounding is unimportant. How- ever, increasing or decreasing C; by as little as 20%

FIG. 15. An expanded view of the harmonic stiffness versus displace- ment curve at the point of contact. Note the minimum observed prior to full contact and the steep rise in stiffness at the point of contact.

FIG. 18. The change in the projected area of contact for a tilted Berkovich indenter versus the ratio of the lengths of the longest to the shortest side. For the experimental data presented here (Figs. 10 and 11), the first approach was taken to determine the area function. A back-reflection laser goniometer was used to measure the face angles to within 0.025°, giving Cy = 24.212. In precision work, this must be modified if the indenter is not aligned with its axis perfectly perpendicu- lar to the specimen surface, as such misalignments in- crease the area at a given contact depth. The degree of tilt can be assessed from measurements of the sides of the hardness impression if a good image is available. A simple but effective method is based on the ratio of the long to short side of the hardness impression. Figure 18 shows how the contact area at a given depth depends on this ratio when the indenter is tilted slightly toward an edge or a face. Other tilt directions lie in-between the two

FIG. 17 Load over stiffness squared versus displacement for three different values for the load frame stiffness. The curve with the correct load frame stiffness is flat at large depths.

FIG. 20. Difference between the areas predicted by the area function and the data used to obtain the fit. This area function works well at small depths but not at large.

FIG. 19. Difference between the areas predicted by the area function and the data used to obtain the fit. This area function can be used at large depths.

TABLE I. Values of parameters characterizing unloading curves as observed in nanoindentation experiments with a Berkovich indenter.* “Data from Ref. 1.

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ANALYSIS OF CRACK FORMATION AND CRACK GROWTH IN CONCRETE BY MEANS OF FRACTURE MECHANICS AND FINITE ELEMENTS

by Noushad binjamal

A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way... more

The crack is assumed to propagate when the stress at the crack tip reaches the tensile strength f,. When the crack opens the stress is not assumed to fall to zero at Once, but to decrease with increas- ing crack width w, for example according to Fig. 3. At the crack width wy, the stress has fallen to zero. For that part of the crack where w<wy, the "crack" in reality corresponds to a microcraced zone with some remaining ligaments for stress transfer. As there is a stress to be overcome in opening the crack, energy is absorbed. The amount of energy absorbed per unit crack area in widening the crack from zero to or beyond wy is

For concrete it seems that Fig. 4c is the best choice as it corresponds reasonably well with tension test results /4/, cf. Fig. 5. It is also simple, continuous and suitable for FEM analysis. For Our purpose we have therefore chosen Fig. 4c. We then obtain

A special feature of the proposed method is that it explains not only the growth of existing cracks, but also the formation of new cracks, as it is assumed that cracks start forming when the tensile stress reaches fy, i.e., the same criterion is used for formation and propagation of cracks.

left end of the beam. The crack iS assumed to open at the section to the right, which is the section of symmetry. Mgis the moment which gives 03] = ft, where o3] is the stress at point 31. Mp would be the failure moment if the material were elas- tic and perfectly brittle. When M is raised above Mj the crack starts Opening at point 31. At that point we introduce a force corresponding to the relation between stress ao and crack width w according to Fig. 4c. With this new finite element system we can calculate the stress at point 32 and we can determine that value M = Mj), which gives a stress 032 = f,. We can now introduce another force at point 32 and calculate a moment M = M2» giving 033 = ft etc. By proceeding in the same way we get a relation between crack depth and applied moment according to Fig. 7.

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Principles of Plasma Discharges and Materials Processing

by Ahmed Medhat

1994

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GENERATING OPTIMAL TOPOLOGIES IN STRUCTURAL DESIGN USING A HOMOGENIZATION METHOD

by Zunyi Duan

Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require... more

Finite element mesh sensitivity for the first cell

Finite element mesh sensitivity for the second cell

Fig. 4. Adapted finite element grid (cell 2). For use in shape optimization, the homogenized elasticity tensor must be obtained for a “continuously” varying size of a rectangular hole in the cell so that the density of the substance of materials can be a continuous design variable for the optimal “material distribution.” To this end, it is certainly impossible to determine the homogenized elastic

constant for all the possibilities of the material density (that is, the size of a rectangular hole in the cell). Thus, we compute the homogenized elastic tensors for certain sizes of the hole, and other values are then interpoiated by, e.g., Legendre polynomials, in order to have a continuous variation with respect to material density. An example for a square hole is shown in Figs. 5 and 6 in which four representative square holes and the interpolated components of the homogenized elastic tensor are given, respectively. It is noted that the variation of the elastic moduli is highly nonlinear, as shown in Fig. 6. This nonlinearity wii! play an important role in the shape optimization and will be examined by comparing the res: sts obtained in the case of a linearly varying elasticity tensor. It is also important to note that if the cell structure is rotated in relation to a fixed reference frame (for example the coordinate system of the shape optimization problem), the transformed elastic tensor is very different from the one for the unrotated case. The influence of the rotation of the cell becomes very strong when the size of the hole becomes large, as shown in Fig. 7, and it can be seen that a possibility of rotation

Fig. 5. Representative square holes in the unit (square) cell.

Fig. 8. Different choices of design domain 2, for a given set of surface tractions.

Gesign area tnat ?s available for the construction of the fillet. For the sake of comparison, a design optimization was also carried out for the case of rigidity that is linear in the design variable, as for variable thickness sheets, cf. Section 2. Suc design problems have been studied in detail in [51], and are very well-behaved problem: Figure 10 shows results for this type of problems and illustrates that this representation stiffness gives a good indication of the two-dimensional optimal shape for high volum fractions, while for low volume fractions it is difficult to interpret the results so as to define two-dimensional shape. This is, of course, not surprising as we are dealing with a tru three-dimensional problem that just happens to have a two-dimensional model. That is th variable thickness is a hidden three-dimensional feature. However, the design of variab] thickness sheets does indeed give well-defined shapes as three-dimensional structures. The testing of the design method using composite materials has been carried out for variou different formulations that all relate to the description of the method given in Section 4. Tw

Fig. 11. Results for two different discretizations. Case B with voids as square holes. Left-hand column for 16 x 10 mesh, right-hand column for 32 x 20 mesh. Volume is 91%, 64%, 36%, respectively. Black areas indicate material, and density of voids is illustrated as a removal of black areas. The voids are drawn element-wise as a rotated, macroscopic hole; note that the voids in reality are at microlevel.

Fig. 12. Comparison with two-variable composite design. Case B with voids as rectangular holes. Volumes are (a): 1%, (b): 64%, (c): 36%.

“MVE PUL HO ‘216 O18 SOUIN[OA ‘sUdIsap podumn] SuNNses oy) UUINTOS pueYy-7Yy3IE ‘SuIduIN] 0} JO y[NsAa1 SMOYs UUIN[OS pueY-2T] °psjej03 aq WED Jey) Sajoy arenbs se sploA YIM Y aseD “ssodoid Suiduiny ayy Jo syNsey “pT “By

Fig. 15. Results obtained by boundary variations. Case A, with volumes 91%, 64% and 369

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Geophysical Fluid Dynamics

by shantanu ghosal

1981, Journal of Applied Mechanics-transactions of The Asme

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Finite element procedures in engineering analysis

by Michael Mera

1984, Journal of Pressure Vessel Technology

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Updated high‐resolution grids of monthly climatic observations–the CRU TS3. 10 Dataset

by Tim Osborn

This paper describes the construction of an updated gridded climate dataset (referred to as CRU TS3.10) from monthly observations at meteorological stations across the world's land areas. Station anomalies (from 1961 to 1990 means) were... more

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Numerical solution of the Navier-Stokes equations

by LUCAS WANGWE

1968, Math. Comp

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Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation

by Greg McCabe

1999, Water Resources Research

Correlation and correlation-based measures (e.g., the coefficient of determination) have been widely used to evaluate the "goodness-of-fit" of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values... more

Correlation and correlation-based measures (e.g., the coefficient of determination) have been widely used to evaluate the "goodness-of-fit" of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values (outliers) and are insensitive to additive and proportional differences between model predictions and observations. Because of these limitations, correlation-based measures can indicate that a model is a good predictor, even when it is not. In this paper, useful alternative goodnessof-fit or relative error measures (including the coefficient of efficiency and the index of agreement) that overcome many of the limitations of correlation-based measures are discussed. Modifications to these statistics to aid in interpretation are presented. It is concluded that correlation and correlation-based measures should not be used to assess the goodness-of-fit of a hydrologic or hydroclimatic model and that additional evaluation measures (such as summary statistics and absolute error measures) should supplement model evaluation tools. 1. Introduction A primary goal of modeling physical processes in the atmospheric and hydrologic sciences is the prediction of a variable in time and/or space from a given set of inputs. How well a model fits the observed data (referred to as model evaluation, or sometimes as model validation) usually is determined by pairwise comparisons of model-simulated (or model-predicted) values with observations. Quantitative assessments of the degree to which the model simulations match the observations are used to provide an evaluation of the model's predictive abilities. Frequently, evaluations of model performance utilize a number of statistics and techniques. Usually included in these tools are "goodness-of-fit" or relative error measures (bounded statistics, usually between 0.0 and 1.0) to assess the ability of a model to simulate reality. Often these statistics are based on the familiar Pearson's product-moment correlation coefficient (r) or its square, the coefficient of determination (R2). These two statistics describe the degree of collinearity between the observed and model-simulated variates. They are almost always discussed in basic statistics texts and, consequently, are familiar to virtually all scientists. Unfortunately, both r and R 2 suffer from limitations that make them poor measures of model performance. Although these statistics continue to be used to determine how well a model simulates the observed data, they nevertheless provide a biased view of the efficacy of a model [}tSllmott, 1981; Willmott et al., 1985; Kessler and Neas, 1994; Legates and Davis, 1997]. As knowledge of physical processes has increased, models have become more complex. Often these models include numerous parameters that are calibrated through optimization procedures, where a range in model parameters is sampled until the differences between the observed and modelsimulated data are minimized [Nash and Sutcliffe, 1970; Song and James, 1991; Hay, 1998]. Stochastic calibration procedures are usually employed, which limits graphical analyses of scatterplots, for example, so that statistical analyses must be solely used. Consequently, statistics other than r and R 2 have been developed to describe better the degree of association between the observed and model-simulated data. The objectives of this paper are to (1) examine various goodness-of-fit measures and to identi• limitations associated with each, and (2) suggest viable alternative measures for the evaluation of hydrologic and hydroclimatic models.

WHT EM VVELU GE SELULOsS LM MIC Gi LU Ue CHU Le PCeLivy of the evaluation. Note, however, that the coefficient of deter- mination is limited in that it standardizes for differences be- tween the observed and predicted means and variances since it only evaluates linear relationships between the variables. It can be easily demonstrated that if P, = (AO, + B) for any nonzero value of A and any value of B, then R? = 1.0. Thus R? is insensitive to additive and proportional differences be- tween the model simulations and observations [see Willmott, 1984]. Large values of R? can be obtained even when the model-simulated values differ considerably in magnitude (i.e., values of B that differ significantly from 0.0) and variability (i.e., values of A that differ significantly from 1.0). Clearly, in such cases, a model would exhibit serious flaws that should preclude the attribution of a “perfect” designation. These lim- itations in the coefficient of determination and other correla- tion-based measures are well documented [cf. Willmott, 1981; Moore, 1991; Kessler and Neas, 1994; Legates and Davis, 1997], although such measures still have been used recently to pro- vide, for example, an assessment of climate change detection [e.g., Santer et al., 1995; Hegerl et al., 1996; Santer et al., 1996] and hydrological and hydroclimatological applications (see McCuen and Snyder [1975] and Willmott [1984] for some ex- amples).

where j represents an arbitrary power (i.e., a positive integer). Note that the original index of agreement d developed by Willmott [1981] becomes d, using this notation.

where O’ is the baseline value of the time series against which the model is to be compared. It usually is a function of time and, in some applications, may be a function of other variables as well. Consequently, d{, is useful in that its interpretation is more conventional, as it more closely follows the interpretation Garrick et al. [1978, p. 376] further argued that the assump- tion of comparing the model to the observed mean was “un- necessarily primitive.” Better methods exist to define the base- line against which a model should be compared. For example, persistence or averages that vary by season or another time period (i.e., a climatology) may provide a more appropriate baseline for most hydrological or hydroclimatological studies than simply the average of the entire time series. Thus both E, and d, can be rewritten in a “baseline adjusted” form as

Figure 2. Scatterplots of the Thornthwaite, Jensen-Haise, van Bavel, and climatological (monthly mean) estimates versus the observed (coefficient adjusted pan evaporation) data pre- sented in Figure 1. An examination of Pearson’s correlation coefficient (r) or the coefficient of determination (R*) yields a misleading pic-

Figure 1. Time series of monthly potential evapotranspiration estimated by the Thornthwaite [1948], Jensen and Haise [1963], and van Bavel [1966] methods compared with observations (measured pan evaporation multiplied by a pan coefficient of 0.76). Data were taken from January 1981 through December 1983 for southern Louisiana (data from McCabe and Muller [1987]).

Figure 4. Scatterplot of the observed and modeled monthly runoff (precipitation runoff modeling system) data presented in Figure 3.

Figure 3. Observed and modeled monthly runoff (precipitation runoff modeling system) for the East River Basin in southwestern Colorado from October 1972 through September 1989 (data from McCabe and Hay [1995]).

Table 1. Means and Standard Deviations of Observed and Simulated Monthly Potentia Evapotranspiration for Baton Rouge, Louisiana, for the Period From January 1981 Through December 1983, and Statistics Comparing the Observed and Simulated Time Series

Table 2. Means and Standard Deviations of Observed and Simulated Monthly Runoff in the East River Basin in Southwestern Colorado for the Period October 1972 Through September 1989, and Statistics Comparing the Observed and Simulated Time Series

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Comparison of Multi‐Objective Evolutionary Algorithms for Long‐Term Monitoring Design

by Joshua Kollat

2005

This paper examines the performance of two multiobjective evolutionary algorithms, NSGA-II and SPEA2, with informed initialization on large instances of United States Navy's Sailor Assignment Problem. The informed initialization includes... more

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A review on machinery diagnostics and prognostics implementing condition-based maintenance

by Dragan Banjevic

2006, Mechanical Systems and Signal Processing

Condition-based maintenance (CBM) is a maintenance program that recommends maintenance decisions based on the information collected through condition monitoring. It consists of three main steps: data acquisition, data processing and... more

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The nondarcy regime for vertical boundary layer natural convection in a porous medium

by husnul khatimah

1984, International journal of heat and mass transfer

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A new Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models

by Ray Ogden

2004, Cardiovascular Soft Tissue Mechanics

In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers... more

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A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities

by william wallace

2003, Earthquake Spectra

This paper presents a conceptual framework to define seismic resilience of communities and quantitative measures of resilience that can be useful for a coordinated research effort focusing on enhancing this resilience. This framework... more

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Multifractal detrended fluctuation analysis of sunspot time series

by M Movahed

2006, Journal of Statistical Mechanics-theory and Experiment

We use multifractal detrended fluctuation analysis (MF-DFA), to See query 1 study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the... more

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Macropores and water flow in soils

by Peter Germann

1982, Water Resources Research

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A PLASTIC-DAMAGE MODEL FOR CONCRETE

by ec pf

AWract-fn this paper a constitutive model based on an internal variable-fo~uiation of plasticity theory for the non-linear analysis of concrete is prcscnted. fhc mod4 uses a new yield criterion which matches expcrimcntal data quite well... more

