# Equations for the soil-water characteristic'curve '

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Equations for the soil-water characteristic'curve ' D.G. FREDLUND AND ANQING XING Departrnent of Civil Engineerirzg, Universitj~ of Saskatchewan, Saskatoon, SK S7N OWO, Canada Received July 27, 1993 Accepted March 7, 1994 The soil-water characteristic curve can be used to estimate various parameters used to describe unsaturated soil behaviour. A general equation for the soil-water characteristic curve is proposed. A nonlinear, least-squares computer program is used to determine the best-fit parameters for experimental data presented in the literature. The equation is based on the assumption that the shape of the soil-water characteristic curve is dependent upon the pore-size distribution of the soil (i.e., the desaturation is a function of the pore-size distribution). The equation has the form of an integrated frequency distribution curve. The equation provides a good fit for sand, silt, and clay soils over the entire suction range from 0 to 10"Pa. Key words: soil-water characteristic curve, pore-size distribution, nonlinear curve fitting, soil suction, water content. La courbe caractkristique sol-eau peut Stre utilisce pour estimer divers paramktres dccrivant le comportement d'un sol non saturk. On propose ici une Cquation pour cette courbe caractkristique sol-eau. Un programme non IinCaire, par moindres cam&, est utilisk pour dkterrniner les paramktres qui permettent d'approcher au mieux les donnkes expcrimentales recueillies dans la IittCrature. L'Cquation est basce sur l'hypothkse que la forme de la courbe caractkristique sol-eau dcpend de la rkpartition de la taille des pores du sol (i savoir que la perte de saturation est une fonction de cette repartition). L'Cquation a la forme d'une intcgrale de courbe de rkpartition, de frcquences. Cette Cquation permet un bon ajustement pour les sols sableux, silteux et argileux sur toute la gamme des valeurs de succion, de 0?I 10"Pa. Mots clis : courbe caractcristique sol-eau, rkpartition de la taille des pores, ajustement non linkaire, succion dans le sol, teneur en eau. [Traduit par la rcdaction] Can. Geotecli. J. 31, (1994) 5 i? Introduction A theoretical framework for unsaturated soil mechanics has been established over the past two decades. The constitutive equations for volume change, shear strength, and flow for unsaturated soil have become generally accepted in geotechnical engineering (Fredlund and Rahardjo 1993a). The measurement of soil parameters for the unsaturated soil constitutive models, however, remains a demanding laboratory process. For most practical problems, it has been found that approximate soil properties are adequate for analysis (Papagiannakis and Fredlund 1984). Hence, empirical procedures to estimate in saturated soil parameters would be valuable. Laboratory studies have shown that there is a relationship between the soil-water characteristic curve for a particular soil and the properties of the unsaturated soil (Fredlund and Rahardjo 19930). For example, it has become an acceptable procedure to predict empirically the permeability fiinction for an unsaturated soil by using the saturated coefficient of permeability and the soil-water characteristic curve (Marshall 1958; Mualem 1986; University of Saskatchewan 1984). Similar procedures have been suggested for the shear strength properties of an ~~nsaturated soil (Fredlund and Rahardjo 1993b). Since the soil-water characteristic curve is ~~sed as the basis for the prediction of other unsaturated soil parameters, such as the permeability and shear-strength fiinctions, it is important to have a reasonably accurate characterization of the soil-water characteristic curve. This paper reviews the forms of mathematical equations that have been s~iggested to characterize the soil-water characteristic curve. It appears that none of the suggested equations accurately fit laboratory data over the entire suction PllilLd lo C,to.ld.~ 1 lniprlinr..la C.io.l&l range. This paper proposes a new equation that can be used to fit laboratory data over the entire soil suction range. A mathematical basis for the equation is described and a best-fit procedure is outlined to obtain the parameters for the equation. The soil-water characteristic curve for a soil is defined as the relationship between water content and suction for the soil (Williams 1982). The water content defines the amount of water contained within the pores of the soil. In soil science, volumetric water content 0 is most commonly used. In geotechnical engineering practice, gravimetric water content w. which is the ratio of the mass of water to the mass of solids, is most commonly used. The degree of saturation S is another commonly used measure to indicate the percentage of the voids that are filled with water. The above variables have also been used in a normalized form the water contents are referenced to a residual water content (or to zero water content). The suction may be either the matric suction (also known as capillary pressure) of the soil (i.e., u, - u,, ua is the pore-air pressure and ci, is the pore-water pressure) or total suction (i.e., matric plus osmotic suction). At high suc- here are several soil terms that are used interchangeably in the literature. The terminology used in the paper is most consistent with that found in the geotechnical literature. Other terms are used in the geo-environmental, petroleum, and some of the soil science disciplines. Some of these equivalences are as follows: matric suction = capillary pressure, air-entry value = displacement pressure, and soil-water characteristic curve = suction - volumetic water content curve.

2 522 CAN. GEOTECH. J. VOL , s i l t y soil 1 I \ FIG. 1. Typical soil-water characteristic curve for a silty soil. tions (i.e., greater than about 1500 kpa), matric suction and total suction can generally be assumed to be equivalent. As a result of the different terminologies used, the soilwater characteristic curves have taken on numerous forms. It is suggested that the term soil-water characteristic curve be used to represent the relationship between volumetric water content 0 and matric suction. Volumetric water content test results in the low suction range are often presented using an arithmetic scale. Soil-water characteristic curves over the entire suction range are often plotted using a logarithmic scale. Figure 1 shows a typical plot of a soil-water characteristic curve for a silty soil, along with some of its key characteristics. The air-entry value of the soil (i.e., bubbling pressure) is the matric suction air starts to enter the largest pores in the soil. The residual water content is the water content a large suction change is required to remove additional water from the soil. This definition is vague and an empirical procedure for its quantification would be useful. A consistent way to define the residual water content is shown in Fig. 1. A tangent line is drawn from the inflection point. The curve in the high-suction range can be approximated by another line. The residual water content 0, can be approximated as the ordinate of the point at which the two lines intersect (Fig. 1). The total suction corresponding to zero water content appears to be essentially the same for all types of soils. A value slightly below lo6 kpa has been experimentally supported for a variety of soils (Croney and Coleman 1961). This value is also supported by thermodynamic considerations (Richards 1965). In other words, there is a maximum total suction value corresponding to a zero relative humidity in any porous medium. The main curve shown in Fig. 1 is a desorption curve. The adsorption curve differs from the desorption curve as a result of hysteresis. The end point of the adsorption curve may differ from the starting point of the desorption curve because of air entrapment in the soil. Both curves have a similar form; however, this paper primarily considers the desorption curve. Typical soil-water characteristic curves (i.e., desorption curves) for different soils are shown in Fig. 2. The saturated water content 0, and the air-entry value or bubbling pressure (u, - u,),, generally increase with the plasticity of the soil. Other factors such as stress history also affect the shape of the soil-water characteristic curves FIG. 2. Soil-water characteristic curves for a sandy soil, a silty soil, and a clayey soil. Literature review Numerous empirical equations have been proposed to simulate the soil-water characteristic curve. Among the earliest is an equation proposed by Brooks and Corey (1964). It is in the form of a power-law is the normalized (or dimensionless) water content = (0-0,)/(0, - Or), 0, and 0, are the saturated and residual volumetric water contents, respectively), \$ is the suction, \$, is the air-entry value, and X is the pore-size distribution index. The degree of saturation S has also been used in place of the normalized water content. Equation [l] has been verified through several studies (Campbell 1974; Clapp and Hornberger 1978; Gardner et al. 1970~1, 1970b; Rogowski 1971; Williams et al. 1983; McCuen et al. 1981). The following linear relationship between the logarithm of volumetric water content and the logarithm of suction was used by Williams et al. (1983) to describe the soil-water characteristic curve of many soils in Australia. 121 ln\$=al +bl In0 a, and b, are curve-fitting parameters. McKee and Bumb (1984) suggested an exponential function for the relationship between the normalized water content and suction. This has been referred to as the Boltzmann distribution: = a, and b, are curve-fitting parameters. Equations [I] and [3] have been found to be valid for suction values greater than the air-entry value of the soil. The equations are not valid near maximum desaturation or under fully saturated conditions. To remedy this condition, McKee and Bumb (1987) and Bumb (1987) suggested the following relationship: a, and b, are curve-fitting parameters. This equation gives a better approximation in the low-suction range. The