AWract-fn this paper a constitutive model based on an internal variable-fo~uiation of plasticity theory for the non-linear analysis of concrete is prcscnted. fhc mod4 uses a new yield criterion which matches expcrimcntal data quite well and it accounts for both elastic and plastic stiffness degradations etfects. On.wt and amount of crackillg can bc studitd by a simple postprocessing of the ~njte-element plasticity solution. The xcuracy of the model is checked with some examplss of application. I. INTROIXJ(I'ION The &t&al theory of pl:tstioity. like Tony twthcnluticnl roprcscntation of the mcchnnicitl bchnvior of solids. may hc vicwcd in two ways : iIS il tr;illSliltiOIl 01' phySiCill reality. ilfld iIS il m&l that ilppronirn;ltcs the hchnvior under certain circumstances. The lirst view is often held with royard to ductile crystalline solids, cspcciillly metals. :llthough the attempts to rclatc mathematical plasticity theory to dislocations hvo not been markedly successful. With reg;trd to concrctc and rock, howcvcr, it hits gcnc~\lly been ~lckn~~w~cd~c~~ that such pr~~mincnt fc:tturcs of pl:isticity theory ;is ii well dcfincd yield criterion and strictly ClilStiC uni~~~Iin~ iwe ~pproxifniltions ilt bCst. ~~v~rt~~~~~ss, many problems involving thcsc mlttcrinls hitvc bren quite succcssfufly trc;ltcd by mcuns of plasticity theory, and these results are not inv~llid~ltc~i by frtct that other problems have not hccn so successfully treated. nor by the fact that other models may h;lvc been cquuily cfl&tivc. The broitdcst arelt of success of pklsticity theory with conorctc is the treatment of reinforced concrete (see Chcn, 1982 for 3 survey of the results) und other situations in which the material acts primarily in compression. In problems in which tension, with the attendant crack development, plays ;L significant rolc-such i\s shear Failure in reinforced-concrete structures-the usual proctdurc nowadays is to apply plasticity theory in the compression zone. tend trtxt the zones in which iit Icnst one principal stress is tensile by one of several versions of fracture mechanics. such as: linc;lr elastic fracture mechanics. Bcinnt and Cedolin (1980) : smeared-crack mod&. Rushid (1968). Suidan and Schnobrich (1973). de Borst and Nrtuta (1984); the fictitious-crack modct, fiiltcrborg ct uf. (1976); and crackband theory, B6tmt rend Oh (1983). In spite of the success of this :tpproitch in solving numcrotjs problems, it presents some inconvenient fcitturcs that limit its usefulness. such ;ts the need for defining uncoupled behavior along each principal stress (or strain) direction. the USC of a quite arbitrary shear retention factor to ensure some shcrtr rcsistancc illong the crack. the lack of equilibrium at the cracking point when mocc than one crack is formed (Ofiatc ct ui.. 1986), the difficulties of defining stress p:lths following the opening and closing of cracks under cyclic loading conditions. and the diflicultics of dealing with the combined cffcct of crrlcking and plilsticity at the damaged points (dc Borst. 1987). Some of these limitations could bo avoided if a single constitutivc model could be used that governs the non-linear behnvior of concrete. including failure. in both tension and compression, with appropriate allowance mrtde for the different values of the parameters describing the two modes. It is the purpose of this paper to formulate such a model in the 30 A plastic-damage model for concrete 301 variable K. similar to the former in that it never decreases, and increases if and only if plastic deformation takes place. However. the plastic-damage variable cannot increase beyond a limiting value, and the attainment of this value at a point of the solid represents rota1 damage, which can be interpreted as the formation of a macroscopic crack. The variable K

Fig. {. Uniaxial curves (a—") : (a) tension; (b) compression

The significance of g, and g.. tt has been made abundantly clear over the past decade that the strain-softening branch of the stress-strain curves of concrete and rock cannot represent a local physical property of the material. The arguments have been advanced both on physical grounds and on the basis of the mesh-sensitivity of numerical solutions obtained by means of the finite-element method. The mesh-sensitivity can be largely elim- inated if one defines g, = G,/land gy, = G,/l, where / is a characteristic length related to the mesh size, and G, and G, are quantities with the dimensions of energy/area that are assumed to be material properties.

where f = (1,1, 1,0,0,0), dev = 1— {tt' (1 being the 6 x 6 identity matrix), and D = All'+GUdev,

Fig. 5. Biaxial compression test. Relevant material parameters and finite-clement mesh.

Fig. 7. Biaxial compression test. Distribution of cracking for pure symmetric compression. 4.1.3. Double non-symmetric compression : 6y.-0 4, = —1/—0.52 anda, = 0. Numeri- cal results obtained for the o3,-62. and @3.-£,, curves are shown in Fig. 9(a). Results agree reasonably well with those reported by Kupfer et a/. (1969), with errors of 3% and 15% in the peak stress and the corresponding strains, respectively, for the o2.-£2, curve for both associated and non-associated plasticity analysis. The use of non-associated plasticity seems to be more important to match experimental results for the o2.-¢,, curve, although the peak response ts not very precisely reproduced in this case. The difliculties of analyzing this problem are evidenced in the reproduction of the numerical results obtained by various researchers shown in Fig. 9(b).

Fig. 9. Biaxial compression test. Compared stress-strain results for double mon-symmetric compression.

Fig. 11. Notched beam. Load -displacement curves, comparison with experimental results. Fig. 10. (a) Notched beam. Relevant material parameters and finite clement mesh. (b) Notched beam. Crack Mouth Sliding Displacement (CMSD).

Fig. 13. Notched beam. Stress field: (a) at the elastic state (A); (b) at the ultimate state (C)

Fig. 14. Notched beam. Deformed shape at ulumate state (displacement magnified 300 times), and localization of the damage.

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P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method

by Jean Virieux

1984, Exploration Geophysics

A new finite-difference (FD) method is presented for modeling SH-wave propagation in a generally heterogeneous medium. This method uses both velocity and stress in a discrete grid. Density and shear modulus are similarly discretized,... more

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Techniques of trend analysis for monthly water quality data

by arun bharathi

1982, Water resources research

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Empirical equations for some soil hydraulic properties

by Roger B Clapp

1978, Water Resources Research

with a power function relating soil moisture and hydraulic conductivitymis used to derive a formula for the wetting front suction required by the Green-Ampt equation. Representative parameters for the moisture charac- teristic, the... more

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Electromagnetic interference shielding with Portland cement paste containing carbon materials and processed fly ash

by Yury Gogotsi

2010, Materiales de Construcción

Función de apantallamiento de interferencia electromagnética de pastas de cemento con materiales carbonosos y cenizas volantes procesadas

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A constitutive model for partially saturated soils

by Antonio Gens and

1990, Géotechnique

The Paper presents a constitutive model for describing the stress-strain behaviour of partially saturated soils. The model is formulated within the framework of hardening plasticity using two iodependent sets of stress variables: the... more

Fig. 2. Relationship between preconsolidation stresses p, and po*: (a) compression curves for saturated and unsaturated soil; (b) stress path and yield curve in (p, s) stress plane

Fig. 3. Wetting and loading stress path in (p, s) stress plane

Fig. 4. Shapes of the LC yield curve fer different values of the parameters py*, r and £

As reviewed in a previous section, an increase in suction may also induce irrecoverable strains.

Fig. 8. Three-dimensional view of the yield surfaces in (p, g, s) stress space where k is a constant. The major axis of the ellipse will span the segment —p,(s) to po(s) and where « is chosen in such a way that the flow tule predicts zero lateral strain for stress states corresponding to Jaky’s (1948) K, values (Ky = 1—sin ¢ = (6 — 2M)((6 + M)). Given the relationship between Ky and M the new flow rule does not introduce any additional constitutive parameter. The components of the plastic strain associated with this yield surface will be given by (de,,°, de”). The expressions for these strain com- ponents can be derived by the application of stan- dard procedures of strain hardening plasticity. For the second yield surface (Equation (13)), the vector of plastic strain increment induced by suction increase will be (de,,?, 0), where de,,” is given by Equation (22).

MPa, p, = 0-15 MPa), three alternative loading stress paths (1, 2, 3) which always involve a non- increasing suction and a common final stress point, s; = 0 and p,; = 0-6 MPa, are represented. The initial position of the yield curves is given by Po* = 0-20 MPa and sy = 0-3 MPa. The different combinations of p-loading and suction reduction, inducing either expansion (A> C—>E-F) or collapse (A>B—>D-F), take the LC yield curve to a final common position LC,. The final volumetric deformation is the same under the three stress paths. These types of loading and suction change sequences lead to volume changes which are stress path independent and they have been used by some authors, quoted before, to for- mulate the volumetric behaviour of partially satu- stress, a larger collapse takes place (segment EF in Fig. 11(b)). Also, the compression curves, once the wetting is completed, follow a unique path for saturated conditions (path DF after wetting 2 follows the saturated compression curve BDF). Experimental results which favour this unique- ness have been reported by Jennings and Burland (1962) and Blight (1965) for collapsing sands, by Erol and El-Ruwaih (1982) testing loess and by Maswoswe (1985) in the case of a low plasticity sandy clay.

Fig. 12. Response of model to increments of net mean stress p and decreasing suction (wetting): (a) stress paths; (b) specific volume-net mean stress relationships

Fig. 13. Response of model to increments of net mean stress p and increasing suction (drying): (a) stress paths; (b) specific volume-net mean stress relationships

Fig. 14. Effect of initial increase of suction: (a) stress paths; (b) specific volume-n mean stress relationships

Fig. 15. Response of model to shear tests at different suctions: (a) stress paths; (b) shear stress—shear strain relationships

In order to obtain A, and x,, tests involving the application of suction cycles at a constant net mean stress p, are ideally suited, provided the

Several shear strength tests were performed at different values of p and s (Fig. 19). Within the The shear modulus G was obtained in drained tests involving the application of a deviatoric stress q at different values of net mean stress and suction. The stress paths selected and the mea- sured shear stress-strain relationships are given in Figs 22(a) and (b) respectively (these tests will be used subsequently to compare with model predictions). As a consequence of the flow rule assumed, no plastic shear strains occur at the start of the test, so the initial part of the stress— strain curves can be used to determine the elastic shear modulus G. A value of 3-3 MPa was obtained. QO... 2.2 ee ee ee ea, a re

Fig. 21. Comparison between measured and predicted results for partially saturated compacted kaolin under isotropic stress changes: (a) stress paths; (b) variation of specific volume with net mean stress

Fig. 22. Shear tests on partially saturated compacted kaolin: (a) stress paths; (b) comparison of measured and predicted shear stress—shear strain relationships

Fig. 24. Results reported by Maswoswe (1985) (Test SK3) and model predictions: (a) variation of void ratio with vertical stress; (b) stress paths in the triaxial plane

Fig. 25. Tests on compacted kaolin reported by Karube (1986): (a) stress paths; (b) comparison between experi- mental and computed results These two tests are particularly interesting since they reveal most of the patterns of behav- iour of partially saturated soil, discussed in pre- OSEAN Svante: Tnygye Rawinupernrws FEMe ier: Ny CRATE TZata ge The results of several tests on partially saturat- ed compacted kaolin in a triaxial cell were report- ed by Karube (1986). The following basic properties of the soil are provided in this refer- ence: w, = 37%; IP = 28%; clay fraction: 22%; maximum size of particles: 0-04mm. Among the different results reported, two tests corresponding to the stress paths shown in Fig. 25{a) have been selected for comparison with the model devel- oped.

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Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States

by Michael Halbleib

2008, International Journal of Climatology

Spatial climate data sets of 1971-2000 mean monthly precipitation and minimum and maximum temperature were developed for the conterminous United States. These 30-arcsec (∼800-m) grids are the official spatial climate data sets of the U.S.... more

Table III. Number of stations used in the mapping process, and native averaging interval. See text for definitions of acronyms.

Figure 1. Locations of (a) surface precipitation stations and (b) surface temperature stations used in the interpolation.

Figure 2. Western U.S. coastal proximity grids for (a) temperature (TW) and (b) precipitation (PW). Coastal proximity describes the optimal path length from the coastline in kilometres, accounting for terrain blockage. Trajectory describes the straight-line path length from the coastline in kilometres, modified by terrain blockage. Topographic facet guidance is provided to PRISM through a series of topographic facet grids (Table ID). The current method for delineating topographic facets is described in Gibson et al. (1997) and Daly et al. (2002). Facet grids are constructed for six DEM smoothing levels, or scales (Daly et al., 1994, 2002). The smoothed DEM for each level is prepared by applying the Gaussian filter (Barnes, 1964) to the precipitation DEM. The horizontal filtering cut-off distance (i.e. how far out the A simple trajectory model was designed to assess rela- tive moisture availability to guide precipitation mapping (abbreviated PW; Table I). The trajectory model is simi- lar to the coastal advection model in that it accounts for changes in moistu re content due to path length and ter- rain effects. It differs in that the air parcel trajectories are straight line and invariant throughout the simulation, as might be the case within large-scale synoptic circula- tions that produce significant precipitation. The premise here is that the mean potential for precipitation expe- rienced at a site is the result of (1) loss of moisture through rainout, which accumulates as the path length over land increases, and (2) enhancement and suppres- sion of precipitation caused by adiabatic cooling and warming during gence is not consi bearing air flow al southwesterly, wit flow over terrain obstacles. Conver- dered in this simple model. Moisture- ong the West Coast is most commonly h some variation around that direction. Therefore, the trajectory model was run for three flow directions: 230, 24 aged as 0.2(230) 4 O, and 250° true, and the results aver- + 0.6(240) + 0.2(250). Algorithms for, and operation of, the trajectory model are given in Daly

Figure 3. Topographic facet grid for the conterminous United States at a filtering distance of 36 km. A simple method was developed to spatially distribute the approximate height of the top of a climatologically persistent inversion layer, should it exist, for use in Our analyses of rawinsonde data from several cities in the United States with persistent climatological inver- sions, mostly during winter, indicated that the inver- sion top typically occurred at roughly 200-300 m above ground level. Therefore, 250 m was added to the base elevation at each grid cell to obtain the potential inver- sion height above sea level. While this is only a rough approximation of the inversion height, it has been effective for modelling purposes (Table II). The poten- tial inversion height grid for the contiguous United States is illustrated in Figure 4. Valleys, plains, and other low-lying areas tend to fall within the bound- ary layer, while local ridge tops and other elevated

Figure 4. Potential inversion height grid for the conterminous United States, illustrated as the difference between the inversion height and the 800-m DEM elevation. Terrain rising above the inversion height (in layer 2) is shaded, and terrain falling below this height (in layer 1) is unshaded.

Figure 5. Topographic index grid for the conterminous United States. The scale indicates metres above the local base terrain. PHYSIOGRAPHICALLY SENSITIVE MAPPING OF CLIMATOLOGICAL TEMPERATURE AND PRECIPITATION

Figure 6. Effective terrain grid for the conterminous United States. Black areas denote terrain features that are expected to produce the strongest terrain-induced (3D) precipitation patterns, and grey areas denote features expected to have some influence on precipitation patterns (2D/3D transition). Unshaded grid cells as far as 100 km away from the shaded areas may also be considered 3D or 2D/3D transition areas. See text and Appendix C for discussion.

Figure 7. Conterminous U.S. maps of PRISM 1971-2000 mean annual precipitation, January minimum temperature, and July maximum temperature. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 8. PRISM mean absolute cross-validation errors (MAE) for 1971—2000 mean: (a) annual precipitation; (b) January minimum temperature; and (c) July maximum temperature. Station density was too high to be shown clearly, requiring that 80% of the stations be randomly omitted from the plots.

Figure 9. Seventy percent prediction intervals (PI70) for: (a) mean annual precipitation; (b) January mean minimum temperature; and (c) July mean maximum temperature. PI70 for precipitation is expressed as a percentage of the pixel’s value.

Figure 10. (a) Scatterplot of the relationship between C-V MAE and PI70 for mean annual precipitation (given in percentage of the estimated grid cell value) when averaged over 300 x 300-km blocks in the western United States; and (b) R? of the linear relationships between CV-MAE and PI70 for mean annual precipitation, January minimum temperature, and July maximum temperature at block sizes ranging from 100 to 500 km in the western United States. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 12. Daymet — PRISM and WorldClim — PRISM difference maps of mean January minimum temperature for the conterminous United States. This figure is available in colour online at www. interscience.wiley.com/ijoc

Figure 13. Daymet — PRISM and WorldClim — PRISM difference maps of mean July maximum temperature for the conterminous United States. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 14. Upper left panel: annual RO + ET (runoff + evapotranspiration), a water balance approximation of total precipitation, for selected basins in Washington’s Olympic Mountains, colour-coded following the precipitation legend. ET was roughly estimated at 500 mm/yr for all basins. Remaining panels: WorldClim, Daymet, and PRISM mean annual precipitation grids, with basin overlays, also colour-coded following the precipitation legend. To agree with the basin water balance estimates, the mean grid colour within a basin should match that shown in the upper left panel. Stations used in the PRISM analysis are shown as black dots. This figure is available in colour online at www. interscience.wiley.com/ijoc

Figure 15. Estimated mean annual precipitation from WorldClim, Daymet, PRISM, and RO + ET (runoff + evapotranspiration), a water balance approximation of total precipitation, for river basins on the windward and leeward slopes of the Olympic Mountains. ET is assumed to be 500 mm for all watersheds. Runoff periods of record are 1971-2000, except for 1975-2000 on the Queets and 1995-2000 on the Quilcene. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 16. PRISM diagnostic grids associated with mean annual precipitation for the Olympic Mountains, Washington: (a) topographic facet grid at a filtering distance of 36 km; (b) PW coastal proximity, which describes a straight line, approximately southwesterly path length from the coastline in km, modified by terrain blockage; (c) vertical precipitation gradient, expressed as a percentage of the pixel’s value per kilometre: and (d) 70% prediction interval (PI70), expressed as a percent of the pixel’s value. in the protected Gunnison Valley and adjacent valleys (Figure 17). PRISM diagnostic grids show an estimated SRRRE Aone tewourn mes Muwemeemn Figen wns emenreated vinta TSR NT So OR OOS cx EN STE NST SPITE ONT ENTREES) RE AUR ST NEZE NNR in Sem ROSETTE TRS IS ge oe fe ENR Cold biases of the Daymet and WorldClim data sets in western Colorado are illustrated in Figure 19. Here, 369 stations were grouped into four topographic index

Figure 17. Comparison of PRISM, Daymet, and WorldClim January mean minimum temperature grids for the Gunnison Valley region. CO. Stations used in the PRISM interpolation are shown as red dots in the PRISM panel. This figure is available in colour online a www.interscience.wiley.com/ijoc

Figure 19. Biases between grid-cell estimates and observed 1971-2000 mean January minimum temperatures (estimate — observation), grouped by topographic index, for 369 stations in western Colorado. Stations with high topographic indexes are on locally elevated terrain, and those with low indexes are in local valley bottoms. Stations with moderate indexes (300—500) are neither in local valley bottoms nor on locally elevated terrain. Figure 18. PRISM diagnostic grids associated with January mean minimum temperature interpolation for the Gunnison Valley region, CO: (a) inversion layer; (b) topographic index; (c) vertical temperature gradient; and (d) 70% prediction interval (PI70).

Figure 20. Comparison of PRISM, Daymet, and WorldClim July mean maximum temperature grids for the central coast, CA. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 21. PRISM diagnostic grids associated with July mean maximum temperature interpolation for the central coast, CA: (a) summer inversion layer, given as layer | (within inversion) or layer 2 (above inversion); (b) western temperature (TW) coastal proximity, expressed as the optimal! path length from the coastline in kilometres, accounting for terrain blockage; (c) vertical temperature gradient; and (d) 70% prediction interval! (PI70).

Figure 22. Bias between grid-cell estimates and observed 1971—2000 mean July maximum temperatures (estimate — observation), grouped by coastal proximity (Figure 2(a)), for 1201 stations in California. Stations with low coastal proximity indexes experience a generally strong marine temperature influence during summer, and those with high indexes experience much less of this influence (see Figures 2(a) and 21(b) for spatial context).

Figure Al. Mean absolute error of the adjusted mean July maximum temperature from the known 30-year mean versus number of anchor stations used to compute the adjusted mean. A total of 84 stations were tested using short-term periods of record of 5, 11, and 21 years. This figure is available in colour online at www.interscience.wiley.com/ijoc

Table I. Methods for preparation of PRISM input grids, part 1. the basis for most of the other physiographic input grids to PRISM (Section 4). The DEM used in this study was derived from the 3-arcsec (~80-m) National Elevation Database (NED) (NED; http://gisdata.usgs.gov/NED/). The NED elevation data was found to be superior to other DEMs for the conterminous United States, such as GTOPO30, Digital Terrain Elevation Database (DTED), and Space Shuttle Radar Topography Mission (SRTM), for this application. The GTOPO30 and DTED DEMs had noticeable elevation breaks, or ‘seams’ along some of the original U.S.Geological Survey (USGS) quad boundaries. The SRTM DEM had numerous grid cells with missing data in areas of steep terrain, and possessed significant ground clutter associated with low microwave signal-to-noise ratios. This 30-arcsec (~800-m) DEM was used for interpolat- ing maximum and minimum temperature. An additional filtering step was performed to obtain a DEM suitable for precipitation interpolation. The Gaussian filter was applied to the 30-arcsec (~800-m) DEM to filter out ter- rain features up to 3.75 arcmin (~7 km) in extent, while retaining the 30-arcsec (~800-m) grid resolution. The direct effects of elevation on precipitation appear to be most important at scales of 5-10 km or greater, owing to a number of mechanisms, including the advective nature of moisture-bearing airflow, the viscosity of the atmo- sphere, delays between initial uplift and subsequent rain- out, and the movement of air around terrain obstacles (Daley, 1991; Daly et al., 1994; Funk and Michaelsen, 2004; Sharples et al., 2005). In this paper, the two DEMs are hereafter referred to as the temperature and precipi- tation DEMs (Table II).

Table II. Methods for preparation of PRISM input grids, part 2.

able IV. PRISM algorithms and associated physiographic climate forcing factors, inputs to the algorithms, and references on their formulation and use. Methods used to prepare the gridded model inputs are summarized in Tables I and 2.

Table V. Vertical gradients in temperature and precipitation, summarized by effective terrain height (precipitation) and layer (temperature).

Table VI. PRISM cross-validation and PI70 statistics for precipitation and minimum and maximum temperature for the western, central, and eastern regions. MAE is the mean absolute (unsigned) difference between the prediction and observation during single-deletion jackknife cross-validation, and PI70 is the mean 70% prediction interval of the PRISM climate-elevation regression function.

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Response of mean annual evapotranspiration to vegetation changes at catchment scale

by Glen Walker

2001, Water Resources Research

It is now well established that forested catchments have higher evapotranspiration than grassed catchments. Thus land use management and rehabilitation strategies will have an impact on catchment water balance and hence water yield and... more

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Linking climate change modelling to impacts studies: recent advances in downscaling techniques for hydrological modelling

by Claudia Tebaldi

2007, International Journal of Climatology

There is now a large published literature on the strengths and weaknesses of downscaling methods for different climatic variables, in different regions and seasons. However, little attention is given to the choice of downscaling method... more

Figure 2. Map showing re-gridded RCM cells on the CRU 0.5° by 0.5° grid for the UK. The two regions used in this study are shown in grey: North West England (dark) and South East England (light). Figure 1. Flow diagram showing steps in the methodology used to produce probabilistic scenarios of climate change impacts for the River Eden. This figure is available in colour online at www.interscience.wiley.com/ijoc

Figure 3. Percentage seasonal change in precipitation projected under the 2070-2100 SRES A2 emissions scenario from the control period, 1961-1990, for two UK regions: North West England (black) and South East England (red). Notations for seasons are winter (DJF, December to February), spring (MAM, March to May), summer (JJA, June to August) and autumn (SON, September to November). The projection from the IPCC AR4 suite of 14 GCMs for all UK is shown in green for comparison. sensible results, being designed to handle an arbitrary number of data points, one caveat of the Bayesian approach is that independence is assumed between ensemble members. This may be an oversimplification, as many climate models share internal numerical and parameterization schemes. Here in particular, as some RCMs are driven by lateral boundary schemes from the same GCM, this assumption may be even less defensible and generate overly confident estimates of the uncertainty in the changes. However, results for two UK regions from the set of RCMs are comparable to the results for the entire UK from the set of IPCC-AR4 GCMs (Figures 3 and 4), suggesting that these RCMs are in fact representative of the IPCC-AR4 results. There is noticeable agreement in the location and even the spread of the pdfs for all seasons but summer, where the GCM

Figure 4. Percentage seasonal change in temperature projected under the 2070-2100 SRES A2 emissions scenario from the control period, 1961-1990, for two UK regions: North West England (black) and South East England (red). Notations for seasons are winter (DJF, December to February), spring (MAM, March—May), summer (JJA, June—August) and autumn (SON, September—November). The projection from the IPCC AR4 suite of 13 GCMs for all UK is shown in green for comparison.

Figure 5. The Eden catchment in northwest England (to Temple Sowerby). . Here, we use the same methodology as Kilsby et al. (2007b) to derive a suite of CFs for each of the six PRUDENCE RCMs for a catchment in northwest Using the calibrated hydrologic model, 100 synthetic 30-year daily flow sequences were then produced for the baseline and each of the six possible futures (one from

Figure 6. Projected percentage changes in flow statistics for the 2070-2100 period (change from 1961-1990): (a) mean flow, (b) standard deviation of flow, (c) 5th percentile of flow, (d) 95th percentile of flow. Seasonal change probabilities are given for winter (DJF, black), spring (MAM, red), summer (JJA, green) and autumn (SON, blue).

Figure 7. Analysis of downscaling literature using the ISI Web of Knowledge: ‘downscaling’ included in title or abstract

Table I. Comparative summary of the relative merits of statistical and dynamical downscaling techniques (adapted from Wilby and Wigley, 1997).

Table II. Examples of recent statistical downscaling studies. This list is not intended to be exhaustive but illustrative of the geographical distribution of downscaling studies and the methods employed. Abbreviations used in this table are: REG - linear regression methods, ANN - artificial neural networks, CCA — canonical correlation analysis, OTH — other, SCA -— scaling methods, SVD — singular value decomposition, WG — weather generators, WT — weather typing. For predictands, T — temperature, P — precipitaion, PE — potential evapotranspiration, H — humidity variables. performance of NCEP reanalysis variables in the sta- tistical downscaling of daily precipitation using ANNs and principal components analysis (PCA). Downscaling methods had the greatest skill in mid-latitude locations for the cool/dry season and showed the largest errors in the wet season. The poorest geographical performance was in the Tropics. However, this may be due to the dominance of convective processes which are harder to predict or due to poor quality of the reanalysis data in this region rather than deficiencies in downscaling method. example, the downscaling skill for mean daily temper- ature in central Europe was found to be dependent upon station elevation, with statistical downscaling methods showing more skill at higher elevation stations, and with increased skill at continental compared to mar- itime sites (Huth, 1999). In contrast, Kleinn et al. (2005) found that for dynamically downscaled and then bias- corrected precipitation and temperature outputs there was less skill at high elevations. Similarly, seasonal and geo- graphical differences in downscaling skill were noted by Cavazos and Hewitson (2005) who examined the

Table IV. Seasonal mean i values for the North West England region of the UK for the six selected regional climate models for (a) precipitation, and (b) temperature. Note that A values for all six models have been standardized to add to 1.0 for each season. (a) results are significantly less warm and less dry than the RCM results. they can be applied as such in the downscaling step. Since the Bayesian analysis produces joint posterior pdfs of the lambda parameters, we use the posterior mean of the distribution as our best estimate of model weights (Table IV).

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STATIC STRESS CHANGES AND THE TRIGGERING OF EARTHQUAKES

by Roger Bilham and

To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a... more

where o, is the greatest principal stress and 9; is the least principal stress. Equation (1) then becomes we can express the stress components applied to it in terms of the principal stresses

Figure 1. The axis system used for calcula- tions of Coulomb stresses on optimum failure planes. Compression and right-lateral shear stress on the failure plane are taken as positive. The sign of tg is reversed for calculations of right-lateral Coulomb failure on specified failure planes. Equation (9) is illustrated in Figure 2a. An elliptical slip distribution is imposed on a master fault in a uni- form, stress-free, elastic half-space. The contributions of the shear and normal components to the failure condi- tion, and the resulting Coulomb stresses, for infinitesi- mal faults parallel to the master fault, are shown in sep- arate panels. Such a calculation represents the change of Coulomb stress on these planes resulting only from slip on the master fault. The calculation is appropriate to de- termine, for example, the effect of Landers on a nearby segment of the San Andreas fault. One need only know the relative location of the San Andreas and Landers faults,

axis as shown in Figure 1 and the other is at @ + 90° From these two directions, the angle of greates compression 6, must be chosen. Thus the optimum fail. ure angle w, is given by @, + 8. Whereas the optimun planes are determined froma}, the normal and shear stress changes on these planes are determined only by the earthquake stress changes a}. Thus the changes ir

Figure 4. The effect of changing the regional stress o’ orientation (compare right and left panels) and the effective coefficient of friction x’ (compare top and bottom panels). The example is for a simplified Landers rupture (5 m of tapered slip on a 70-km-long, 12.5-km-deep fault). Regional stress magnitude is 100 bars. Friction controls the internal angle between right- and left-lateral slip planes, and the influence of the normal stress change on failure. The regional stress orientation controls the size of off-fault to fault-end lobes. Both Figures 5 and 6 show the four characteristic lobes of increased Coulomb stress rise and four lobes of Coulomb stress drop. The lobes at the ends of the fault extend into the fault zone, while the off-fault lobes are separated from the fault over most of its length by a zone where the Coulomb stress is reduced. The distributions of aftershocks are consistent with these patterns. In- creases of Coulomb stress of less than 1 bar appear to be sufficient to trigger events, while reductions of the same amount effectively suppress them. Relatively few events fall in the regions of lowered Coulomb stress, and the clusters of off-fault aftershocks are separated from the fault itself by a region of diminished activity. The distributions of Coulomb stresses can be modified as de- scribed earlier by adjusting the regional stress direction and changing 4’. However, any improvements in the correlation between stress changes and aftershock oc- currence are modest. Consequently, we have chosen to show examples with an average py’ of 0.4. Whatever val- ues we adopt, we find that the best correlations of Cou- lomb stress change to aftershock distribution are at dis- tances greater than a few kilometers from the fault. Closer to the fault, unknown details of fault geometry and slip distribution influence stress changes. At distances larger than about three fault lengths, the correlations are less clear because there are fewer aftershocks.

Figure 6. Coulomb stress changes calculated for the 23 April 1992 M, = 6.1 Joshua Tree earth- quake. The mainshock is indicated by the star. The model fault is 8-km long and 12.5-km deep with 0. 5. m of right-lateral slip, for a moment of 2 X 10° dyne-cm, following Savage et al. (1993) and Ammon et al. (1993). Stress is sampled halfway down the fault.

Figure 5. Coulomb stress changes associated with the 15 March 1979 Homestead Valley earth- quake sequence (M, = 4.9, 5.2, 4.5, and 4.8). The fault (enclosed white line) is 5.5-km long by 6-km deep, with 0.5 m of tapered slip and a mo- ment of 4.2 x 10” dyne-cm, following Stein and Lisowski (1983) and King et al. (1988). Stress is sampled halfway down the fault.