3 equation is not suitable in the high-suction range, since the curve drops exponentially to zero at high suction values. Equation [l] implies that there is a sharp discontinuity in suction near saturation. Although some coarse-grained sands may have a rapid change in suction at low suctions, most soils, particularly medium- and fine-textured soils, show a gradual curvature in the air-entry region near saturation. A modification of [I] was suggested by Roger and Hornberger (1978) to account for gradual air entry. In the case the volumetric water content is referenced to zero water content and the normalized volumetric water (i.e., 810,) is plotted as the abscissa, the general soilwater characteristic plot has an inflection point the slope changes from an increasing value to a decreasing value decreases. The inflection point is assigned the coordinates (Oi, \$;), and the interval Oi 4 1 can be described by a parabola: [5] * = -a, - - 1) a, and b, are curve-fitting parameters. The parameters a, and b, are obtained by forcing [5] through the two points (Oi, IJJJ and (1, 0). The slopes of both [l] and [5] are equal at the inflection point. Another frequently used form for the relationship between suction and the normalized water content was given by van Genuchten (1980): r 1!?I FREDLUND AND XING 523 \ is not suitable as a general fdrm, allhough it might apply for some soils over a limited range of suction values. To establish a theoretical basis for the soil-water characteristic curve, let us consider the pore-size distribution curve for the soil. The soil may be regarded as a set of interconnected pores that are randomly distributed. The pores are characterized by a pore radius r and described by a fimction f(r), f(r) dr is the relative volume of pores of radius r to r + dr. In other words, f(r) is the density of pore volume corresponding to radius r. Since f(r) dr is the contribution of the pores of radius r to r + dr that are filled with water, the volumetric water content can be expressed as PI R 0(R)= Jf(r)dr R,," 8(R) is volumetric water content when all the pores with radius less than or equal to R are filled with water, and Rmi, is minimum pore radius in the soil. Let R,,, denote the maximum pore radius. Then, for the saturated case, [lo1 0(RmaX)=0, i The capillary law states that there is; an inverse relationship between matric suction and the ra'dius of curvature of the air-water interface. In other words, the air-water interface bears an inverse relationship to the pore size being desaturated at a particular suction: p, n, and m are three different soil parameters. This form of the equation gives more flexibility than the previous equations described. In an attempt to obtain a closed-form expression for hydraulic conductivity, van Genuchten (1980) related m and n through the equation nz = 1 - lln. This, however, reduces the flexibility of [6]. More accurate results can be obtained by leaving m and n parameters with no fixed relationship. In 1958, Gardner proposed an equation for the permeability function. The equation emulates the soil-water characteristic curve and can be visualized as a special case of [6]: : q is a curve-fitting parameter related to the air-entry value of the soil, and iz is a curve-fitting parameter related to the slope at the inflection point on the soil-water characteristic curve. Theoretical basis for the shape of the soil-water characteristic curve The equations proposed in the research literature are empirical in nature. Each equation appears to apply for a particular group of soils. There are other equations of slightly differing forms that could be tested to assess their fit with experimental data. For example, the soil-water characteristic curve appears to have the form of the right-hand side of a normal-distribution curve. Therefore, the following equation can be used to approximate the soil-water characteristic curve: e-(f)s\$)"' a,, b,, and m are curve-fitting parameters. Equation [8] C = 2T cos cp, a constant, T is surface tension of water, and cp is angle of contact between water and soil. Two particular suction conditions can be defined as follows: and Jr,,, is the suction value corresponding to the minimum pore radius, and \$, is the air-entry suction value of the soil. Using the capillary law, [9] can be expressed in terms of suction: 1 8 f d = C C d h h h' 4, 'b ma". 12 is a dummy variable of integration representing suction. Equation [14] is the general form describing the relationship between volumetric water content and suction. If the pore-size distribution f(r) of a soil is known, the soilwater characteristic curve can be uniquely determined by [14]. Several special cases are as follows. (I) Case of a constant pore size function - The pore sizes are uniformly distributed, that is, f(r) = A, A is a constant. It follows, from [14], that

4 524 CAN. GEOTECH. J. VOL B = AC, a constant, and D = ACI\$,l,,,, a constant. (2) Case pore-sizefctnction varies inversely as r" - For the case of f(r) = Alr', the relationship between volumetric water content and suction is B = A\$,,,IC, a constant, and D = AIC, a constant. Equation [ 161 represents a linear variation in the pore sizes. In other words, there is a linear relationship between volumetric water content and suction. (3) Cnse pore-size function varies inversely as r("'") - For the case of f(r) = Air""+", rn is an integer, the relationship between volumetric water content and suction is B = A(\$,,,)"'I(rnC"'), a constant, and D = AI(mCn'), a constant. The power-law relationship (i.e., eq. [I]) proposed by Brooks and Corey (1964) is simply a special case of In other words, the Brooks and Corey (1964) power-law relationship is valid only when the pore-size distribution is close to the distribution f(r) = ~lr""'. To describe the soil-water characteristic curve over the entire suction range from 0 to lo6 kpa, volumetric water content is referenced to zero water content (otherwise, the normalized water content becomes negative if 0 is less than 0,). In this case, the normalized water becomes 010,. Equation [14] suggests that the following integration form can be used as a general form to approximate the soil-water characteristic curve: erfc(x) is the complement of the error function erf(x). Equation [20] describes a symmetrical S-shaped curve. Therefore, if the pore-size distribution of a soil can be approximated by a normal distribution, the soil-water characteristic curve of the soil will be close to a symmetrical S-shaped curve, and [20] can be used as a model to describe this relationship. The two fitting parameters (i.e., the mean value p, and the standard deviation o) in 1201 are related to the air-entry value of the soil and the slope at the inflection point on the soil-water characteristic curve. If the slope at the inflection point is s and the air-entry value is +, then the standard deviation o can be written as and the mean value can be calculated as (2) Cnse of a gamma distt-ibutiorz Consider the case of a gamma-type distribution for the function f(r). That is, f(h) takes the following form: 10, else f(h) is the pore-size distribution as a function of suction. Equation [18] will generally produce a nonsymmetrical S-shaped curve. Several special cases are as follows. (I) Case of a tiorma1 distribution Let us assume that f(h) is a normal distribution. That is, In this case, the soil-water characteristic curve defined by (181 has a smaller air-entry value, a steeper slope near saturation, and a gentler slope near the residual water content. In the special case when a is an integer, the soil-water characteristic curve defined by [I81 becomes k is mean value of the distribution of f(h), and o is standard deviation of the distribution of f(h). The soil-water characteristic curve defined by [18] can be expressed as follows: For a = 1, the gamma distribution becomes an exponential distribution: [ 0, else and the soil-water characteristic curve defined by [ 181 can be