Figure 7. A depth cross section of Coulomb stress changes for the 1979 Homestead Valley fault (essentially the L/W = 1 fault in Fig. 8 made along the distance = 0 km line), with aftershocks from Hutton et al. (1980). Because the section does not pass through the centers of the off-fault lobes, the lobes appear shallower and smaller than at their maxima. The stress concentration at base of fault is exaggerated because fault slip is not tapered with depth.

Figure 8. Coulomb stress changes as a function of fault length, L. Off-faul stress lobes diminish as the fault lengthens relative to its down-dip dimension, W. Both faults are 12.5-km deep with a stress drop of ~45 bars. Stress is sampled halfway down the fault.

Figure 11. Coulomb stress change caused by the Landers rupture. The left- lateral M; = 6.5 Big Bear rupture occurred along dotted line 3 hr 26 min after the Landers mainshock. The Coulomb stress increase at the future Big Bear ep- icenter is 2.2 to 2.9 bars. Figure 10. Distribution of modeled fault slip for the Landers earthquake from Wald and Heaton (1994), derived from joint inversion of strong motion, telese- ismic, geodetic, and surface slip data. Three planar fault segments are used, which correspond approximately to the mapped fault trace. Although the surface rupture is 70-km long, the fault slip is concentrated over a strike length of just 40 km.

Figure 12. Coulomb stress changes at a depth of 6.25 km caused by the Lan- ders, Big Bear, and Joshua Tree earthquakes. The Big Bear earthquake, which lacked surface rupture, is modeled as an 18-km-long by 12.5-km-deep vertical fault with 0.83 m of left-lateral slip, for a moment of 5.5 x 10” dyne-cm, fol- lowing limited seismic (Hauksson et al., 1993) and geodetic (Murray et al., 1993, Massonnet et al., 1993) evidence. Most M, > 1 aftershocks occur in regions where the failure stress is calculated to have increased by = 0.1 bar, and few events are found where the stress is pre- dicted to have dropped (Fig. 12). Even when all seis- micity within 5 km of the Landers, Big Bear, and Joshua Tree faults is excluded, more than 75% of the after- shocks occur where the stress is predicted to have risen by >0.3 bar. In contrast, less than 25% of the after- shocks occur where the stress dropped by >0.3 bar. The same correspondence can be found among M, = 4 earth- quakes that took place during the 9-month period April through December 1992 from Hauksson et al. (1993). The largest shock to fall on or near the San Andreas, the 29 June 1992 M, = 4.7 Yucaipa event (due east of San Bernardino in Fig. 13), occurred where the failure stress change on the San Andreas is calculated to have risen by 5 bars. Aftershocks to Landers also occurred as far as 1250 km north of the mainshock, largely in geother- mal areas (Hill et al., 1993). At these distances, the static Coulomb stress changes are much smaller than the tidal

Figure 13. The largest Coulomb stress changes at depths between 0 and 12.5 km caused by the Landers, Big Bear, and Joshua Tree earthquakes, shown with the first 25 days of seismicity from Hauksson ef al. (1993). Also shown are the largest two aftershocks to occur during the following 8 months, the 17 November 1992 M, = 5.3 and 4 December 1992 M, = 5.1 shocks. Few aftershocks are seen near Indio in the Coachella Valley where the San Andreas was loaded by the Lan- ders earthquake and, to a lesser extent, by the Imperial Valley (Hanks and Allen, 1989), Elmore Ranch, and Su- perstition Hills (Hudnut et al., 1989) events [the effect of these earthquakes is shown in Stein et al. (1992)]. The lack of earthquakes near Indio appears to be an ex- ception to the observation that Coulomb stress rises are accompanied by at least some activity, although trig- gered surface slip was seen at several points between Indio and the southeastern end of the San Andreas (D. Ponti, personal comm., 1992). Landers aftershocks could be absent in the Coachella Valley because the total stress there is lower, because the fault is locally tougher, or because modulus contrasts modify the Coulomb stresses. We examined the effect of a low-modulus Mojave tec-

Group on California Earthquake Probabilities, 1988). The San Bernardino Mountain segment last ruptured in 1812 (Fumal et al., 1993); given its 24 + 3 mm/yr slip rate (Weldon and Sieh, 1985), a =4.3-m slip deficit has since accumulated, which could yield an M = 7.5 event. The Coachella Valley segment last ruptured in 1680, has a Because the southern San Andreas fault is late in the earthquake cycle, the long-term probability of a great earthquake on any of its three southern segments was high before the Landers earthquake took place (Working

Figure 15. Coulomb’ stress change caused by the Landers, Big Bear, and Joshua Tree earth- quakes resolved on the San Jacinto fault. The San Jacinto is assumed to be vertical, right-lateral, and 12.5-km deep; stress is sampled every 5 km along the fault at a depth of 6.25 km. The lower panel depicts the slip required to relieve the imposed stress increase. depths shown in our figures, the stress change on the San Andreas and surrounding faults roughly doubles (Fig. 14, middle panel, and Fig. 15, upper panel) and the slip required to relieve the stresses likewise grows (Fig. 14, lower panel, and Fig. 15, lower panel). The time needed for substantial relaxation depends on the viscosity of the lower crust, or on the rate at which creep propagates down the fault, which is perhaps in the range of 30 to 100 yr. Thus, the stress changes caused by major events such as Landers do not diminish with time; rather they grow and diffuse outward from the source. If one were also to include the secular rate of stressing caused by the

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Multivariate geostatistics: an introduction with applications

by Hoa Do

2003

Fic. 1. Slices through a 3-D magnetic susceptibility model composed of a dipping slab in a nonsusceptible half-space. The slab is buried at a depth of 50 m and extends to 400-m depth at a dip angle of 45° . The gray scale indicates the value of magnetic susceptibility in SI units.

Fic. 2. The total field anomaly produced by the slab moe a Fi ure 1. The inducing field has direction | = 75° and D a strength of 50 000 nT. Uncorrelated Gaussian noise, with a S standard eviation of 2% of the datum magnitude plus 1 nT, is added to the data. The gray scale indicates the magnetic anomaly in nT.

Fic. 3. The susceptibility model constructed by minimizing ||1\| subject to fitting the data in Figure 2. As a mathematical solution, this model provides little, if any, information about the subsurface susceptibility distribution. It effectively illus- trates the nonuniqueness inherent to the inversion of static magnetic field data.

3-D Inversion of Magnetic Data where functions w, Ww, wy , and w, are spatially dependent weighting functions while a,, a,, a,, and a, are coefficients that affect the relative importance of different components in the objective function. Here, w ( z ) is a depth weighting function. It is convenient to write equation (2) as o,,(m) = ms + Omp» Where o,,, refers to the first term in equation (2) and ©), refers collectively to the remaining three terms that involve variation of the model in three spatial directions.

Fic. 4. A 1-D example showing the use of a weighting function in the inversion procedures to counteract the natural decay in the kernel function. In all panels the dashed line shows the true model. Panels (a) and (b) show, for the two different true models, respectively, the model constructed using the original kernel functions with the decaying factor e°’. Notice the shift of the recovered model towards the small z region. Panels (c) and (d) show the weighted models recovered by applying a weighting function w(z) =e" They are better representations of the true model. This is shown in Figure 4a and 4b for two different models. These models are constructed from five data ( i = 0,4) to which noise has been added. It is apparent that the constructed model is shifted toward small z where the amplitude of kemels is relatively large. One way to counteract the bias is to seek a solution in model space that is spanned by the nondecaying portion of the kernels, in this case just the cosine functions. The desired model would have the form

Fic. 5. Comparison of the kernel function (solid) directly beneath the open gion point with, the estimated curve (dashed) given by w (z) =(z+2z 9)” with z 9 = 25 m. The source cell is a cube tr 50 m ona side, Here, z denotes the depth to the center of the cell. Both curves are normalized for comparison. In the above analysis we have established a practical way for estimating an appropriate depth weighting function that dis- tributes the susceptibility more uniformly with depth. The weighting is valid when the model objective function consists only of ,,,. In general, we like to include a penalty against roughness and thereby produce a model that is smooth. To incorporate the above weighting scheme in the spatial varia tions, we make the following argument. Since minimizing 9,,,, tends to provide a reasonable depth distribution, we wish only to improve the model’s smoothness while maintaining the depth characteristic. A conceptually consistent approach would be to apply the roughness measures to the weighted model. We form a generic model objective function

Fic. 6. Cross-sections through the center of the recovered model for a cube at a central depth of 150,200, and 250 m. The cube is 200 m on a side. The inversion uses the weighting function derived from the kernel decay estimated in Figure 5. The true position of the cube is outlined in each cross-section. As the true source depth increases and, as a result, the high-frequency content in the data decreases, the recovered model becomes increasingly smooth and attains a smaller amplitude. However, the depth of the recovered model is close to the true value. Before proceeding further, we remark that the above weighting represents only one possibility. One could poten- tially design a different weighting by incorporating the depth weighting in the usual 3-D weighting functions w,, W,, Wy, W,. Such an approach applies the depth weighting outside the deriv- ative operators directly. However, the decay rate of the depth weighting for each component will be different, and it is difficult to establish a consistent rule for the choice of the different weight- ings. In addition, the extra set of parameters required by such a weighting scheme introduces more subjectivity into the inversion process. We have not explored this approach in detail; however,

Fic. 7. The misfit between magnetic field as a result of a small cubic source and the field as a result of a larger cubic model cell having a best fitting susceptibility. The numbers indicate the ratio of the cell width. The misfit is plotted as a function of the observation height normalized by the width of the model cell. Note that the misfit decreases rapidly until the height is approximately equal to the width of the model cell, and that it changes slowly thereafter. ine data used in me inversion are the residual dala ODtained by subtracting a regional field from the initial observation. The inversion algorithm has been developed under the assumptions that the surface magnetic anomaly is produced by the induced magnetization only and that there are no remanent magneti- zation or demagnetization effects present. Incorrect removal of regional field, or any deviation from the above assumptions, is expected to cause a deterioration in the inversion results. Furthermore, the susceptibility distribution is mathematically represented by a piece-wise constant function defined on a user-specified grid of cells. Magnetic sources, however, have a wide range of physical sizes. In some cases, source dimensions will be significantly smaller than the size of cells in the mathematical model. If measurements are taken close to such a source, the resulting anomaly will have a width that is significantly smaller than that produced by a single cell in the mathematical model and this may produce artifacts. We ame- liorate this problem by inverting data that have been upward continued to a height approximately equal to the width of the surface cells in the model. We arrive at this conclusion from a numerical experiment. We first generate the magnetic field H, from a small localized surface source that is assumed to be a cube of width £. At each height h above the surface, a one-parameter inverse problem is carried out to find a uniform susceptibility of a large surface cube that has a width of L and shares a common horizontal center with the small cube. If H;, is the field of the large cell that best reproduces Hy then the misfit functional,

Fic. 8. Model obtained from inverting the data shown in Figure 2 by minimizing only 6,,,, which has the depth weight- ing applied. This is to be compared with the true model in Figure 1. The major features in the true model, such as dip angle and depth exte nt, are evident in the recovered model.

Fic. 10. The model obtained from inverting the data shown in Figure 2 by using m = In (x) as the model and minimizing 9,,,, with the reference model removed. The inverted logarithmic susceptibility in cross-section at x = 500 m is shown in (a) and it is replotted on a linear scale in (b). As a comparison, the result obtained by using m = x, and the same objective function is shown in (c).

Fic. 9. The model derived from inverting the slab model data in Figure 2 by minimizing the model objective function having both Om; and m,. The same depth weighting is used. This model appears to be smoother and has a smaller amplitude than that in Figure 8.

Fic. 11. The second synthetic test example. The top and bottom portions of the anomalous susceptibility are offset to simulate a norm fault structure. It also has a large strike length in the north direction.

Fic. 12. The surface total field anomaly produced by the faulted slab in Figure 11, under an inducing field at I = 45° and D = 45°. Uncorrelated Gaussian noise is again added to the data.

Fic. 13. The susceptibility model recovered from the data shown in Figure 12. It is seen that both the top and bottom block of the true model are recovered and the strike direction and length are well defined.

Fic. 14. The surface total field anomaly produced by the faulted slab in Figure 11 under an inducing field at I = 0° and D = 45°. Uncorrelated Gaussian noise is added to the data. Magnetic data from a larger area were first upward contin- ued to 20 m. A regional field was then defined and removed from the upward continued data. The continuation operation suppresses the noise in the data and also facilitates the discretization of the topographic surface for the model so that all observation points remain above the discretized surface. Although the original data were collected at 12.5-m spacing, we use the data at 25-m spacing. This yields 1029 data points at varying elevations. Figure 16 shows the data contoured accord- ing to their horizontal locations. The direction of the inducing field is I = 75° and D = 25.73°. Several major magnetic highs are observed in the map. However, the influence of anomalies adjacent to the map is also visible along the edges. We choose a model domain that is horizontally larger than the data area, coincides at the top with the highest point on the topographic surface, and extends to 450-m depth. The model is discretized horizontally at a 25-m interval beneath the area of data. In the

Fic. 15. The susceptibility model recovered from the data shown in Figure 14. This model is similar to that shown in Figure 13. vertical direction, the first 100 m is divided at a 12.5-m interval so that the surface can be adequately discretized onto the model mesh. Below the depth of 100 m, an interval of 25 m is used. This results in a mesh with 52 x 44 x 22 cells. Once the mesh is defined, the topography is discretized onto it. The 43 428 cells below this surface define the susceptibility model, and the inverse problem is therefore formalized by inverting 1029 data to recover the susceptibilities in those cells. The depth weighting is referenced to the top of the model domain. Each datum is assumed to have an error whose standard deviation is equal to 5% of its magnitude plus 10 nT. The error estimate includes not only the repeatability of the instrument reading but also the geological noise and errors introduced by the inaccurate recording position and by separating the anom- alous field from the initial total field measurements. One

Fic. 16. The extracted total field anomaly from ground mag- netic data at Mt. Milligan Coppergold porphyry deposit. The data are contoured according to their horizontal locations in this map, although thev are at different elevations. We have developed an algorithm to invert surface magnetic data for general 3-D susceptibility distributions. Although we have illustrated the algorithm using examples on the scale pertinent to mining applications, the method is general and applicable to problems on different scales ranging from envi- ronmental to regional investigations. To overcome the inher- ent nonuniqueness, we obtain the solution by minimizing a

Fic. 17. The recovered susceptibility model shown in one plan-section and three cross-sections. The plan-section is at the depth of 150 m and the three cross-sections are at x = 600,500, and 400 m, respectively. specific objective function of the model. Our model objective function has the ability to incorporate prior information into the inversion via a reference model and 3-D weighting functions. A crucial feature of the objective function is a depth weighting function that counteracts the natural decay of the kemel func- tions. The parameters of the depth weighting depend upon the discretization of the model but are easily calculated. The minimi- zation is carried out using a subspace technique that reduces the computational effort and allows the positivity constraint of sus- ceptibility to be incorporated. Both susceptibility and logarithmic susceptibility can potentially be used as the model in the inver- sion. Since the data are linearly related to susceptibility, and since usually absolute values of susceptibility are required for interpre- tation rather than relative values, especially in regions of very low susceptibility, we have generally chosen to work with susceptibil- ity. To suppress the noise from small magnetic bodies near the surface, we recommend in general that the data be upward continued to a height comparable with the width of the surface cell before inversion.

Fic. 18. Comparison of the recovered susceptibility model in a cross-section ( x = 600) with the geology for the Mt. Milligan deposit. The susceptibility high within the MBX stock reflects the initial magnetite in the intrusive while the susceptibility highs near the Rainbow dyke are related to the magnetite produced by potassic alteration.