5 FREDLUND AND XING Integration of the FIG. 3. A sample distribution using [29] and its integration (eq. [61) FIG. 4. A sample distribution using [30] and its integration. written as Note that [26] has the same form as [3], which was used by McKee and Bumb (1984) to describe the soil-water characteristic curve. Therefore, [3] gives the best results if the pore-size distribution of the soil is close to a gamma distribution. (3) Case of a beta distribution Consider the case of a beta distribution for the function f(r>: ( 0, else to FIG. 5. Sample plots of [31] with n = 2 and nz = 1 (a varies). Proposal for a new equation The pore-size distribution of [6] can be written as follows: In this case, the soil-water characteristic curve given by [18] has greater flexibility. For a equal to P, [la] generates a symmetrical S-shaped curve. For a greater than P, the curve is nonsymmetrical and has a higher air-entry value, a gentler slope near saturation, and a steeper slope near the residual water content. For a less than P, the curve has a smaller air-entry value, a steeper slope near saturation, and a gentler slope near the residual water content. In the case when a and p are integers, the soil-water characteristic curve defined by [la] and [27] is related to the binomial probability function as follows (Mendenhall et al ): Equation [28] has a form similar to that of [5] suggested by Roger and Hornberger (1978), which was used to account for a gradual air entry. Note that defining r over the interval [O, 11 does not restrict its use. The beta density function can be applied to any interval by translation and a change in the scale. Figure 3 shows a sample probability distribution for [29] along with its integration (i.e., eq. [6]). It can be seen that the integration drops to zero over a narrow suction range. Therefore, [6] is not suitable in the high-suction region. Experimental data show that after the residual water content, the plot should decrease linearly to a value of about lo6 kpa (Croney and Coleman 1961). To describe the soilwater characteristic curve more accurately, the following distribution is suggested: Equation [30] and its integration form are shown in Fig. 4 for the same set of parameters (i.e., a = llp, n, in). This distribution function drops more slowly than [29] as Jl increases and, therefore, [30] produces a nonsymmetrical curve that is closer to the experimental data. Integrating [30] using [la] gives the following relationship between volumetric water content and suction: r Figures 5-7 show the effect of varying the three parameters a, tz, and in on the shape of the soil-water characteristic 1 I n

6 526 CAN. GEOTECH. J. VOL. 31, 1994 FIG. 6. Sample plots of [31] with a = 100 and m = 1 (n varies) FIG. 9. A best-fit curve to the experimental data of a till (S. Vanapalli, personal communication, 1993). FIG. 7. Sample plots of [31] with n = 100 and n = 2 (m varies). 0-1 I! -!! I FIG. 10. A best-fit curve to the experimental data of a silty loam (data from Brooks and Corey 1964). 0 Slope - - Wp - WI and draw a tangent line through this point (Fig. 8). Let s denote the slope of the tangent line. Then, the three parameters a, n, and m are determined as follows: 0 20 Yi 40 '+'P FIG. 8. A sample plot for the graphical solution of the three parameters (a, n, and m) in [31]. curve. From Fig. 5 it can be seen that when n and m are fixed, parameter a (with a unit of kpa) is closely related to the air-entry value. In general, the value for the parameter a would be higher than the air-entry value. However, for small values of m, the air-entry value can be used for parameter a. Figure 6 indicates that parameter n controls the slope of the soil-water characteristic curve. The distribution given by [30] attains its maximum value approximately at the value of a. Therefore, the point (a, 0(a)) can be used to approximate the inflection point. Using this information, a graphical estimation for the three parameters can be obtained from the soil-water characteristic curve. First, locate the inflection point (+;, Oi) on the soil-water characteristic plot [34] n =- "'+I 3.72 s+ me, The slope s of the tangent line can be calculated as 4, is the intercept of the tangent line and the matricsuction axis (Fig. 8). Small values of m result in a moderate slope in the highsuction range, and large values of n produces sharp corner near the air-entry value (see Fig. 9). Another example of a best-fit curve to the experimental data for a silty loam from Brooks and Corey (1964) is shown in Fig.lO. In [31], 0 becomes equal to 0, when the suction is zero, and 0 becomes zero when suction goes to infinity. It is also possible to use the degree of saturation for curve fitting, since the degree of saturation varies from 0 to 1. Gravimetric water content can be similarly normalized for curve-fitting purpose. Three plots are shown for the same soil (i.e., silty

7 FREDLUND AND XING 527, A Gravmetnc water content (Computed from experimental data) o Volumetric water content (Computed from expenmental data) ln~tial water content: 43.5% Total density: 2.60 ~ ~ l r n ~ Degree of saturat~on (Expenmental data) , 350 FIG. 11. Best-fit curves to the experimental data of a silty loam using three different representations bf the water content, i.e., degree of saturation, volumetric water content, and gravimetric water content (data from Brooks and Corey 1964). o Experimental dat Preconsolidated load: 100 kpa Initial water content: 16.3% Total density: 1.80 ~~11-n~ FIG. 12. A sample plot of [36]. loam) in Fig. 11, using different ways of representing the water content of the soil (i.e., degree of saturation, volumetric water content, and gravimetric water content). Experimental data have previously shown that the suction of a soil reaches a maximum value of approximately lo6 kpa at zero water content. This upper limit can be built into [31] as follows: A C(+) is a correction function defined as ln(1++/+,> C(*)= I~[I+(~oooooo/+,)~ +, is the suction corresponding to the residual water content 0,. It can be seen that C(l ) is equal to zero. Therefore, at the limiting point + = lo6 kpa, the water content 0 calculated from [36] is zero. A sample plot for [36] is shown in Fig. 12. The curve at the low-suction range is not sig- FIG. 13. A best-fit curve to the experimental data of a till using [31] (S. Vanapalli, personal communication, 1993). nificantly affected, since the correction function C(+) is approximately equal to 1 at low suctions. Figure 13 shows a best-fit curve to the experimental data obtained for a glacial till, using [31]. A best-fit curve to the same experimental data using [36] is shown in Fig. 14. It can be seen that the modified equation (i.e., eq. [36]) fits the data better than [31]. The main difference is that the curve is forced by C(+) to zero at a suction of lo6 kpa. A graphical estimation of the four parameters a, n, rn, and +,, in [36] can be obtained from a semilog plot of the soil-water characteristic curve. First, determine the suction corresponding to the residual water content +, by locating a point the curve starts to drop linearly in the highsuction range (Fig. 15). Numerical results show that, in most cases, [36] gives a satisfactory approximation for +, 1500 kpa. Its magnitude will generally be in the range kpa. Figure 15 uses +, = 3000 kpa for illustration purposes. Next, locate the inflection point (+i, Oi) on the semilog plot and draw a tangent line through this point

8 528 CAN GEOTECH J VOL 31, 1991 i Matr~c Suctton (kpa) Matr~c Suct~on (kpa) FIG. 14. A best-fit curve to the experimental data in Fig. 13 using [36]. FIG. 17. A best-fit curve to the experimental data of a sand (Soil Laboratory data, University of Saskatchewan). 1 W i Wp 1OOOWr1OOOO FIG. 15. A sample plot for the graphical solution of the four parameters (a, la, m, and JI,) in [36]. FIG. 18. A best-fit curve to the experimental data of Kidd Creek tailings (N. Yang, personal communication, 1992) Best-fit curve C g 0.4 0) 0" I I I I FIG. 16. A best-fit curve to the experimental data of a sand (data from Moore 1939). (Fig. 15). Let s denote the slope of the tangent line on the semilog plot. Then, the fitting parameters a, tz, and In can be determined as follows: [37] a =+i The slope s of the tangent line can be calculated as follows: \$, is the intercept of the tangent line on the semilog plot and the matric-suction axis (Fig. 15). A graphical estimation only gives approximate values for the parameters. To obtain a closer fit to experimental data, the three parameters (a, 11, and in) in [36] can be determined using a least-squares method, if the measured data for 0 and t) are available. The idea is to choose the three parameters such that the calculated values from [36] are as close as possible to the measured values. Therefore, the following objective function (i.e., sum of the squared deviations of the measured data from the calculated data) is minimized with respect to the three parameters a, n, and In. : O(a, n, tn) is the objective function, M is the total number of measurements, and Bi and \$i are measured values.