The numerical evaluation of this functional is carried out by introducing the model mesh and evaluating all terms using a finite-difference approximation. The discretized model objec- tive function has the form MODEL OBJECTIVE FUNCTION APPENDIX

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The shear strength of rock joints in theory and practice

by v k

1977, Rock Mechanics and Rock Engineering

The Shear Strength of Rock Joints in Theory and Practice The paper describes an empirical law of friction for rock joints which can be used both for extrapolating and predicting shear strength data. The equation is based on three index... more

The Shear Strength of Rock Joints in Theory and Practice The paper describes an empirical law of friction for rock joints which can be used both for extrapolating and predicting shear strength data. The equation is based on three index parameters; the joint roughness coefficientJRC, the joint wall compressive strengthJCS, and the residual friction angleφ r . All these index values can be measured in the laboratory. They can also be measured in the field. Index tests and subsequent shear box tests on more than 100 joint samples have demonstrated thatφ r can be estimated to within ± 1° for any one of the eight rock types investigated. The mean value of the peak shear strength angle (arctanτ/σ n ) for the same 100 joints was estimated to within 1/2°. The exceptionally close prediction of peak strength is made possible by performing self-weight (low stress) sliding tests on blocks with throughgoing joints. The total friction angle (arctanτ/σ n ) at which sliding occurs provides an estimate of the joint roughness coefficientJRC. The latter is constant over a range of effective normal stress of at least four orders of magnitude. However, it is found that bothJRC andJCS reduce with increasing joint length. Increasing the length of joint therefore reduces not only the peak shear strength, but also the peak dilation angle and the peak shear stiffness. These important scale effects can be predicted at a fraction of the cost of performing large scale in situ direct shear tests. Die Scherfestigkeit von Kluftflächen in Theorie und Praxis Zur Ermittlung der Reibungswerte in Kluftflächen wird ein empirisches Gesetz beschrieben, das sowohl das Extrapolieren als auch das Voraussagen von Scherfestigkeitszahlen ermöglicht. Die Gleichung ist auf drei Indexzahlen gegründet: Den Rauhigkeitskoeffizienten der KluftJRC (Joint Roughness Coeff.), die Druckfestigkeit des Felses der KluftwändeJCS (Joint Wall Compression Strength) und der residuelle Reibungswinkel der Trennflächeφ r . Die Indexzahlen können alle im Laboratorium bestimmt oder am Ort gemessen werden. Bestimmung von Indexzahlen mit nachfolgenden Prüfungen im Scherapparat von mehr als 100 Kluftproben haben erwiesen, daß für jede beliebige der acht untersuchten Gesteinsarten der Reibungswinkelφ r auf ± 1° genau geschätzt werden kann. Der Durchschnittswert des Reibungswinkels (arc tan (τ/σ n ) der Höchstscherfestigkeit wurde für dieselben 100 Klüfte auf ± 1/2° genau geschätzt. Die besonders genaue Vorausschätzung der Höchstscherfestigkeit ist durch Eigengewicht-Gleitversuche (niedrige Spannungen) auf Gesteinsblöcken mit durchgehenden Trennflächen ermöglicht. Der totale Reibungswinkel (arc tanτ/σ n ), bei dem das Gleiten eintrifft, ergibt eine Abschätzung des Rauhigkeitskoeffizienten der KluftJRC. Der Rauhigkeitskoeffizient bleibt über einen Normal-Spannungsbereich von mindestens vier Größenanordnungen konstant. Die IndexzahlenJRC (Rauhigkeitskoeffizient) undJCS (Druckfestigkeitskoeffizient) reduzieren sich aber bei zunehmenden Kluftlängen. Bei zunehmender Kluftflächengröße nehmen nicht nur die Höchstscherfestigkeit, sondern auch der zugehörige Dilatanzwinkel und die Schubsteifigkeit ab. Diese wichtigen Einflüsse der geometrischen Abmessungen können geschätzt und zahlenmäßig erfaßt werden, und zwar mit Kosten, die nur einen Bruchteil von denen betragen, die für große, direkte Scherversuche in situ erforderlich wären. La résistance au cisaillement des joints de roches en théorie et en pratique Le rapport traite d'une loi empirique du frottement dans les joints de roches, loi pouvant être utilisée tant pour l'extrapolation que pour la prédiction de données relatives à la résistance au cisaillement. L'équation est basée sur trois indices de paramètres: coefficient de rugosité du joint (joint roughness coefficient —JRC), résistance de la paroi à la compression (joint wall compressive strength —JCS), et l'angle de frottement résiduelφ r . Toutes ces valeurs d'indice peuvent être mesurées au laboratoire. Elles peuvent aussi l'être in situ. Des tests d'indice, avec ensuite des tests en boîte de cisaillement, sur plus de 100 échantillons de joints, ont permis de constater que, pour n'importe quel des huit types de roche étudiés, l'angle de frottementφ r peut être évalué avec une précision de ± 1°. La valeur moyenne de l'angle maximum de la résistance au cisaillement (arctanτ/σ n ) pour les mêmes 100 joints fut évaluée avec une précision de 1/2°. La prédiction particulièrement précise de la résistance maximum au cisaillement est rendue possible par la réalisation d'essais de glissement dits “de poids propre” (faible contrainte) sur des blocs à joints passant de part en part. L'angle de frottement total (arctanτ/σ n ) auquel le glissement se manifeste, fournite une estimation du coefficient de rugosité du joint,JRC. Ce dernier est constant à l'intérieur d'une plage de tensions normales effectives d'au moins quatre ordres de grandeur. Cependant, on a trouvé que les indicesJRC (rugosité) comme ceuxJCS (compression) diminuent quand la longueur du joint augmente. Ainsi, si la langueur du joint augmente, cela réduira non seulement la résistance maximum au cisaillement, mais aussi l'angle maximum de dilatation et la rigidité maximum de cisaillement. Ces importants effets d'échelle peuvent être prédits, et ce à des coûts ne représentant qu'une fraction de ceux liés à des tests directs de cisaillement effectués in situ.

Fig. 14. Range of peak shear strength for 136 joints representing eight different rock types. Curves 1, 2 and 3 are evaluated in the text

Fig. 15. Distribution of peak and initial dilation angles and their relationship with the asperity component of shear strength

Fig. 16. Results of in situ shear tests on joints in quartz diorite, after Pratt et al. (1974). Envelope (1) represents specimens with an average joint area of approximately 200 cm2, (2) an average area of 1500 cm?, and (3) an average of 5000 cm? Resultate von in situ Scherversuchen auf Kluftflachen in Quarz-diorite nach Pratt et al. (1974). Die Umhiillungskurven 1, 2, 3 reprasentieren Proben mit Kluftflachen von durch- schnittlich folgenden Groen: 200 cm?, 1500 cm? und 5000 cm2

Fig. 17. Tilt tests of large scale and small scale joint samples to investigate the scale effect on JRC. Due to increased roughness (JRC>8.0) 12 of the 18 small samples had to be push tested

Fig. 18. Cross-joints reduce the stiffness of a rock mass, and probably reduce the scale effect on t, 6 (peak), Ks and dy. The magnitude of 6 (peak) is exaggerated for clarity

Fig. 19. Typical envelope of failure for intact rock. At the critical state the confined com- pression strength 01-03 (=JCS) is of equal magnitude to the mobilized effective normal stress (i. e. JCS/on = 1) Enveloppe opie dune rupture de roche saine. A l'état limite, la résistance selon trois axes o1—63 (=JCS) est du méme ordre de grandeur que la tension normale en jeu (c.-a-d. JCS/on = 1)

Fig. 20. Photograph illustrating the range of joint surfaces and rock types tested. See Table 9 for descriptions

Table 1. Basic Friction Angles of Various Unweathered Rocks Obtained From Flat and Residual Surfaces weathered. If the joints are completely unweathered then JCS will be equal to the unconfined compression strength of the unweathered rock (o¢). The compression strength can be estimated quite well from point load tests on rock core or irregular lumps, as described by Broch and Franklin (1972). How- ever, in general rock joint walls are weathered to some extent and JCS will be lower than o¢. The relevant value is then measured using a Schmidt hammer applied directly to the exposed joint walls. The rebound value is converted to an estimate of compressive strength using Miller’s (1965) method.

Table 2. Corrections for Reducing Measured Schmidt Hammer Rebound (R) When the Hammer Is Not Used Vertically Downwards (from Manufacturer’s data) In the field, and the Schmidt hammer is essentially a field tool, such problems do not normally arise. However, if the rock mass is “drummy” for instance due to slabbing in a tunnel wall, artificially low rebound values may be obtained. A closely spaced and loose joint structure (i. e. phyllite) will also render results unreliable. It is normally possible to “hear” un- reliable results during a set of tests, in just the same way that a geological hammer helps a geologist identify “drummy” rock. Sample extraction and clamping might be the only solution if heavily jointed rocks like phyllite are to be Schmidt hammer tested.

Table 5. Mean Dilation Angles and Damage Coefficients It will be clear from examination of Table 5 that the estimation of peak dilation angle for a given joint is not a simple matter. The damage coefficient is generally higher when JCS/on is low as one would except, but the value of the joint roughness coefficient (JRC) complicates this picture since smooth joints such as the cleavage joints in slate suffer very little damage, even when the value of J/CS/on is low enough to suggest considerable damage. This influence of roughness is of course quite logical, since a steep asperity with a small base area (high JRC) will be sheared off more readily than a gently sloping asperity of large base area (low JRC). The results given in Table 5 were plotted to dry to establish the main apes ies: me

Table 6. Comparison of Predicted and Measured Dilation Angles and Damage Coefficients

Table 7. Variation of Mean 6 (Peak) for the Eight Rocks Studied An earlier study of joint displacement effects by Barton (1971a) in- dicated that model tension fractures representing prototype joint lengths from 225 cm up to 2925 cm required approximately 1% displacement (i. e. 6 (peak)/L* 0.01) to reach peak strength throughout this range of simulated joint lengths. The present test results from 10cm long rock joints appear to fit these observations quite well.

Table 8. Results of Tilt, Push and Shear Box Tests on Joints in Drammen Granite (¢r = 29°)

surface characteristics (including mean JRC) is given in Table 9. The same joint type numbers (1 to 15) are used in each case.

Fig. 2. Correlation chart for Schmidt (L) hammer, relating rock density, compressive strength and rebound number, after Miller (1965)

Fig. 3. Richards’ (1975) results for seven weathered joints in sandstone, when tested at low normal stress (0.17 MN/m?) Die Ergebnisse fiir sieben verwitterte Kliifte in Sandgestein unter kleinen Normalspannungen 0.17 MN/m? gepriift. Richards, 1975 Résultats de sept joints délités dans du erés, testés a4 de faibles tensions normales (0,17 MN/m?). Richards (1975) Under low levels of effective normal stress the thin layers of weathered material, perhaps less than 1 mm in thickness, may continue to control the shear strength past peak strength and even for displacements up to residual strength. Richards’ tests on weathered sandstone joints showed that it was possible to have residual friction angles (¢r) for unfilled joints as low as 12°, if normal stress levels were low. His test results are reproduced in Fig. 3,

Fig. 5. Estimated values of ¢r obtained from Eq. (7) using the data in Fig. 4. The values are relevant to saturated surfaces Résultats moyens obtenus aux essais de basculement destinés 4 déterminer langle ¢, pour roche non délitée. Les tests de basculement, comme ceux de rebondissement Schmidt, furent effectués sur des surfaces de roches séches

For the benefit of those who are inherently and justifiably suspicious of empirical methods it should be pointed out that the ¢; values represented in Fig. 5, which ranged from 19° to 31°, were the values used in the shear strength prediction exercise summarized earlier. The fact that the mean peak shear strength angle of over 100 joint specimens can be estimated to within 1/29 based on Eqs. (6) and (7) suggests that these empirical relationships reflect

Fig. 8. Roughness profiles corresponding to the joints shown in Fig. 7, showing the typical range of JRC values associated with each one

Fig. 10. Tilt test to determine the joint roughness coefficient (JRC) of a surface. The top half of the jointed sample slid when the joint was dipping at 69.79

Fig. 12. The results of laboratory tilt tests (A) and push tests ([), and the corresponding values of peak shear strength measured in the direct shear box using the same joints, under conventional levels of normal stress (approx. 0.05 to 1.5 MN/m2)

Fig. 13. Peak arctan (t/on) predicted from tilt and push tests compared with the measured values obtained from conventional shear box tests on the same joint samples

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Analysis and Design of Structural Sandwich Panels Against Denting

by ismail koc

The problem of local bending often encountered in laterally loaded sandwich panels is analyzed by considering the deflection of the loaded facing against the not loaded facing as being governed by an elastic foundation model. This is... more

Figure 1 illustrates the considered problem with its constituent parts: the loaded facing of a 2.1 Formulation of Two-Parameter Foundation Model

Figure 2. Notation and Sign Convention for Equilibrium of Loaded Face-Beam. derivations is to formulate and solve the equations determining these functions. proportional to the angular rotation dw/dx of the neutral axis of the face-beam. The interfacial

By combination of Equations 7 and 8 followed by successive differentiation as well as introduction of the equilibrium Equation 6, the following expressions appear:

From the first of Equation 1 the following is derived:

The first and the second of Equation 21 represent the conditions of symmetry about the center of the beam span of the facing (x=0); the third and the fourth of Equation 21 represent the conditions at the free end of the facing (x=L); and the last two of Equation 21 represent the conditions of horizontal and vertical equilibrium, respectively, for the loaded facing of the considered sandwich beam, where p,(x)=p,(x)=0 (see Figure 3). The last of the seven boundary conditions is derived by combination of the second of

Figure 4. Longitudinal distribution of 0,/tayg in upper and lower fibre of the loaded facing obtained by the analytical and FEM salitans,

Figure 6 shows the distribution of the normalized transverse normal and shear stress components, O,/Tavg, Tx/Tavg at the interface between the loaded face-beam and the core material. Focusing at first on the curves (1) and (2) of Figure 6, showing the distribution of G,/Tayg, it is observed that the results obtained by the analytical and FEM solutions, respectively, show a very close match. The predicted peak values (x=0) are very close to each other, and the characteristic decay with increasing values of x is also observed for both solutions. Furthermore, the wavy harmonic character of the “decay function" predicted by the elastic foundation formulation is confirmed by the finite element solution. Curves (3) and (4) of Figure 6 show the interfacial distribution of Tx/Tave obtained by the material. Focusing at first on the curves (1) and (2) of Figure 6, showing the distribution of

The parameters L and c (see Figure 3) also influence the stress distribution within the sandwich beam, and therefore they will not be included in the presented parametric study. Figures 7 and 8 show the effects of altering the stiffness ratio E,/E,. on the interfacial

It is seen that (O,/Tavg) max Shows a strong dependency of E¢/E, as expected from the results shown in Figure 7. A significant feature of the plots shown is that the peak value of ©,/Tayg attains very large values for very small values of E¢/E,, even though it should be recalled that the elastic foundation approach, on which the results are based, becomes inadequate for very small values of E,/E,, (corresponding to deflections of short wave-length). recalled that the elastic foundation approach, on which the results are based, becomes

A EE | Figure 10 shows the peak values of the interfacial shear stress Tz/Tavg as function of the stiffness ratio Es/E,, for three different values of the thickness t of the loaded facing (t=0.5, 1.0 and 2.5 mm). It is recognized that the peak values of Tzx/Tavg are strongly dependent on the E,/E,-values in the way, that very large peak shear stresses are obtained for very small values of the stiffness ratio (it is emphasized that the calculated peak stress values for low values of EE, are questionable as mentioned earlier), and that the peak values of Tx Olav decreases strongly as the stiffness ratio is increased. The peak value of t,x — /Tavg approaches unity asymptotically as E,/E, goes to infinity, i.e., the interfacial shear stress contribution induced by local bending diminishes as the stiffness ratio becomes large. Again it is clear, that the peak value of Tx ie, depends on the face thickness t in the vay, that the larger the value of t, the lower the peak value of T,x total avg. contribution induced by local bending diminishes as the stiffness ratio becomes large.