9 FREDLUND AND XING 529 FIG. 19. A best-fit curve to the experimental data of a sand (Soil Laboratory data, University of Saskatchewan) FIG. 21. A best-fit curve to the experimental data of a silt (S. Huang, personal communication, 1993) FIG. 20. A best-fit curve to the experimental data of a sand (University of Toronto data; University of Saskatchewan 1984). This is a nonlinear minimization problem. A curve-fitting utility CFvIEW was coded based on [36] and [41] using a quasi-newton method. The detailed nonlinear curve-fitting algorithm is presented in the Appendix. Best-fit curves for a tailings sand, a silt, and a clay are shown in Figs An arithmetic scale has been used when the experimental data in the high-suction range are not available. It can be seen, from these results, that [36] can be used to fit the experimental data reasonably well over the entire suction range 0-10"~a. Some applications require an estimation of the residual water content. The following slightly different form of [3 11 can be used to estimate the residual water content 0,: FIG. 22. A best-fit curve to the experimental data of a silt (Soil Laboratory data, University of Saskatchewan). Here, 0, and 0, are treated as two additional parameters. The five parameters a, n, m, 0,, and 0, in [42] can be systematically identified through a best-fit analysis on experimental data. Conclusions General empirical equations have been proposed to describe the soil-water characteristic curve. Each equation has its own limitations. A general form of the relationship between water content and suction was developed based on the poresize distribution of the soil. If the pore-size distribution of a soil can be obtained or predicted, then the soil-water char- FIG. 23. A best-fit curve to the experimental data of an initially slurried Regina clay (data from Fredlund 1964). acteristic curve is uniquely determined from the proposed general equation. The analysis in this paper provides not only a theoretical basis for most of the empirical equations but also proposes a new, more general equation to describe the soil-water characteristic curve. Based on the proposed equation, a curve-fitting utility, CFVIEW, was coded. It was found that the equation fits experimental data reasonably well over the entire suction range from 0 to lo6 kpa.

10 530 CAN. GEOTECH. J. VOL. 31, 1994 Acknowledgement The authors would like to thank Sai Vanapalli for supplying experimental data and for helpful suggestions for the curve-fitting program. Brooks, R.H., and Corey, A.T Hydraulic properties of porous medium. Colorado State University (Fort Collins), Hydrology Paper 3. Bumb, A.C Unsteady-state flow of methane and water in coalbeds. Ph.D. thesis, Department of Chemical Engineering, University of Wyoming, Laramie. Campbell, G.S A simple method for determining unsaturated conductivity from moisture retention data. Soil Science, 117: Clapp, R.B., and Hornberger, G.M Empirical equations for some soil hydraulic properties. Water Resources Research, 14: Croney, D., and Coleman, J.D Pore pressure and suction in soils. In Proceedings of the Conference on Pore Pressure and Suction in Soils. Butterworths, London. pp Fredlund, D.G Comparison of soil suction and onedimensional consolidation characteristics of a highly plastic clay. M.Sc. thesis, Department of Civil Engineering, The University of Alberta, Edmonton. Fredlund, D.G., and Rahardjo, H. 1993a. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc., New York. Fredlund, D.G., and Rahardjo, H. 1993b. An overview of unsaturated soil behaviour. In Proceedings of ASCE Specialty Series on Unsaturated Soil Properties, Dallas, Tex., October. Gardner, W.R Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water-table. Soil Science, 85: Gardner, W.R., Hillel D., and Benyamini, Y. 1970a. Post irrigation movement of soil water. I. Redistribution. Water Resources Research, 6: Gardner, W.R., Hillel D., and Benyamini, Y. 1970b. Post irrigation movement of soil water. IS. Simultaneous redistribution and evaporation. Water Resources Research, 6: Marshall, T.J A relation between permeability and size distribution of pores. Journal of Soil Science, 9: 1-8. McCuen, R.H., Rawls, W.J., and Brakensiek, D.L Statistical analyses of the Brook-Corey and the Green-Ampt parameters across soil textures. Water Resources Research, 17: McKee, C.R., and Bumb, A.C The importance of unsat- r) \ urated flow parameters i; designing a monitoring system for hazardous wastes and envitonmehtal emergencies. Itz Proceedings, Hazardous Materials Control Research Institute National Conference, Houston, Tex., March pp McKee, C.R., and Bumb, A.C Flow-testing coalbed methane production wells in the presence of water and gas. In SPE Formation Evaluation, December, pp Mendenhall, W., Scheaffer, R.L., and Wackerly, D.D Mathematical statistics with applications. 2nd ed. Duxbury Press, Boston. Moore, R.E Water conduction from shallow water tables. Hilgardia, 12: Mualem, Y Hydraulic conductivity of unsaturated soils: prediction and formulas. In Methods of soil analysis. Part 1. Physical and mineralogical methods. 2nd ed. Agronomy. Edited by A. Klute. American Society of Agronomy, Inc. and Soil Society of America, Inc., Madison, Wis., U.S.A., pp Papagiannakis, A.T., and Fredlund, D.G A steady state model for flow in saturated-unsaturated soils. Canadian Geoetechnical Journal, 21: Richards, B.G Measurement of the free energy of soil moisture by the psychrometric technique using thermistors. In Moisture equilibria and moisture changes in soils beneath covered areas. Edited by G.D. Aitchison. Butterworth & Co. Ltd., Sydney, Australia, pp %. Roger, B.C., and Hornberger, G.M Empirical equations for some soil hydraulic propert2ees. Water Resources Research, 14: Rogowski, AS Watershed physics: model of the soil moisture characteristic. Water Resources Research, 7: Sadler, D.R Numerical methods for nonlinear regression. University of Queensland Press, St. Lucia, Queensland, Australia. University of Saskatchewan KCAL user's manual. A computer program for calculating unsaturated permeability. Department of Civil Engineering, University of Saskatchewan, Saskatoon. van Genuchten, M.T A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44: Williams, P.J The surface of the Earth, an introduction to geotechnical science. Longman Inc., New York. Williams, J., Prebble, R.E., Williams, W.T., and Hignett, C.T The influence of texture, structure and clay mineralogy on the soil moisture characteristic. Australian Journal of Soil Research. 21: Appendix: nonlinear curve-fitting algorithms for the soil-water characteristic curve The proposed equation for the soil-water characteristic curve is Let p = (a, n, m) denote the unknown vector of the three parameters a, n, and m and suppose that measured data (0,, (J~) (i = l, 2,..., M) are available, M is the number of measurements. The leastsquares estimate of p is the vector p:" which minimizes the following objective function (i.e., sum of the squared deviations of the measured data from the calculated data). [A21 0(p)= 0(a,m,n)=~[8~-0(\$~, a,m,n)12 M i=l In other words, the least-squares method determines the three parameters such that the calculated values from [All are as close as possible to the measured values. A standard requirement of iterative minimization algorithms is that the value of the objective function decreases monotonically from iteration to iteration. Let pi be the estimate of p at the beginning of the ith iteration (po is the initial guess and, theoretically, it is arbitrary). The new estimate pi+, is chosen such that

11 FREDLUND AND XING O(p,,,) < O(p,). The steepest descent method is one of the easiest methods for mirhnizing' a general nonlinear function of several variables. It exploits the fact that from a given starting point a function decreases most rapidly in the direction of the negative gradient vector evaluated at the starting point. Let g denote the gradient of O(p) at p,. That is, The steepest descent iteration is defined by a is a scalar that determines the length of the step taken in the direction of -g. From [A21 it follows that Similarly, From [All, the partial derivatives in [A5]-[A71 can be obtained as follows: The steepest descent method is not efficient for practical use, since the rate of convergence is slow, especially near the stationary point. The following quasi-newton method (Sadler 1975) was used for the curvefitting program: : g, is the gradient of the objective function evaluated at pi, and A, is the operative matrix at the ith iteration. Equation [A1 1] becomes the steepest descent method if Ai is the identity matrix multiplied by a step length (a scalar). Denote pi+, - pi by di and g,,, - g, by q,. Then Ai is updated using the following formula: the superscript T denotes the transpose of a vector matrix. A suitable choice for A, is the diagonal matrix defined by : ai is the ith element of the starting vector p,, p, is the ith element of the gradient go evaluated at the starting vector. The quasi-newton method does not require matrix inversion or equivalent, since the sequence Ai (i = 0,

12 CAN GEOTECH J VOL 31, , 2,...) converges to the inverse Hessian. In practice, the objective function is oftkn app;oximately quadratic near the minimum, so a second-order convergence can be eventually expected. However, th&e is no guarantee that A, remain positive definite, even for a quadratic function. The product g?d, should be checked and dl replaced by its negative, if gltd1 > 0. Numerical difficulties may also arise when the scalar product (dl- A,qJTq, is very small, resulting in unduly large elements in A,,,. One of several possible strategies is to reinitialize A,,, if the cosine of the angle between (dl- A,q,) and q, is less than For a nonquadratic objective function it is reasonable to adjust the step length so that the objective function is reduced at each iteration. b

### INTERPRETATION OF THE SHEAR STRENGTH OF UNSATURATED SOILS IN UNDRAINED LOADING CONDITIONS

INTERPRETATION OF THE SHEAR STRENGTH OF UNSATURATED SOILS IN UNDRAINED LOADING CONDITIONS S.K. Vanapalli, D.E. Pufahl, and D.G. Fredlund Department of Civil Engineering, University of Saskatchewan, Saskatoon,

### Soil Mechanics for Unsaturated Soils

Soil Mechanics for Unsaturated Soils Delwyn G. Fredlund University of Saskatchewan Saskatoon, Sask., Canada and Harianto Rahardjo Nanyang Technological University Singapore John Wiley & Sons Notes by:

### Interpretation of soil-water characteristic curves when volume change occurs as soil suction is changed

Advances in Unsaturated Soils Caicedo et al. (eds) 2013 Taylor & Francis Group, London, ISBN 978-0-415-62095-6 Interpretation of soil-water characteristic curves when volume change occurs as soil suction

### Volume Change Consideration in Determining Appropriate. Unsaturated Soil Properties for Geotechnical Applications.

Volume Change Consideration in Determining Appropriate Unsaturated Soil Properties for Geotechnical Applications by Elham Bani Hashem A Dissertation Presented in Partial Fulfillment of the Requirements

### Poisson s ratio effect of slope stability calculations

Poisson s ratio effect of slope stability calculations Murray Fredlund, & Robert Thode SoilVision Systems Ltd., Saskatoon, SK, Canada ABSTRACT This paper presents the results of a study on the effect of

### The 1999 R.M. Hardy Lecture: The implementation of unsaturated soil mechanics into geotechnical engineering

The 1999 R.M. Hardy Lecture: The implementation of unsaturated soil mechanics into geotechnical engineering Delwyn G. Fredlund 963 Abstract: The implementation of unsaturated soil mechanics into geotechnical

### STUDY OF THE BARCELONA BASIC MODEL. INFLUENCE OF SUCTION ON SHEAR STRENGTH

STUDY OF TH BARCLONA BASIC MODL. INFLUNC OF SUCTION ON SHAR STRNGTH Carlos Pereira ABSTRACT The Barcelona Basic Model, BBM, is one of the most used elasto-plastic models for unsaturated soils. This summary

### CPT Data Interpretation Theory Manual

CPT Data Interpretation Theory Manual 2016 Rocscience Inc. Table of Contents 1 Introduction... 3 2 Soil Parameter Interpretation... 5 3 Soil Profiling... 11 3.1 Non-Normalized SBT Charts... 11 3.2 Normalized

### Experiment and Modeling of Soil-Water Characteristic Curve of Unsaturated Soil in Collapsing Erosion Area

Pol. J. Environ. Stud. Vol. 25, No. 6 (2016), 2509-2517 DOI: 10.15244/pjoes/64307 Original Research Experiment and Modeling of Soil-Water Characteristic Curve of Unsaturated Soil in Collapsing Erosion

### Slope Stability Model of the Questa Rock Pile Phase 2

2 Proceedings Tailings and Mine Waste 2011 Slope Stability Model of the Questa Rock Pile Phase 2 Murray Fredlund SoilVision Systems Ltd., Saskatoon, Canada Haihua Lu SoilVision Systems Ltd., Saskatoon,

### Outline. In Situ Stresses. Soil Mechanics. Stresses in Saturated Soil. Seepage Force Capillary Force. Without seepage Upward seepage Downward seepage

Soil Mechanics In Situ Stresses Chih-Ping Lin National Chiao Tung Univ. cplin@mail.nctu.edu.tw Outline Without seepage Upward seepage Downward seepage Seepage Force The total stress at the elevation of

### In all of the following equations, is the coefficient of permeability in the x direction, and is the hydraulic head.

Groundwater Seepage 1 Groundwater Seepage Simplified Steady State Fluid Flow The finite element method can be used to model both steady state and transient groundwater flow, and it has been used to incorporate

### Durham Research Online

Durham Research Online Deposited in DRO: 3 May 28 Version of attached le: Published Version Peer-review status of attached le: Peer-reviewed Citation for published item: Toll, D. G. and Ong, B. H. (23)

### Analysis of Transient Seepage Through Levees

Analysis of Transient Seepage Through Levees Matthew David Sleep Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements

### C. Lanni(1), E. Cordano(1), R. Rigon(1), A. Tarantino(2)

Landslide Processes: from geomorphologic mapping to dynamic modelling (6-7 February, 2009 - Strasbourg, France) A tribute to Prof. Dr. Theo van Asch C. Lanni(1), E. Cordano(1), R. Rigon(1), A. Tarantino(2)

### Chapter 7 Permeability and Seepage

Permeability and Seepage - N. Sivakugan (2005) 1 7.1 INTRODUCTION Chapter 7 Permeability and Seepage Permeability, as the name implies (ability to permeate), is a measure of how easily a fluid can flow

### SOIL MOISTURE CONTENT AND EVAPOTRANSPIRATION

SOL MOSTURE CONTENT AND EVAPOTRANSPRATON W.C. VSSER nstitute for Land and Water Management Research, Wageningen, the Netherlands SUMMARY The moisture content at which the évapotranspiration decreases with

### STABILITY OF RESIDUAL SOIL SLOPES BASED ON SPATIAL DISTRIBUTION OF SOIL PROPERTIES. Harianto Rahardjo*, Alfrendo Satyanaga

STABILITY OF RESIDUAL SOIL SLOPES BASED ON SPATIAL DISTRIBUTION OF SOIL PROPERTIES Harianto Rahardjo*, Alfrendo Satyanaga * Professor, School of Civil and Environmental Engineering, Nanyang Technological

### Computer-Aided Data for Machinery Foundation Analysis and Design. Galal A. Hassaan*, Maha M. Lashin** and Mohammed A. Al-Gamil***

Computer-Aided Data for Machinery Foundation Analysis and Design Galal A. Hassaan*, Maha M. Lashin** and Mohammed A. Al-Gamil*** * Mechanical Design & Production Department, Faculty of Engineering, Cairo

### Seepage. c ZACE Services Ltd. August 2011

Seepage c ZACE Services Ltd August 2011 1 / 50 2 / 50 Seepage analysis for fully/partially saturated media 1 Steady state v F k,k = 0 2 Transient v F k,k c p = 0 Darcy velocity v F i = k ij k r (S) ( p

### Drained Against Undrained Behaviour of Sand

Archives of Hydro-Engineering and Environmental Mechanics Vol. 54 (2007), No. 3, pp. 207 222 IBW PAN, ISSN 1231 3726 Drained Against Undrained Behaviour of Sand Andrzej Sawicki, Waldemar Świdziński Institute

### Chapter 6 Effective Stresses and Capillary

Effectie Stresses and Capillary - N. Siakugan (2004) 1 6.1 INTRODUCTION Chapter 6 Effectie Stresses and Capillary When soils are subjected to external loads due to buildings, embankments or excaations,

### SOME OBSERVATIONS RELATED TO LIQUEFACTION SUSCEPTIBILITY OF SILTY SOILS

SOME OBSERVATIONS RELATED TO LIQUEFACTION SUSCEPTIBILITY OF SILTY SOILS Upul ATUKORALA 1, Dharma WIJEWICKREME 2 And Norman MCCAMMON 3 SUMMARY The liquefaction susceptibility of silty soils has not received