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Water Waves: The Mathematical Theory with Application

by Patrick BarAvi

1995, Shock and Vibration

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Detection of Structural Damage Through Changes In Frequency: a Review

by Giulia Mennella

1997, Engineering Structures

The use of natural frequency as a diagnostic parameter in structural assessment procedures using vibration monitoring is discussed in the paper. The approach is based on the fact that natural frequencies are sensitive indicators of... more

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Validity of Cubic Law for fluid flow in a deformable rock fracture

by shura tadesse

1980, Water Resources Research

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2/zm. The... more

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Statistical and Econometric Methods for Transportation Data Analysis:Statistical and Econometric Methods for Transportation Data Analysis

by Sharmarke Ahmed

2004, Technometrics

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Slightly curved or kinked cracks

by Brian Cotterell

1980, International Journal of Fracture

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Three-dimensional stochastic analysis of macrodispersion in aquifers

by Lynn Gelhar

1983, Water Resources Research

The dispersive mixing resulting from complex flow in three-dimensionally heterogeneous porous media is analyzed using stochastic continuum theory. Stochastic solutions of the perturbed steady flow and solute transport equations are used... more

The dispersive mixing resulting from complex flow in three-dimensionally heterogeneous porous media is analyzed using stochastic continuum theory. Stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three-dimensional, statistically anisotropic input covariance describing the hydraulic conductivity. With a statistically isotropic input covariance, the longitudinal macrodispersivity is convectively controlled, but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term. With an arbitrarily oriented anisotropic conductivity covariance, all components of the macrodispersivity tensor are convectively controlled, and the ratio of transverse to longitudinal dispersivity is of the order of 10 -•. In this case the off-diagonal components of the dispersivity tensor are significant, being numerically larger than the diagonal transverse terms, and the transverse dispersion process can be highly anisotropic. Dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and Monte Carlo simulations. The theory, which treats the asymptotic condition of large displacement, indicates that a classical gradient transport (Fickian) relationship is valid for large-scale displacements. 1. INTRODUCTION Recent studies have shown that field-observed dispersion coefficients are orders of magnitude larger than those found in small-scale laboratory tests [see, e.g., Fried, 1975; Anderson, 1979]. Similarly, field observations show that the dispersion coefficient increases with displacement distance at a given site [e.g., Sudicky and Cherry, 1979; Dieulin et al., 1980]. Summaries of field observations [Lallemand-Barres and Peaudecerf, 1978; Anderson, 1979] illustrate the wide range of dispersivities encountered in the field.

Fig. 10. Comparisons of theory (A\,; = o/7)/7) with Monte Carlo simulations.

Equation (22) is the tensorial expression of the Fickian- type gradient transport relationship. In order to evaluate the macroscopic dispersivity tensor Aj, it is necessary to relate the spectrum of the local flow variation to that of the local log hydraulic conductivity perturbations. This relationship, which depends on the type of covariance function used to describe the heterogeneity of the medium, is developed for several cases in the following sections. where S_q, is the cross spectrum of c and q; and Sj, is the cross spectrum of the j and i components of the specific discharge. Equation (21) relates the spectra of flow variation with that of the dispersive flux. To evaluate the mean dispersive flux, we integrate its spectrum,

Fig. 1. Logarithmic plot of longitudinal (A,,) and transverse (A22) macrodispersivities for a statistically isotropic medium with correlation scale \ and isotropic local dispersivity a. With q2 = q3 = 0 and a statistically isotropic In K field, the transverse mean hydraulic gradients J, = J; = 0 (see section 5); then, by using the representation theorem with (28), the spectrum of the specific discharge becomes

diffusion, then (29) takes on a relatively simple form which can be evaluated exactly; this involves extensive manipula- tions which are available from Gelhar and Axness [1981]. The results, are seen to agree, to lowest order in ¢, with the asymptotic results (33) and (36), when a, = az. Figure 1 shows a comparison of the exact and aproximate results; this indi- cates that the approximate solution is adequate for « < 0.01. Note that the ratio of transverse to longitudinal macroscopic dispersion is ¢/3, which will be very small under typical conditions.

Fig. 2. Longitudinal (A,,) and transverse (A33) macrodispersivi- ties with flow parallel to bedding: A. = o/l;7/ary, 1, is the correlation scale parallel to bedding, and /; is that perpendicular to bedding; a7 is the local transverse dispersivity. All results use the modified exponential covariance (6), except (47), the dot-dashed line, which is based on the exponential covariance (4). The dashed lines show the asymptotic result (42) for Aj.

The F; integral is transformed from the (k,, k2, k3) coordinate system to the (k;’, kz’, k3') system by k; = ajk;’, where a, = cos (x;’, x;) denotes the matrix of direction cosines; noting that ko = ky? + ky? + ky? = ky'2 + ky’? + ky!” = k’? and that the Jacobian of the transformation matrix is 1, Fig. 3. Coordinate systems for the case x2 = x,'; the dashed ellipse represents the e' level of correlation in the covariance function (4), the x,’ direction being that of bedding. The x,’ coordi- nates are the principal axes of the effective hydraulic conductivity tensor and the x,* coordinates are the principal axes of the macrodis- persivity tensor.

3. 4a. This shows g), and g2. as a function of A,/A3 and Aj/A2. Equations (53) and (54) are shown in Figure 4 along with the general numerical results. A two-dimensional flow system results if \; — © or p> 0

Fig. 4b. This shows g33 as a function of A,/A3 and Aj/A2. in the g,,,, integrals; straightforward integrations in that case produce

Fig. 5. Effective hydraulic conductivities parallel (K,,) and per- pendicular (K33) to bedding; the solid lines are the generalization (60) and the dashed lines are the first order results (59): A, = Ao. from the neglect of higher order terms in the perturbation analysis. Since some natural media have o/ this large, it may be useful to consider a generalization which properly ap- proaches the limiting case of one-dimensional flow parallel and perpendicular to layers. One possible way of generaliz- ing (59) is to consider the quantities in parenthesis as the first two terms of the Taylor series expansion for e*. The general- ization of (59) for of > 1 then becomes,

Fig. 6. Anisotropy of effective hydraulic conductivity as a func- tion of the variance of In K, 7, and aspect ratio A,/A3 for the case A, — and y = q/KJ;. When using (63) it is easily seen that Ay = Aji, Since Rijmn = Rjimn, thus confirming that the macroscopic

. 7. (a) Principal angle, 7. (6) Principal components of macro- dispersivity tensor. Both for case 1 with A; = Az. To illustrate the structure of (65), the dependence of A; on 6 was calculated for a specified medium (8 = K33'/K1)' = 4, Ai/ h3 = 5, and of = 2.58 (from (60)). Figure 7 shows the principal components of Aj, A,\*, A22*, and A33* in normal- ized form, along with the angle y. The most notable feature of these results is the fact that 7» is negative when @ is positive. In other words, the principal axis associated with the maximum principal component of Aj is deflected in a direction opposite to that of the stratification. Note also that the transverse dispersivities Az.* and A33* are of similar magnitude and attain a maximum of about 8% of A,,*. For 0 = 0° and 90°, Ax* = A33* = 0, as would be expected, since local dispersion was neglected in the asymptotic analysis leading to (65). These cases with flow parallel or perpendicu- lar to stratification are similar to those analyzed in sections 3 and 4 including the effect of local dispersion, where it was found that the transverse dispersivity was of order ofa7// (see (36) and Figure 2). Typically, for these special cases the transverse macrodispersivities will be several orders of

Fig. 8. Coordinate systems for case 2 (x3 = x,'); the dashed ellipse represents the e ' level of correlation in the covariance function (4), the x,’ direction being that of maximum correlation scale in the horizontal. The x;’ coordinates are the principal axes of the effective hydraulic conductivity tensor, and the x,* coordinates are the principal axes of the macrodispersivity tensor.

Fig. 9a. Configuration of a dispersing pulse and bedding for item D of Table 3 with mean flow inclined to bedding (case 1); A, = 10 m, of = 2.5, \y/dz = 1, Ay/A3 = 20; x, is the mean flow direction.

Fig. 9b. Configuration of dispersing pulse for item J of Table 3 with horizontal anisotropy (case 2); A, = 10 m, of = 2.5, A,/d2 = 5, A /A3 = 20; x, is the mean flow direction.

APPENDIX: GENERAL SOLUTION OF THE P, Qj, Rymn INTEGRALS The stochastic theory developed here provides a specific predictive model of large-scale field dispersion. If the scien- tific community is to develop reliable predictions of large- scale, long-term transport of solutes in the subsurface envi- ronment, this and competing theories must be tested under large-scale controlled field conditions. This will require carefully designed tracer experiments which are monitored over several years at several different sites representative of important geologic settings (fluvial deposits, glacial out- wash, shoreline sandstone, alluvial basin fill). Detailed mea- surements of the variability of hydraulic conductivity will be required at each site.

Acknowledgments. This research was supported in part by grants from the National Science Foundation (ENG75-14184) and the Environmental Protection Agency (R-806092). Part of the work was done while the first author held visiting appointments with the Sonderforschungsberiech 80 (a special research program on trans- port processes in flow) at the Universitat Karlsruhe, West Germany, and the Centre D’Informatique Geologique (Fontainebleau), Ecole des Mines de Paris, France. The support of the Geophysical Research Center at New Mexico Institute of Mining and Technology is also acknowledged. Discussion with A. L. Gutjahr and G. de Marsily have influenced this work.

TABLE 1. Summary of Asymptotic Results for the Macroscopic Dispersivity Tensor A, Notation: of = variance of In K; \,, J, = correlation scales (see (4), (6)); az, ar = local dispersivities; y = q/K, J;

TABLE 2. Calculated Macrodispersivities for the Quadra Sand, Vancouver, British Columbia of = 0.71, \y = dg = 5m, dy = 0.38 m, a, = 10 a7 = 1 cm, Ki'/K33' = 1.80 (equation (60)

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The green, blue and grey water footprint of crops and derived crop products

by Arjen Hoekstra

2010, American Journal of Hematology

This study quantifies the green, blue and grey water footprint of global crop production in a spatially-explicit way for the period 1996-2005. The assessment improves upon earlier research by taking a high-resolution approach, estimating... more

This study quantifies the green, blue and grey water footprint of global crop production in a spatially-explicit way for the period 1996-2005. The assessment improves upon earlier research by taking a high-resolution approach, estimating the water footprint of 126 crops at a 5 by 5 arc minute grid. We have used a grid-based dynamic water balance model to calculate crop water use over time, with a time step of one day. The model takes into account the daily soil water balance and climatic conditions for each grid cell. In addition, the water pollution associated with the use of nitrogen fertilizer in crop production is estimated for each grid cell. The crop evapotranspiration of additional 20 minor crops is calculated with the CROPWAT model. In addition, we have calculated the water footprint of more than two hundred derived crop products, including various flours, beverages, fibres and biofuels. We have used the water footprint assessment framework as in the guideline of the Water Footprint Network. Considering the water footprints of primary crops, we see that the global average water footprint per ton of crop increases from sugar crops (roughly 200 m3 ton-1), vegetables (300 m3 ton-1), roots and tubers (400 m3 ton-1), fruits (1000 m3 ton-1), cereals (1600 m3 ton-1), oil crops (2400 m3 ton-1) to pulses (4000 m3 ton-1). The water footprint varies, however, across different crops per crop category and per production region as well. Besides, if one considers the water footprint per kcal, the picture changes as well. When considered per ton of product, commodities with relatively large water footprints are: coffee, tea, cocoa, tobacco, spices, nuts, rubber and fibres. The analysis of water footprints of different biofuels shows that bio-ethanol has a lower water footprint (in m3 GJ-1) than biodiesel, which supports earlier analyses. The crop used matters significantly as well: the global average water footprint of bio-ethanol based on sugar beet amounts to 51 m3 GJ-1, while this is 121 m3 GJ-1 for maize. The global water footprint related to crop production in the period 1996-2005 was 7404 billion cubic meters per year (78 % green, 12 % blue, 10 % grey). A large total water footprint was calculated for wheat (1087 Gm3 yr-1), rice (992 Gm3 yr-1) and maize (770 Gm3 yr-1). Wheat and rice have the largest blue water footprints, together accounting for 45 % of the global blue water footprint. At country level, the total water footprint was largest for India (1047 Gm3 yr-1), China (967 Gm3 yr-1) and the USA (826 Gm3 yr-1). A relatively large total blue water footprint as a result of crop production is observed in the Indus river basin (117 Gm3 yr-1) and the Ganges river basin (108 Gm3 yr-1). The two basins together account for 25 % of the blue water footprint related to global crop production. Globally, rain-fed agriculture has a water footprint of 5173 Gm3 yr-1 (91 % green, 9 % grey); irrigated agriculture has a water footprint of 2230 Gm3 yr-1 (48 % green, 40 % blue, 12 % grey).

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Rolling element bearing diagnostics—A tutorial

by Robert B Randall

2011, Mechanical Systems and Signal Processing

This tutorial is intended to guide the reader in the diagnostic analysis of acceleration signals from rolling element bearings, in particular in the presence of strong masking signals from other machine components such as gears. Rather... more

This tutorial is intended to guide the reader in the diagnostic analysis of acceleration signals from rolling element bearings, in particular in the presence of strong masking signals from other machine components such as gears. Rather than being a review of all the current literature on bearing diagnostics, its purpose is to explain the background for a very powerful procedure which is successful in the majority of cases. The latter contention is illustrated by the application to a number of very different case histories, from very low speed to very high speed machines. The specific characteristics of rolling element bearing signals are explained in great detail, in particular the fact that they are not periodic, but stochastic, a fact which allows them to be separated from deterministic signals such as from gears. They can be modelled as cyclostationary for some purposes, but are in fact not strictly cyclostationary (at least for localised defects) so the term pseudo-cyclostationary has been coined. An appendix on cyclostationarity is included. A number of techniques are described for the separation, of which the discrete/random separation (DRS) method is usually most efficient. This sometimes requires the effects of small speed fluctuations to be removed in advance, which can be achieved by order tracking, and so this topic is also amplified in an appendix. Signals from localised faults in bearings are impulsive, at least at the source, so techniques are described to identify the frequency bands in which this impulsivity is most marked, using spectral kurtosis. For very high speed bearings, the impulse responses elicited by the sharp impacts in the bearings may have a comparable length to their separation, and the minimum entropy deconvolution technique may be found useful to remove the smearing effects of the (unknown) transmission path. The final diagnosis is based on ''envelope analysis'' of the optimally filtered signal, but despite the fact that this technique has been used for 40 years in analogue form, the advantages of more recent digital implementations are explained.

Fig. 33. Wavelet kurtograms: (a) before application of MED and (b) after MED. Fig. 32. (a) Accumulated metal wear debris and (b) kurtosis of the filtered signal.

Fig. 1. Typical signals and envelope signals from local faults in rolling element bearings.

Fig. 2. Bearing fault pulses with and without random fluctuations: (a), (d) time signals; (b), (e) raw spectra; and (c), (f) envelope spectra.