### A MODEL TO PREDICT THE UNSATURATED HYDRAULIC CONDUCTIVITY FROM BASIC SOIL PROPERTIES

57ième CONGRÈS CANADIEN DE GÉOTECHNIQUE 5ième CONGRÈS CONJOINT SCG/AIH-CNN 57TH CANADIAN GEOTECHNICAL CONFERENCE 5TH JOINT CGS/IAH-CNC CONFERENCE A MODEL TO PREDICT THE UNSATURATED HYDRAULIC CONDUCTIVITY

### Darcy s Law, Richards Equation, and Green-Ampt Equation

Darcy s Law, Richards Equation, and Green-Ampt Equation 1. Darcy s Law Fluid potential: in classic hydraulics, the fluid potential M is stated in terms of Bernoulli Equation (1.1) P, pressure, [F L!2 ]

Instructor : Dr. Jehad Hamad Chapter (7) 2017-2016 Soil Properties Physical Properties Mechanical Properties Gradation and Structure Compressibility Soil-Water Relationships Shear Strength Bearing Capacity

### Correlation Between Resistivity Index, Capillary Pressure and Relative Permeability

Proceedings World Geothermal Congress 2010 Bali, Indonesia, 25-29 April 2010 Correlation Between Resistivity Index, Capillary Pressure and Kewen Li Stanford Geothermal Program, Stanford University, Stanford,

### Seismic Stability of Tailings Dams, an Overview

Seismic Stability of Tailings Dams, an Overview BY Gonzalo Castro, Ph.D., P.E. Principal International Workshop on Seismic Stability of Tailings Dams Case Western Reserve University, November 2003 Small

### CHAPTER 2. SOIL-WATER POTENTIAL: CONCEPTS AND MEASUREMENT

SSC107 Fall 2000 Chapter 2, Page - 1 - CHAPTER 2. SOIL-WATER POTENTIAL: CONCEPTS AND MEASUREMENT Contents: Transport mechanisms Water properties Definition of soil-water potential Measurement of soil-water

### Transient Analysis on Infiltration and Stability for Unsaturated Soils in Busan Landslide Area

Transient Analysis on Infiltration and Stability for Unsaturated Soils in Busan Landslide Area FAUZI ACHMAD ZAKY, SEBOONG OH Department of Civil Engineering Yeungnam University 8 Daehak-Ro, Gyeongsan,

### A METHOD FOR MEASURING SMOOTH GEOMEMBRANE / SOIL INTERFACE SHEAR BEHAVIOUR UNDER UNSATURATED CONDITIONS

A METHOD FOR MEASURING SMOOTH GEOMEMBRANE / SOIL INTERFACE SHEAR BEHAVIOUR UNDER UNSATURATED CONDITIONS A thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the

### Farimah MASROURI. Professor in Geotechnical Engineering. LAEGO : Research Center In Geomechanics & Geoenvironmental Engineering

Farimah MASROURI Professor in Geotechnical Engineering LAEGO : Research Center In Geomechanics & Geoenvironmental Engineering Nancy Université France http://www.laego.org 1/29 Nancy 90 min by TGV Paris

### Geotechnical Properties of Soil

Geotechnical Properties of Soil 1 Soil Texture Particle size, shape and size distribution Coarse-textured (Gravel, Sand) Fine-textured (Silt, Clay) Visibility by the naked eye (0.05 mm is the approximate

### Studies of rainfall-induced slope failures

Invited Lecture. National Seminar Slope 2000, 27 April 2002, Bandung, Indonesia. In Paulus P Rahardjo (edt.) Slope 2002. Proceedings of the National Seminar, Slope 2002. 27-April 2002. Bandung, Indonesia.

### Bilinear Modelling of Cellulosic Orthotropic Nonlinear Materials

Bilinear Modelling of Cellulosic Orthotropic Nonlinear Materials E.P. SALIKLIS, T.J. URBANIK and B. TOKYAY The proposed method of modelling orthotropic solids that have a nonlinear constitutive material

### Durham Research Online

Durham Research Online Deposited in DRO: 08 June 2017 Version of attached le: Accepted Version Peer-review status of attached le: Peer-reviewed Citation for published item: Toll, D. G. and Ali Rahman,

### Geotechnical Testing Journal Subject Index Volume 19, 1996

Geotechnical Testing Journal Subject Index Volume 19, 1996 A-B Adsorption isotherm Discussion on "Geo-environmental assessment of a micaceous soil for its potential use as an engineered clay barrier" by

### COMPARING SLOPE STABILITY ANALYSIS BASED ON LINEAR ELASTIC OR ELASTO PLASTIC STRESSES USING DYNAMIC PROGRAMMING TECHNIQUES

57ième CONGRÈS CANADIEN DE GÉOTECHNIQUE 5ième CONGRÈS CONJOINT SCG/AIH-CNN 57TH CANADIAN GEOTECHNICAL CONFERENCE 5TH JOINT CGS/IAH-CNC CONFERENCE COMPARING SLOPE STABILITY ANALYSIS BASED ON LINEAR ELASTIC

### Interslice force functions for computing active and passive earth force

1015 Interslice force functions for computing active and passive earth force Noshin Zakerzadeh, D.G. Fredlund, and D.E. Pufahl Abstract: Recent methods to calculate the lateral earth force on a retaining

### 2nd International Conference Mechanics of Unsaturated Soils 7 th 9 th March 2007

2nd International Conference Determination of the Soil Water Retention Curve and the Unsaturated Hydraulic Conductivity from the Particle Size Distribution Alexander Scheuermann & Andreas Bieberstein Motivation

### INFERRING RELATIVE PERMEABILITY FROM RESISTIVITY WELL LOGGING

PROCEEDINGS, Thirtieth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 3-February 2, 25 SGP-TR-76 INFERRING RELATIVE PERMEABILITY FROM RESISTIVITY WELL LOGGING

### Impact of Effective Stress on the Dynamic Shear Modulus of Unsaturated Sand

Impact of Effective Stress on the Dynamic Shear Modulus of Unsaturated Sand Ali Khosravi 1, Majid Ghayoomi 1, John McCartney 2, Hon-Yim Ko 3 1 Graduate Research Assistants, University of Colorado at Boulder,

### METHODOLOGY FOR DRENABILITY STUDIES OF STACKED MINING COARSE TAILINGS

MEHODOLOGY FOR DRENABILIY SUDIES OF SACKED MINING COARSE AILINGS J. C. Machado Júnior Departamento de Engenharia Civil, Universidade Federal de Ouro Preto W. L. Oliveira Filho Departamento de Engenharia

### Numerical analysis for an interpretation of the pressuremeter test in cohesive soil

Numerical analysis for an interpretation of the pressuremeter test in cohesive soil J. Monnet Joseph Fourier University L3S-R Domaine Universitaire, BP n 53, 3841, Grenoble, Cedex 9, France jmonnet@ujf-grenoble.fr

### The Casagrande plasticity chart does it help or hinder the NZGS soil classification process?

Hind, K.J. (2017) The Casagrande plasticity chart does it help or hinder the NZGS soil classification process? Proc. 20 th NZGS Geotechnical Symposium. Eds. GJ Alexander & CY Chin, Napier The Casagrande

### Can we distinguish Richards and Boussinesq s equations for hillslopes?: The Coweeta experiment revisited

WATER RESOURCES RESEARCH, VOL. 35, NO. 2, PAGES 589 593, FEBRUARY 1999 Can we distinguish Richards and Boussinesq s equations for hillslopes?: The Coweeta experiment revisited T. S. Steenhuis, 1 J.-Y.

### Use of CPT for design, monitoring, and performance verification of compaction projects

Cone Stress, q t (MPa) 2 3 Sleeve Friction (KPa) 2 4 Pore Pressure (KPa) 2 7, Friction Ratio (%) 2 3 4 Profile Mixed Y 2 2 2 2 CLAY 3 3 3 3 4 4 4 4 SAN D Use of CPT for design, monitoring, and performance

### MOISTURE PERMEABILITY DATA PRESENTED AS A MATHEMATICAL FUNCTION APPLICABLE TO HEAT AND MOISTURE TRANSPORT MODELS

MOISTURE PERMEABILITY DATA PRESENTED AS A MATHEMATICAL FUNCTION APPLICABLE TO HEAT AND MOISTURE TRANSPORT MODELS Dr. Graham H. Galbraith Glasgow Caledonian University Mr. R. Craig McLean The University

### Soil strength. the strength depends on the applied stress. water pressures are required

Soil Strength Soil strength u Soils are essentially frictional materials the strength depends on the applied stress u Strength is controlled by effective stresses water pressures are required u Soil strength

### Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

56 Module 4: Lecture 7 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-Coulomb failure

### Estimation of the Pre-Consolidation Pressure in Soils Using ANN method

Current World Environment Vol. 11(Special Issue 1), 83-88 (2016) Estimation of the Pre-Consolidation Pressure in Soils Using ANN method M. R. Motahari Department of Civil Engineering, Faculty of Engineering,

### DETERMINATION OF COEFFICIENTS OF INFILTRATION EQUATIONS

DETERMINATION OF COEFFICIENTS OF INFILTRATION EQUATIONS Wender Lin Research Engineer ~nvironment Alberta Edmonton, Alberta T5J OZ6 and Don M. Gray Chairman, Division of Hydrology College of Engineering

### Liquefaction potential of Rotorua soils

Pearse-Danker, E. (2013) Liquefaction potential of Rotorua soils Proc. 19 th NZGS Geotechnical Symposium. Ed. CY Chin, Queenstown Liquefaction potential of Rotorua soils E Pearse-Danker Coffey Geotechnics

### Soil Mechanics Permeability of Soils and Seepage page 1 CHAPITRE 9. PERMEABILITY OF SOILS AND SEEPAGE...1

Soil Mechanics Permeability of Soils and Seepage page 1 Contents of this chapter : CHAPITRE 9. PERMEABILITY OF SOILS AND SEEPAGE...1 9.1 INTRODUCTION...1 9.2 DARCY S LAW...1 9.2.1 DEFINITION OF HEAD...1

### Chapter (5) Allowable Bearing Capacity and Settlement

Chapter (5) Allowable Bearing Capacity and Settlement Introduction As we discussed previously in Chapter 3, foundations should be designed for both shear failure and allowable settlement. So the allowable

### Module 2 Lecture 9 Permeability and Seepage -5 Topics

Module 2 Lecture 9 Permeability and Seepage -5 Topics 1.2.7 Numerical Analysis of Seepage 1.2.8 Seepage Force per Unit Volume of Soil Mass 1.2.9 Safety of Hydraulic Structures against Piping 1.2.10 Calculation

### Field measurement of shear wave velocity of soils

GeoEdmonton08/GéoEdmonton2008 Field measurement of shear wave velocity of soils Fanyu Zhu, K.R. Peaker and Shaheen Ahmad Shaheen and Peaker Limited, Toronto, Ontario, Canada ABSTRACT In this study, S-wave

### The Role of Slope Geometry on Flowslide Occurrence

American Journal of Environmental Sciences 3 (3): 93-97, 27 ISSN 1553-345X 27 Science Publications Corresponding Author: The Role of Slope Geometry on Flowslide Occurrence Chiara Deangeli DITAG, Politecnico

### 7. STRESS ANALYSIS AND STRESS PATHS

7-1 7. STRESS ANALYSIS AND STRESS PATHS 7.1 THE MOHR CIRCLE The discussions in Chapters and 5 were largely concerned with vertical stresses. A more detailed examination of soil behaviour requires a knowledge

### Large-Strain 1D, 2D, and 3D Consolidation Modeling of Mine Tailings

Large-Strain 1D, 2D, and 3D Consolidation Modeling of Mine Tailings M.D. Fredlund and M. Donaldson SoilVision Systems Ltd., Saskatoon, SK, Canada G.G. Gitirana Praca Universitaria, Goiania, GO, Brazil

### Soil type identification and fines content estimation using the Screw Driving Sounding (SDS) data

Mirjafari, S.Y. & Orense, R.P. & Suemasa, N. () Proc. th NZGS Geotechnical Symposium. Eds. GJ Alexander & CY Chin, Napier Soil type identification and fines content estimation using the Screw Driving Sounding

### Soil-Water Characteristics of Huai-an Expensive Soil

20 2 2014 4 JOURNAL OF SHANGHAI UNIVERSITY (NATURAL SCIENCE) Vol. 20 No. 2 Apr. 2014 DOI: 10.3969/j.issn.1007-2861.2013.07.007, (, 200072) :, 3,, 0 378 MPa.,,, 100 MPa, ;., 1 000 MPa.,,, ;,. : ; ; ; ;

### Seepage Analysis for Shurijeh Reservoir Dam Using Finite Element Method. S. Soleymani 1, A. Akhtarpur 2

Seepage Analysis for Shurijeh Reservoir Dam Using Finite Element Method S. Soleymani 1, A. Akhtarpur 2 1 Group of Dam Construction, Toossab Company, P.O. Box 917751569, Mashhad City, Iran, PH (+98) 511-7684091;

### APPROPRIATE PARAMETERS FOR PREDICTION OF SWELLING PRESSURE OF EXPANSIVE CLAYS

Appropriate IGC 009, Guntur, Parameters INDIA for Prediction of Swelling Pressure of Expansive Clays APPROPRIATE PARAMETERS FOR PREDICTION OF SWELLING PRESSURE OF EXPANSIVE CLAYS Sudha Rani Associate Professor,

### Flood Forecasting Tools for Ungauged Streams in Alberta: Status and Lessons from the Flood of 2013

Flood Forecasting Tools for Ungauged Streams in Alberta: Status and Lessons from the Flood of 2013 John Pomeroy, Xing Fang, Kevin Shook, Tom Brown Centre for Hydrology, University of Saskatchewan, Saskatoon

### Course Scheme -UCE501: SOIL MECHANICS L T P Cr

Course Scheme -UCE501: SOIL MECHANICS L T P Cr 3 1 2 4.5 Course Objective: To expose the students about the various index and engineering properties of soil. Introduction: Soil formation, various soil

6 th International Conference on Earthquake Geotechnical Engineering 1-4 November 015 Christchurch, New Zealand Unloading-Reloading Rule for Nonlinear Site Response Analysis S. Yniesta 1, S. J. Brandenberg

### APPENDIX F CORRELATION EQUATIONS. F 1 In-Situ Tests

APPENDIX F 1 APPENDIX F CORRELATION EQUATIONS F 1 In-Situ Tests 1. SPT (1) Sand (Hatanaka and Uchida, 1996), = effective vertical stress = effective friction angle = atmosphere pressure (Shmertmann, 1975)

### Sensitivity Analysis of the Effective Parameters with Respect to Cantilever Type Failure in Composite Riverbanks

Sensitivity Analysis of the Effective Parameters with Respect to Cantilever Type Failure in Composite Riverbanks A. Samadi 1, E. Amiri-Tokaldany 2, and M. H. Davoudi 3 1 Ph.D. Candidate, Department of

### Unified Model for Small-Strain Shear Modulus of Variably Saturated Soil

Unified Model for Small-Strain Shear Modulus of Variably Saturated Soil Yi Dong, A.M.ASCE 1 ; Ning Lu, F.ASCE 2 ; John S. McCartney, Ph.D., P.E., M.ASCE 3 Downloaded from ascelibrary.org by Colorado School

### Back Analysis of the Lower San Fernando Dam Slide Using a Multi-block Model

Proceedings Geohazards Engineering Conferences International Year 2006 Back Analysis of the Lower San Fernando Dam Slide Using a Multi-block Model C. A. Stamatopoulos P. Petridis Stamatopoulos and Associates

### Validation of empirical formulas to derive model parameters for sands

Validation of empirical formulas to derive model parameters for sands R.B.J. Brinkgreve Geo-Engineering Section, Delft University of Technology, Delft, Netherlands/Plaxis B.V., Delft, Netherlands E. Engin