Fig. 3. Typical modulating signal from the effect of an extended inner race fault on a gear signal. However, the way of modelling the random variation in pulse spacing in Ref. [13] (model 1) was later found to be incorrect, and in [14] a more correct model (model 2) was proposed. As illustrated in Fig. 4, the variation in model 1 was Model 1 For localised faults, the question arises as to the correct way to model the random spacing of the impacts. Perhaps the first publication to model bearing fault signals as cyclostationary was [12], but the results were not very convincing, possibly because the main resonances excited by the faults may have been outside the measured range up to about 6 kHz. Results are shown below (Fig. 18) where localised faults on a very similar sized bearing only manifested themselves at frequencies above 8 kHz. Good results were obtained in [13], by modelling the vibration signals from localised bearing faults as CS2 cyclostationary. Random variable is the jitter Of. around each period

Fig. 5. Frequency spectra for the two models: (a) model 1 and (b) model 2.

Fig. 7. Spectral correlation for a mixture of first and second-order cyclostationarity, illustrated using modulation by gear and bearing signals: (a) gearmesh modulation by a gear signal; (b) gearmesh modulation by an extended inner race bearing fault; and (c) spectral correlation for case (b). From [14]. Fig. 6. Spectral correlation and spectrum of the squared envelope for a local inner race bearing fault. BPFI=120 Hz, shaft speed=9.5 Hz.

Fig. 8. Spectral correlation evaluated for cyclic frequency equals shaft speed: (a) localised fault and (b) extended fault

Fig. 9. Comparison of spectral correlation evaluated for cyclic frequency equals zero (normal power spectrum) and shaft speed Q for the depicted extended inner race spall. The fault is only apparent at ~=Q. Discrete frequency components were removed before the spectral correlation analysis.

Fig. 31. Squared envelope spectra showing two fault frequencies: (a) cage speed (9.8 Hz) and (b) BPFI (117.7 Hz).

Fig. 10. Schematic diagram of self-adaptive noise cancellation used for removing periodic interference (gear) leaving random signal (bearing). In Ref. [22] SANC was likened to prediction theory, and it was pointed out that the asymptotic result in Fig. 11 is in agreement with the analytical result that the bandwidth of the SANC filter is the reciprocal of the period of the frequency being separated, and the filter characteristic is almost identical to that for the equivalent comb filter for synchronous For fewer than 12 spectral components some saving can be made, but above this the minimum order corresponds to approximately one period of the frequency spacing. Ho recommends that the order should be at least double the minimum for best results.

Fig. 11. Minimum filter order vs number of discrete spectrum components. averaging (e.g. Fig. 13). In [23] it was also pointed out that it can be advantageous to vary the convergence factor exponentially, to start with a larger value and reduce it as the convergence proceeds.

Fig. 12. Example of enhancement of an outer-race fault signal in a gearbox: (a) measured vibration signal, (b) extracted periodic part (gears), an (c) extracted non-deterministic part (bearing). The filter characteristic corresponding to this expression is shown in Fig. 13 ([25]) for the case where N=8, and is seen to be a comb filter selecting the harmonics of the periodic frequency. The greater the value of N the more selective the filter and greater the rejection of non-harmonic components. The noise bandwidth of the filter is 1/N, meaning that the improvement in signal/noise ratio is 10 log;, N dB for additive random noise. For masking by discrete frequency signals, it should be noted that the characteristic has zeros which move with the number of averages, so it is often possible to choose a number of averages which completely eliminates a particular masking frequency. The above characteristic is for an infinitely long time signal x(t), and in Ref. [25] it is shown that for the practical situation of a finite length of signal with

Fig. 13. Filter characteristic corresponding to 8 synchronous averages (from [25]).

Fig. 14. Power spectrum of (a) order tracked signal; (b) residual signal obtained by setting the rotor related harmonics to the mean of adjacent (noise) lines; (c) residual signal obtained by subtracting the synchronous average and (d) DRS residual (removing discrete components using DRS).

Fig. 16. Example of applying both AR and MED filtering to bearing signals with an inner race fault in a high speed bearing: (a) original time signal; (b) after application of AR filtering; and (c) after additional MED filtering. The linear prediction (AR) filtering has made the pulses visible, but because of the high speed (12,000 rpm), the impulse responses excited have a length comparable to their spacing, and tend to overlap. The kurtosis has only improved from —0.40 to 1.25 in the AR operation, but increased to 38.6 after applying MED. This fault is at a fairly advanced stage, but using MED meant that it could be detected much earlier. Note that the kurtosis used here is based on cumulants, and is adjusted so as to give a value of zero for Gaussian signals. This means subtracting 3 from the normalised fourth order (centred) moment.

Fig. 17. Calculation of SK from the STFT for a simulated bearing fault signal: (a) simulated time signal, (b) STFT, and (c) SK as a function of frequency.

Fig. 18. Comparison of SK with dB spectrum difference for an inner race bearing fault. Frequency scale normalised to sampling frequency 48 kHz: (a) dB spectrum comparison over frequency range 0-24 kHz with and without the fault; (b) dB spectrum difference; and (c) spectral kurtosis.

Fig. 19. (a) PSD spectra with the different window lengths and (b) SK calculated for the indicated window length in samples (from [35]

Fig. 20. Kurtogram for a weak bearing fault in a gearbox [35]. Nw is window length defining spectral resolution. SK is spectral kurtosis. Maxima are projected onto each plane.

Fig. 21. (a) Optimal bandpass filter compared with SK at N,=44 and (b) outer race fault signal obtained using the filter of (a) (from [35])

Fig. 22. Combinations of centre frequency and bandwidth for the 1/3-binary tree kurtogram estimator [37].

‘ig. 23. Comparison of the fast kurtogram with the full kurtogram for an impulsive signal from loose parts monitoring [37] time averages in Eq. (21). This is rather similar in principle to the FFT algorithm and even more similar to the “discret wavelet packet transform” (DWPT). In Ref. [37], an even finer decomposition is proposed, based on a “1/3-binary tree’ where each halved-band is further split into 3 other bands, thus producing a frequency resolution as illustrated in Fig. 22 in the sequence 1/2, 1/3, 1/4, 1/6, 1/8, 1/12,...,2~*~', with corresponding “scale levels” k=0, 1, 1.6, 2, 2.6,..., that enforce | similarity in notation with the DWPT transform. It should be noted that, however, in addition to providing a fine resolution than allowed by the DWPT (actually limited to integer values of k only), the proposed solution also has mucl better filtering characteristics as demonstrated in Ref. [37].

Fig. 24. Example of advanced wavelet denoising: (a) raw vibration signal; denoised signal using NeighCoeff shrink based on (b) DTCWT; (c) DW (discrete wavelet transform), and (d) SGWT (second-generation wavelet transform). From [43].

Fig. 25. Procedure for envelope analysis using the “Hilbert transform” method [45].

Fig. 26. Potential aliasing given by squaring and rectifying a sinusoidal signal. With just squaring, but not rectification, aliasing can be avoided b' doubling the sampling frequency before squaring.

Fig. 27. Generation of spectrum of squared envelope (or signal) for three cases: (a) analytic signal; (b) equivalent real signal; and (c) frequency shifted real signal downward arrow indicates complex conjugate.

Fig. 30. Wavelet kurtogram for 4 filter banks; namely (3, 6, 12, and 24) filters/octave. Fig. 29. Time signals (one rotation of the carrier): (a) order tracked signal and (b) residual signal—passage of the three planets is seen.

Measurements were made on a bearing test rig at the FAG bearing company in Germany, on which bearings are tested to failure. At several points through their life, the bearings are dismantled and inspected. The bearing being tested is for ¢ high speed application, and is thus tested at 12,000 rpm, typical of gas turbine bearings. The accelerometer used to capture data was mounted using a magnet, and it is suspected (from inspection of the spectra) that the mounting resonance frequency was of the order of 12 kHz.

Fig. 34. Envelope spectrum of signal of Fig. 16(c) showing harmonics of BPFI 1398 Hz, and harmonics and sidebands spaced at shaft speed 196 Hz.

Fig. 35. The development of kurtosis with and without MED, compared against fault size.

Fig. 36. Results of applying DRS to signal with faulty bearing: (a) original signal; (b) deterministic part; and (c) random part.

Fig. 37. Effect of optimal SK filtering: (a) time signal and (b) envelope spectrum.

Fig. A1. Example of amplitude modulated white noise (from Antoni [10]): (a) time signal over four periods of cyclic frequency; (b)two-dimension. autocorrelation function vs time (sample) n and time lag t. is a periodic function of time, ie. Ryx(t,t)=Rxy(t+T,t) (this is not to be confused with the stationary enforce autocorrelation function computed as the time averaged <Rx(t,T)> =Rxx(t)). A simple example is provided by a whit noise modulated by a periodic amplitude, as illustrated in Fig. A1(a). Note that, in spite of the periodic modulation, this i still a completely random signal. The autocorrelation function, by virtue of the second-order non-linearity it introduce:

Fig. A2. Spectral correlation for the case of Fig. Al(a) (from [10]). where X;(f) stands for the Fourier transform of signal x(t) over an interval of duration T. Formula (A3) is probably most convenient when it comes to estimate the spectral correlation from finite-length measurements since it is easily amenable

Fig. A3. Wigner-Ville spectrum for the case of Fig. A1(a) (from [10]).

Fig. B1. Digital resampling with four times higher sampling frequency: (a) signal sampled at f,, and its spectrum; (b) addition of zeros which change. sampling frequency to fj2; and (c) lowpass filtration and rescaling.

Fig. B3. Use of tracking to avoid smearing of shaft speed related components. Fig. B2. Comparison of frequency characteristics for interpolation at different orders (from [49]).

1. Introduction Rolling element bearings are one of the most widely used elements in machines and their failure one of the most frequent reasons for machine breakdown. However, the vibration signals generated by faults in them have been widely studied, and very powerful diagnostic techniques are now available as discussed below.

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Daily dataset of 20th-century surface air temperature and precipitation series for the European Climate Assessment

by albert westermeier

2002, International Journal of Climatology

We present a dataset of daily resolution climatic time series that has been compiled for the European Climate Assessment (ECA). As of December 2001, this ECA dataset comprises 199 series of minimum, maximum and/or daily mean temperature... more

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A critical review of data on field-scale dispersion in aquifers

by Lynn Gelhar

1992, Water Resources Research

A critical review of dispersivity observations from 59 different field sites was developed by compiling extensive tabulations of information on aquifer type, hydraulic properties, flow configuration, type of monitoring network, tracer,... more

A critical review of dispersivity observations from 59 different field sites was developed by compiling extensive tabulations of information on aquifer type, hydraulic properties, flow configuration, type of monitoring network, tracer, method of data interpretation, overall scale of observation and longitudinal, horizontal transverse and vertical transverse dispersivities from original sources. This information was then used to classify the dispersivity data into three reliability classes. Overall, the data indicate a trend of systematic increase of the longitudinal dispersivity with observation scale but the trend is much less clear when the reliability of the data is considered. The longitudinal dispersivities ranged from 10 -2 to 10 4 m for scales ranging from 10 -1 to 105 m, but the largest scale for high reliability data was only 250 m. When the data are classified according to porous versus fractured media there does not appear to be any significant difference between these aquifer types. At a given scale, the longitudinal dispersivity values are found to range over 2-3 orders of magnitude and the higher reliability data tend to fall in the lower portion of this range. It is not appropriate to represent the longitudinal dispersivity data by a single universal line. The variations in dispersivity reflect the influence of differing degrees of aquifer heterogeneity at different sites. The data on transverse dispersivities are more limited but clearly indicate that vertical transverse dispersivities are typically an order of magnitude smaller than horizontal transverse dispersivities. Reanalyses of data from several of the field sites show that improved interpretations most often lead to smaller dispersivities. Overall, it is concluded that longitudinal dispersivities in the lower part of the indicated range are more likely to be realistic for field applications. --+vi•=• Dij at Oxi Oxi i,j= 1, 2, 3 (1) where c is the solute concentration, v i is the seepage velocity component in the xi direction, and Dij are the components of the dispersion coefficient tensor. The fighthand side of (1) represents the net dispersive transport which is presumed to be Fickian, i.e., the dispersive mass flux is proportional to the concentration gradient. Some investigators [e.g., Robertson and Barraclough, 1973; Bredehoeft and Pinder, 1973] alternatively define the dispersion coefficient tensor including the porosity n as D•j =nD ij. When it was clear that D•j was used in a study, we converted to the more common form used in (1). The mean flow direction is taken to be Xl, with vl = v, v2 = v3 = 0. Assuming that xl, x2, and x 3 are principal directions, the dispersivity is simply the ratio of the appropriate component of the dispersive coefficient tensor divided by the magnitude of the seepage velocity, v. To distinguish the field-scale dispersivities from laboratory values, the field-scale values are designated by the uppercase letter A [see Ge!har and Axness, !983] and, to allow for anisotropy of transverse dispersion, a third dispersivity coefficient is used as follows: Dll = ALV D22 = Arv D33 = Avv (2) where A t• is the longitudinal macrodispersivity (field scale), and A T is the horizontal transverse macrodispersivity, and A v is the vertical transverse macrodispersivity. The classical equation (1) with macrodispersivities (2) is standardly used for applied modeling of field-scale solute transport. The macrodispersivities are considered to be a property of some region of the aquifer. Although the macrodispersivity may be a function of space, in most applications it is assumed constant over a region of the aquifer that encompasses the entire plume both horizontally and vertically. Real solute plumes are observed to be threedimensional [LeBlanc, 1982; Perlmutter and Lieber, 1970; MacFarlane et al., 1983] and often of limited vertical extent. Although the classical equation is three-dimensional, the two-dimensional form is most commonly applied. Reasons for the use of the two-dimensional form of the equation include lack of three-dimensional data and in the case of Geophys. Res., 72(16), 4081-4091, 1967. Wilson, L. G., Investigations on the subsurface disposal of waste effluents at inland sites, Res. Develop. Progress Rep. 650, U.S.

Fig. 1. Longitudinal dispersivity versus scale of observation identified by type of observation and type of aquifer. The data are from 59 field sites characterized by widely differing geologic materials.

Fig. 2. Longitudinal dispersivity versus scale with data classified by reliability.

Fig. 3. Longitudinal dispersivity versus scale of observation with adjustments resulting from reanalyses. Arrows indicate reported values at tails and corresponding values from reanalyses at heads. Dashed line connects two dispersivity values determined at the Hanford site.

Fig. 5. Vertical transverse dispersivity as a function of observation scale.

ontal and vertical transverse dispersivities; largest symbols are high reliability and smallest symbols are low reliability. Vertical dashed lines connecting two points indicate sites where all three principal components of the dispersivity tensor have been measured. Horizontal dashed line indicates a ratio of A; /Ay = 1/3. which has been widely used in numerical simulations. Fig. 6. Ratio of longitudinal to horiz When the data on longitudinal dispersivity are classified according to reliability, the pattern regarding scale depen- dence of dispersivity is less clear (see Figure 2). There are no

*TDS denotes total dissolved solids; EC, electrical conductivity; PFB, pentafluorobenzoate; MTFMB, metatrifluoromethylbenzoate; MEB, metafluorobenzoate; Para-FB, parafluorobenzoate; RhWT, rhodamine-WT dye; and SCN, thiocyanate. +A, denotes longitudinal dispersivity; A, horizontal transverse dispersivity; and A y, vertical transverse dispersivity. Reported values for A;, Ay, and Ay are separated by slashes. Absence of slashes means that values were reported for A; only. A comma or a dash separating entries means that multiple values or a range of values, respectively, were reported for a particular dispersivity component. +For description of classification criteria, see text. 8B. E. Adams and L. W. Gelhar, Field study of dispersion in a heterogeneous aquifer: Spatial moments analysis (submitted to Water Resources Research, 1991). ||Porosity-corrected dispersivity value.