### WMS 9.0 Tutorial GSSHA Modeling Basics Infiltration Learn how to add infiltration to your GSSHA model

v. 9.0 WMS 9.0 Tutorial GSSHA Modeling Basics Infiltration Learn how to add infiltration to your GSSHA model Objectives This workshop builds on the model developed in the previous workshop and shows you

### SOME GEOTECHNICAL PROPERTIES OF KLANG CLAY

SOME GEOTECHNICAL PROPERTIES OF KLANG CLAY Y.C. Tan, S.S. Gue, H.B. Ng 3, P.T. Lee 4 ABSTRACT A series of subsurface investigation including in-situ and laboratory tests has been carefully planned and

### Numerical analysis of slope stability in expansive soil: a case study of field test in Henan province, China

Numerical analysis of slope stability in expansive soil: a case study of field test in Henan province, China Shunchao Qi & Sai K. Vanapalli Department of Civil Engineering University of Ottawa, Ottawa,

### Consolidation Properties of NAPL Contaminated Sediments

Consolidation Properties of NAPL Contaminated Sediments M. B. Erten 1, C. S. El Mohtar 2, D. D. Reible 3, R. B. Gilbert 4 1 Graduate Research Assistant, University of Texas at Austin, 1 University Station

### Shear Strength of Soils

Shear Strength of Soils Soil strength Most of problems in soil engineering (foundations, slopes, etc.) soil withstands shear stresses. Shear strength of a soil is defined as the capacity to resist shear

### Dynamic Landslide Warning from Rainfall and Soil Suction Measurement

Dynamic Landslide Warning from Rainfall and Soil Suction Measurement Warakorn Mairaing Associate Professor, Civil Engineering Department, Kasetsart University, Jatuchak, Bangkok, Thailand Santi Thaiyuenwong

### CHARACTERISTICS OF LIQUEFIED SILTY SANDS FROM MEIZOSEISMAL REGION OF SHILLONG PLATEAU, ASSAM AND BHUJ IN INDIA

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 2375 CHARACTERISTICS OF LIQUEFIED SILTY SANDS FROM MEIZOSEISMAL REGION OF SHILLONG PLATEAU, ASSAM AND BHUJ

### Engineering Geology (2012) Contents lists available at SciVerse ScienceDirect. Engineering Geology

Engineering Geology 141 142 (2012) 45 56 Contents lists available at SciVerse ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo Experimental evaluation of mechanical behavior

### 12 SWAT USER S MANUAL, VERSION 98.1

12 SWAT USER S MANUAL, VERSION 98.1 CANOPY STORAGE. Canopy storage is the water intercepted by vegetative surfaces (the canopy) where it is held and made available for evaporation. When using the curve

### Properties of Derivatives

6 CHAPTER Properties of Derivatives To investigate derivatives using first principles, we will look at the slope of f ( ) = at the point P (,9 ). Let Q1, Q, Q, Q4, be a sequence of points on the curve

### Energy Method for Predicting Installation Torque of Helical Foundations and Anchors

Revised August 10, 2001. Original published in New Technological and Design Developments in Deep Foundations, Proceedings of GeoDenver 2000, Norman D. Dennis, Jr., Ray Castelli, and Michael W. O Neill,

### NEW DOWN-HOLE PENETROMETER (DHP-CIGMAT) FOR CONSTRUCTION APPLICATIONS

NEW DOWN-HOLE PENETROMETER (DHP-CIGMAT) FOR CONSTRUCTION APPLICATIONS 1 2 C. Vipulanandan 1, Ph.D., M. ASCE and Omer F. Usluogullari 2 Chairman, Professor, Director of Center for Innovative Grouting Materials

### Date: April 2, 2014 Project No.: Prepared For: Mr. Adam Kates CLASSIC COMMUNITIES 1068 E. Meadow Circle Palo Alto, California 94303

City of Newark - 36120 Ruschin Drive Project Draft Initial Study/Mitigated Negative Declaration Appendix C: Geologic Information FirstCarbon Solutions H:\Client (PN-JN)\4554\45540001\ISMND\45540001 36120

### 3. The map below shows an eastern portion of North America. Points A and B represent locations on the eastern shoreline.

1. Most tornadoes in the Northern Hemisphere are best described as violently rotating columns of air surrounded by A) clockwise surface winds moving toward the columns B) clockwise surface winds moving

### PRESSURES RECORDED DURING LABORATORY FREEZING AND THAWING OF A NATURAL SILT-RICH SOIL

PRESSURES RECORDED DURING LABORATORY FREEZING AND THAWING OF A NATURAL SILT-RICH SOIL Charles Harris 1, Michael C.R. Davies 2 1. Department of Earth Sciences, Cardiff University, P.O. Box 914, Cardiff

### Fundamentals of Engineering (FE) Exam Mathematics Review

Fundamentals of Engineering (FE) Exam Mathematics Review Dr. Garey Fox Professor and Buchanan Endowed Chair Biosystems and Agricultural Engineering October 16, 2014 Reference Material from FE Review Instructor

### Earth dam steady state seepage analysis

Engineering manual No. 32 Updated 3/2018 Earth dam steady state seepage analysis Program: FEM Water Flow File: Demo_manual_32.gmk Introduction This example illustrates an application of the GEO5 FEM module

### STUDY ON CONSOLIDATION OF ALLUVIAL CLAY IN NORTHERN QUEENSLAND

STUDY ON CONSOLIDATION OF ALLUVIAL CLAY IN NORTHERN QUEENSLAND Barry Wai Choo, Kok Geotechnical Services Manager, Abigroup Australia Dr. Richard Gong Senior Geotechnical Engineer, AECOM Australia ABSTRACT

### CPTu in Consolidating Soils PAULUS P. RAHARDJO. PROFESSOR OF GEOTECNICAL ENGINEERING, UNIVERSITAS KATOLIK PARAHYANGAN - INDONESIA

CPTu in Consolidating Soils PAULUS P. RAHARDJO. PROFESSOR OF GEOTECNICAL ENGINEERING, UNIVERSITAS KATOLIK PARAHYANGAN - INDONESIA Outline of Presentation 1. Background of Study 2. CPTu and its interpretation

### An application of nested Newton-type algorithm for finite difference method solving Richards' equation

IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn:239-765x. Volume, Issue Ver. II. (Feb. 24), PP 2-32 An application of nested Newton-type algorithm for finite dference method solving Richards'

### The Conjugate Gradient Method for Solving Linear Systems of Equations

The Conjugate Gradient Method for Solving Linear Systems of Equations Mike Rambo Mentor: Hans de Moor May 2016 Department of Mathematics, Saint Mary s College of California Contents 1 Introduction 2 2

### Module 1 GEOTECHNICAL PROPERTIES OF SOIL AND OF REINFORCED SOIL (Lectures 1 to 4)

Module 1 GEOTECHNICAL PROPERTIES OF SOIL AND OF REINFORCED SOIL (Lectures 1 to 4) Topics 1.1 INTRODUCTION 1.2 GRAIN-SIZE DISTRIBUTION Sieve Analysis Hydrometer Analysis 1.3 SIZE LIMITS FOR SOILS 1.4 WEIGHT-VOLUME

### Centrifuge Evaluation of the Impact of Partial Saturation on the Amplification of Peak Ground Acceleration in Soil Layers

Centrifuge Evaluation of the Impact of Partial Saturation on the Amplification of Peak Ground Acceleration in Soil Layers M. Ghayoomi, Ph.D. A.M.ASCE 1, and J.S. McCartney, Ph.D., P.E., M.ASCE 2 1 Research

### Effects of Soil Heterogeneity on One-Dimensional Infiltration

Utah State University DigitalCommons@USU Reports Utah Water Research Laboratory January 1977 Effects of Soil Heterogeneity on One-Dimensional Infiltration Charles Courette Roland W. Jeppson Follow this

### Recent Advances in Profile Soil Moisture Retrieval

Recent Advances in Profile Soil Moisture Retrieval Jeffrey P. Walker, Garry R. Willgoose and Jetse D. Kalma Department of Civil, Surveying and Environmental Engineering The University of Newcastle, Callaghan,