1. The tracer test was either ambient flow with known input, diverging radial flow, or a two-well pulse test (without recirculation). These three test configurations produce break- through curves which are sensitive to the dispersion coefficient and appear to work well in field applications [Welty and Gelhar, 1989]. The radial converging flow test is generally considered less satisfactory than the diverging test because breakthrough curves at the pumping well for the converging test frequently exhibit tailing, which complicates the interpre- tation of these tests. Some researchers attribute this behavior to two or more discrete geologic layers and try to reproduce the observed breakthrough curve by superposition of break- through curves in each layer, where the properties of each layer may differ [e.g., Ivanovitch and Smith, 1978, Sauty, 1977]. The problem with this interpretation is that there are typically numerous heterogeneities on a small scale that cannot be attributed solely to identifiable layers. One possible expla- nation of the tailing in radial convergent tests is sometimes termed ‘‘borehole flushing,’’ where the tail of the breakthrough curve is attributed to the slow flushing of the input slug of tracer out of the injection borehole by the ambient groundwater flaw. Goblet [1982] measured the slow flushing of tracer out of the values that do not fall into the high or low groups. These classifications do not place strict numerical confidence limits on reported dispersivities, but rather are intended to provide an order-of-magnitude estimate of the confidence we place on a given value. In general, we consider high-reliability dispersivity values to be accurate within a factor of 2. Low-reliability values are considered to be no more accurate than within 1 or 2 orders of magnitude. Intermediate reliabil- ity falls somewhere between the extremes. We wish to make a distinction between the judgment of the reliability of the reported dispersivity and the worth of a study. Often, the Purpose of a study was for something other than the deter- mination of dispersivity. Our classification of dispersivity is not intended as a judgment on the quality of a study as 2 whole, but rather to provide us with some criteria with which to screen the large number of data values obtained. By then examining the more reliable data, conclusions which evolve from the data will be more soundly based and alternative interpretations may’ become apparent.

TABLE 2. Numbers of Dispersivities for Different Types of Tests and Media se cen

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The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models

by N Quinn

1991, Hydrological Processes

The accuracy of the predictions of distributed hydrological models must depend in part on the proper specification of flow pathways. This paper examines some of the problems of deriving flow pathways from raster digital terrain data in... more

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a Lagrangian-Eulerian Finite-Element Formulation for Steady-State Solidification Problems

by Yimin Ruan

1994, Numerical Heat Transfer Part B-fundamentals

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The influence of autocorrelation on the ability to detect trend in hydrological series

by Sheng Yue

2002, Hydrological Processes

This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial... more

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Supplementary cementitious materials

by Barbara Lothenbach

2011, Cement and Concrete Research

The use of silica rich SCMs influences the amount and kind of hydrates formed and thus the volume, the porosity and finally the durability of these materials. At the levels of substitution normally used, major changes are the lower Ca/Si... more

Fig. 1. A) CaO-Al,03-SiO, ternary diagram of cementitious materials, B) hydrate phases in the CaO-Al,03-SiO2 system. Note that in the absence of carbonate or sulfate, C;AHg will be more stable than the AFm phases. Most of the available studies on the properties of blended systems composition and the hydrates formed as well as their impact on t processes taking place in the hydration of Portland cements (PC) well known (see e.g. the comprehensive book of Taylor [1]). clinker phases hydrate at various rates resulting mainly in t formation of C-S-H, portlandite, ettringite and AFm phases. T system where the hydration of the Portland cement and hydrauli reaction of the SCM occur simultaneously and may also influence t! reactivity of each other. The reaction of most SCMs is slower than t ong-term development of such systems is insufficient. The main are The blending of SCMs with Portland cement leads to a more complicated focus on mechanical or durability aspects of a specific fly ash or slag. Our knowledge about fundamental connections between the overall ne ne ne 1c ne ne reaction of the clinker phases and difficult to follow as many SCMs

Fig. 2. Schematic representation of the average chain length and the Al-uptake by bridging tetrahedra.

Fig. 3. SEM-BSE from a 60% Portland cement-40% slag blend (B-S1) hydrated for 1 year From Kocaba [13]. The hydrate assemblage observed experimentally in Si02—-PC blends agrees well with the modelling results shown in Fig. 5. It consists of mainly C-S-H, ettringite, AFm phases [20-22] and a reduced quantity of portlandite [22-25]. The blending of PC with >24wt% silica fume resulted after longer hydration times in the entire consumption of portlandite with ettringite and C-S-H with a reduced Ca/Si ratio as the only hydrate phase observed ([22,23,25,26], Fig. 6). As the silica fume continued to react, the low pH values and the absence of portlandite destabilized the monocarbonate with time [26,27]. The calculations in Fig. 5 indicate, that upon further replacement of PC by silica fume (or upon further reaction of the silica fume), ettringite will become unstable. The dissolution of

‘ig. 4. Ca/(Si+ Al) ratio in Portland cement (B) and 60% Portland cement-40% slag blends (B-S1; B-S8) hydrated up to 1 year. The lines indicate the Ca/(Si+ Al) ratio of the pure slag slags 1 and 8). (ram Kocaha [13].

Fig. 5. Modelled changes in hydrated Portland cement upon blending with SiOz, assuming complete reaction of the Portland cement (CaO 60, SiO, 22, Al,03 4.6, Fe203 2.7, MgO 1.9, Na20 0.3, K20 1.0, SO3 3.2, CO2 2 wt.%) and SiO. Fig. 5 illustrates an important aspect related to the partial replacement of Portland cement with SCMs — the decrease in the total volume of hydrates formed. This should mean that blended pastes have higher total porosities than pure PC pastes. This seems paradox as it is well established that PC-SCM blends can develop higher strengths and lower permeabilities than plain PC pastes (e.g. 29]). This poses the question as to whether the effective density, or space filling capacity of C-S-H in blended pastes is the same as in plain Portland pastes. Measurements indicate that blended systems show often equal or even higher total porosities than pure PC pastes, but a refined pore structure [30-33]. In particular, slag-PC pastes have been observed to contain more fine pores and less coarse capillary pores than PC pastes, resulting in a reduced permeability 30,32]. Fly ashes consist mainly of SiOz, but can contain also significant quantities of Al,O3. The amount of CaO is limited but highly variable depending on the origin of the fly ash (e.g. [1], Fig. 1). The ASTM C618 standard differentiates high calcium Class C-fly ashes and low-calcium Class F ashes. As the latter are the most abundant, the following discussion focuses on Class F fly ash. The blending of Portland cement with fly ash results in the reduction of the total amount of portlandite in the hydrated mixture, somewhat less pronounced than for silica fume as (i) the reactivity of fly ash is very limited and (ii) as the CaO in the fly ash is an additional source of calcium. Class F fly ashes contain between 15 and 35% alumina, so the blending of PC with such fly ash results in high amounts of Al-rich phases. As systematic information about the Al-uptake by C-S-H are still missing (see also discussion in Appendix A), the high aluminium content in the system, coupled with a potentially high aluminium uptake in C-S-H introduces a consider- able error in the thermodynamic calculations. For our calculations, a constant Al/Si of 0.1 in C-S-H was assumed. The results indicate, in the presence of moderate amounts of fly ash, the destabilization of

Fig. 6. Phase composition observed by XRD in a hydrated Portland cement, a CEM III/B blended with 10% SiOz and a CEM I blended with 40 wt.% SiO after one year of hydration. Graph modified from [26].

Fig. 7. Modelled changes in hydrated Portland cement upon blending with fly ash, assuming complete reaction of the Portland cement (CaO 60, SiO2 22, Al,03 4.6, Fe203 2.7, MgO 1.9, Na20 0.3, K20 1.0, SO3 3.2, and CO2 3 wt.%) and 50% reaction of a low Ca fly ash (CaO 4.4, SiOz 54, AlpO3 31, Fe203 4.6, MgO 0.8, Na20 0.6, K20 0.8, and SO3 0.4 wt.%).

Fig. 8. Modelled changes in hydrated Portland cement upon blending with blast furnace slag, assuming complete reaction of the Portland cement (CaO 60, SiO, 22, Al,03 4.6, Fe203 2.7, MgO 1.9, Naz20 0.3, K20 1.0, SO3 3.2, and CO 3 wt.%) and 75% reaction of a blast furnace slag (CaO 39, SiO 38, AlgO3 11, Fe203 1, MgO 10, K20 0.3, and S 1 wt.%). Al/Si in C-S-H=0.1.

Fig. 9. Hydration of 100% PC compared to 70% PC with 30% fine quartz filler. The rate of heat evolution is normalised to the PC content [53]. The quartz, as it does not react significantly, gives more space for hydration product of the PC so the acceleration period is prolonged. Recent results from Fernandez [53] and Kocaba [13] illustrate these effects. Figs. 9 and 10 show the heat evolution curves for blends with quartz filler and silica fume compared to reference cements. In both cases the heat evolution is normalized to the amount of clinker phases present. Quartz was chosen as a nominally inert material, although there may be some reaction of an amorphized surface layer

Fig. 10. a) 100% PC compared to 90% PC with 10% silica fume, the fine particles of silica fume act as nucleation sites to give a steeper acceleration and higher maximum rate of heat evolution [56]. Panel b shows simulation results in which the number of nucleation sites increased by 30% [57].

Fig. 11. Heat evolution for PC blended with corundum, rutile or quartz. Fineness corundum 5.4 m? g~!; rutile 9.1 m? g~!; quartz 0.76 m? g~!. Adapted from [58]. The technique which has been used most widely to try and measure the reactions of SCMs in blended systems is selective dissolution [62]. The intention of such methods is that the unreacted clinker phases and the hydrates from the clinker and slag reaction are dissolved, leaving only the unreacted slag or fly ash as a residue. Study of residues by X-ray diffraction and SEM reveals that significant amounts of clinker and hydrate phases remain after dissolution [13,62-64]. It is claimed that the effects of incomplete dissolution can be corrected for. However, recent independent work by two of the authors of this paper [13,63-65] indicates that large, non-quantifiable systematic errors remain as different assumptions lead to large differences in the quantity of FA or slag reacted. This probably explains why different authors report very different amounts of slag

Fig. A1. Aqueous concentrations and mole fractions of the C-S-H solid solution end-members (jennite-tobermorite) as a function of the Ca/Si ratio. The presence of portlandite and amorphous SiOz is indicated by horizontal lines (out of scale). Modified from [84,106].

Contents well captured by thermodynamic modelling, although better knowledge of the C-S-H is needed. At early ages, “filler” effects lead to an increased reaction of the clinker phases. Reaction of SCMs starts later and is enhanced with pH and temperature. Composition, fineness and the amount of glassy phase play also an important role. Due to the diverse range of SCM used, generic relations between composition, particle size, exposure conditions as temperature or relative humidity become increasingly crucial.

Average chain length of Portland cement (PC) with metakaolin (MK). Table 1 consist of X-ray amorphous glasses. The kinetics of the SCM reaction depends on the chemical composition, the fineness, and on the amount of reactive phases such as glass or zeolites of the SCM used as well as on the composition of the interacting solution. Comparatively little is known about the detailed effect of these parameters due to the difficulty to measure the reaction of SCMs quantitatively in blended systems.

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Underestimating Costs in Public Works Projects: Error or Lie?

by Bent Flyvbjerg

2002, Journal of the American Planning Association, vol. 68, no. 3, pp. 279-295

This article presents results from the first statistically significant study of cost escalation in transportation infrastructure projects. Based on a sample of 258 transportation infrastructure projects worth US$90 billion and... more

Figure 3. Inaccuracy of cost estimates in transportation projects over time, 1910-1998 (fixec

lable 1. Inaccuracy of transportation project cost estimates by type of project (fixed prices)

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A Statistical Exploration of the Relationships of Soil Moisture Characteristics to the Physical Properties of Soils

by Timothy Ginn and

1984, Water Resources Research

Stochastic modeling of soil water fluxes in the absence of measured hydraulic parameters requires a knowledge of the expected distribution of the hydraulic parameters in different soil types. Predictive relationships describing the... more

Fig. 1. (a) The USDA soil texture triangle. (b) Reclassification of the texture categories into four broad regions for the two and four group discriminant analyses.

Fig. 2. Values of the F ratios from the one-way analyses of variance. The dashed line represents a significant result (p = 0.10).

Fig. 3. Percent of variance explained by each factor in the two- way analyses of variance. The dashed line represents the percent of variance explained by texture alone.

Fig. 4. Plots of the mean values of the hydraulic parameters for each textural class versus the most important variable (percent sand, silt, or clay) determined from the multiple linear regression analysis. The solid line is the univariate regression line.

Fig. 5. Plots of the standard deviations of the hydraulic parame- ters within each textural class versus the most important variable (percent sand, silt, or clay) determined from the multiple linear regres- sion analysis. The solid line is the univariate regression line.

Fig. 6. F ratios from the one-way analysis of variance for each parameter, before (a) and after normalization of the parameter values using (b) the univariate expressions of Table 5 and (c) the multivariate expressions of Table 4. All F ratios are significant (p = 0.10).

Fig. 7. Plot of the two significant discriminant function scores for the four group analysis. The modified USDA textural triangle is superimposed on the discriminant space. A similar plot of the discriminant scores based on the 11 group analysis is presented in Figure 8. A distorted version of the textural triangle (Figure 1a) is superimposed on the dis- criminant space. Again, the similarity between the two spaces is striking. While the relative areas of the textural classes have changed, the neighbor-to-neighbor relationship is identical in the two spaces. The only textural class which falls outside its expected region is the sandy clay class. It should be noted, however, that this class was represented by only 16 samples in the total sample population of 1448.

Fig. 8. Plot of the two most important discriminant function scores for the eleven group analysis. A distorted USDA textural trian- gle is superimposed on the discriminant space.

TABLE 1. List of Sample and Site Descriptors and the Classes for Each Descriptor The number in parentheses is the number of samples in each classi- fication. Texture, land use, and horizon were available for all samples. Other descriptors were not always available for each sample. Un- classified samples were not included in statistical analyses using that descriptor.

TABLE 2. Values of Percent Silt, Sand, and Clay Content Used for Each Textural Class in the Regression Analyses The percentages were obtained from midpoint values of each tex- tural class using the USDA textural triangle.

TABLE 3. Means and Standard Deviations for the Four Hydraulic Parameters in Each Textural Class Parameters: b is the slope of log Y versus log (@/®,) regression, Y in centimeters H,O; log '¥, is the intercept of log ¥ versus log (@/@,) regression, in centimeters H,O; log K, is the log of the saturated hydraulic conductivity in inches per hour; ©, is the saturated water content in percent (volume/volume).

TABLE 4. Results of Multiple Linear Regression Analyses on the Means and Standard Deviations of the Parameters

TABLE 5. Results of the Univariate Regressions of the Hydraulic Parameters on Percent Sand, Silt, or Clay

TABLE 6. Correlation Coefficients (r) Between Canonical Discriminant Function Scores and the Hydraulic Parameter Values

TABLE 7. Correlation Coefficients (r) Between Discriminant Function Scores clays (the coefficients are —0.99 for both correlations). This suggests that we might interpret the second discriminant func- tion as a silt axis. The first function for each group might likewise be interpreted as a clay-sand axis. The two discrimi- nant functions can be used to define a planar parameter space similar to the sand, silt, clay planar space defined by the USDA triangle. Figure 7 shows a plot of the two discriminant function scores for the four group case. The functions were evaluated for each group using the mean of the parameter values within each group. Superimposed on the discriminant space is the modified USDA triangle from Figure 1b. The similarity between the classification scheme based on weighted combinations of the hydraulic parameters and the classifi- cation scheme based on particle size distributions of the soils is striking.

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Climatic warming in the Tibetan Plateau during recent decades

by XIAODONG LIU

2000, International Journal of Climatology

Adequate knowledge of climatic change over the Tibetan Plateau (TP) with an average elevation of more than 4000 m above sea level (a.s.l.) has been insufficient for a long time owing to the lack of sufficient observational data. In the... more

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