Soil Mechanics for Unsaturated Soils phần 5 pptx

8.3 SOLUTIONS OF THE PORE PRESSURE EQUATIONS AND COMPARISONS 21 1 Ngure 8.34 The development of pore pressures and pore pressure parameters for a more com- pressible soil. (a) Development of pore-air and pore-water pressures; @) pore pressure parame- ters. 212 8 PORE PRESSURE PARAMETERS - rnt (assumed)= 1.21 x (l/kPa) Rs = 0.7 Re = 0 1 1 1 1 I Q1 6 E 0 c 9 1 .o 0.9 0.8 0.7 0.6 0.5 A -Pore-air pressure measurements from -Predicted oore-oressure in accordance Gibbs (1 963) with Hilf's analisis 1 0.9 0.8 a, 0 E 0.7 - 8 0.6 0.5 -500 -400 -300 -200 -100 0 100 200 300 400 500 Pore pressures, u (kPa) (a) 60 s 70 C c E 3 2 - 80 a 0) 90 O" 100 .~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pore pressure parameters (b) Figure 8.35 Comparison of theoretical predictions and laboratory measurements of pore-water pressures under undrained loading conditions. (a) Development of pore-air and pore-water pres- sures; @) pore pressure panmeters. 8.3 SOLUTIONS OF THE PORE PRESSURE EQUATIONS AND COMPARISONS 213 0 200 400 goo 800 Isotropic pressure, (I, (kPa) Figure 8.36 Comparison of theoretical computations and laboratory measurements of pore-air and pore-water pressures (data from Bishop and Henkel, 1962). A comparison of the theoretically computed pore pres- sures and pore-water pressure measurements (Gibbs, 1963) is presented in Fig. 8.35. Coefficients of volume change (i.e., mi and rnl) must be assumed in order to compute the tangent B, and B, pore pressure parameters. The coeffi- cients are also assumed to be constant during the undrained loading process. The assumption of constant coefficients of volume change may contribute to deviations between the measured and predicted pore-water pressures. In general, the soil compressibility will decrease as the total stress in- creases. The predicted pore-air pressure from Eq. (8.83) is in good agreement with predictions using Hilf s analysis [Le., Eq. (8.65)]. The agreement between Hilfs analysis and the more rigorous equations is the result of setting the parameter R, (i.e., ~/rny) to zero. This assumption means that the volume change associated with the air phase does not depend on the matric suction change, but only on the total stress change. This, in essence, is the assumption in- volved in Hilfs analysis. This agreement may not occur when the parameter R, is not zero. The tangent B, and B, parameters increase to unity as saturation is approached, while the secant B: and BL pa- rameters approach a value of 0.7 [Fig. 8.35@)]. The secant B: pore pressure parameter using the marching-forward Table 8.3 CoefRcients of Volume Change used in the Theoretical Computations of Pore Pressures on Test Data Presented by Bishop and Henkel(1962) Test No. Coefficients of Volume Change No. 1 u3 c 70 kPa (#la) u3 > 70kPa(#lb) Soil structure, my 4.0 x 10-~ 2.9 x 10-5 Air phase, my 2.6 x 2.9 x 10-~ No. 2 u3 c 140 kPa (#2a) u3 > 140 kPa (#2b) Soil stmcture, mf 1.0 x 10-4 2.6 x 10-5 Air phase, my 8.7 x 10-~ 2.6 x 10-5 214 8 WRE PRESSURE PARAMETERS 700 600 500 - 400 - 2 f 300 ; 200 In Y) Y) 100 0 -100 68 0 2 4 AV VO Volume change,- (%) (a) 0 100 200 300 400 500 600 Isotropic pressure, us (kPa) (b) I I I I 0 100 200 300 400 500 600 (C) 1 501 I Deviator stress, (a, - as) (kPa) Figure 8.37 Pore pressure development during undrained triax- ial test no. 1. (a) Stress-strain behavior during an undrained, triaxial test (from Knodel and Coffey, 1966); (b) B, and B, pore pressure parameters; (c) D, and D, pore pressure parameters. technique is slightly different from the secant BA,, pore pressure parameter obtained from Hilf s analysis. The dif- ference could be attributed to the assumption of zero matric suction in Hilf s analysis. Measurements of pore-air and pore-water pressures for 600 500 -400 I 300 f 200 100 0 -100 ?.! a 2 4 6 8 AV Volume change,- VO (%I (a) a I 1 I I 100 200 300 400 Isotropic pressure, US (kPa) (b) -100; ! I I -50!l 100 2;)o 3bo 4k 5bo 6k Deviator stress, (a, - a,) (kPa) (C) Figure 8.38 Pore pressure development during undrained triax- ial test no. 2. (a) Stress-strain behavior during an undrained, triaxial test (from Knodel and Coffey, 1966); (b) B, and B,,, pore pressure parameters; (c) D, and D, core pressure parameters. two unsaturated soils under isotropic, undrained loading have been presented by Bishop and Henkel(l962) and are shown in Fig. 8.36. The theoretical predictions of the pore- air and pore-water pressures can be made using varying coefficients of volume change, as outlined in Table 8.3. As 8.3 SOLUTIONS OF THE PORE PRESSURE EQUATIONS AND COMPARISONS 215 AV VO Volume change,-(%) (a) Isotropic pressure, u3 (kPa) (b) '-0 100 200 300 400 500 600 Deviator stress, ((11 - US) (kPe) (C) Figure 8.39 Pore pressure development during undrained triax- ial test eo. 3. (a) Stress-strain behavior during an undrained, triaxial test (from Knadel and Coffey, 1%); (b) B, and B, pore pressure parameters; (c) D, and D, pore pressure parameters. the isotropic pressure is increased, the soil compressibility is decreased. The results indicate that the theoretical com- putations better predict the measured pore pressures when the coefficients of volume change are varied during load- ing. Evidence indicates that the assessment of the coeffi- 150 1 1 I I I I 22 0 22 0 0 50 100 150 200 250 Net isotropic pressure, (a, - u.) (kPa) (a) 0.10 I I I I 0 200 400 800 800 lo00 Net isotropic pressure, (u3 - u.) (kPa) (b) Figure 8.40 Experimental results showing the o parameters of two soils. (a) Development of the o parameter for compacted shale; (b) development of the o parameter for a compacted boul- der clay. (Bishop, 1961a). cients of volume change during loading is an important fac- tor in predicting the pore-water pressures. 8.3.5 Experimental Results of Tangent B and A Parameters for Triaxial Loading Undrained, triaxial testing is commonly performed by first increasing the isotropic pressure of the soil specimen to a given minor principal stress, 4. The pore pressures devel- oped during the isotropic pressure increase, du3, can be written as tangent B pore pressure parameters. The second step in the triaxial test is to increase the ver- tical stress on the soil specimen to produce a maximum value for the major principal stress, uI . The minor principal stress, u3, remains constant. The change in pore pressures during an increment of deviator stress, d(u, - u3), gives the tangent D pore pressure parameter. The resultant pore- air and pore-water pressures can be obtained by a super- position method, as expressed by Eqs. (8.107) and (8.101), respectively. Figures 8.37-Fig. 8.39 present pore pressure measure- ments obtained from undrained, triaxial tests performed by the U.S. Department of the Interior Bureau of Reclamation (U.S.B.R. (1966)). The plotted volume changes are ex- pressed in terms of the initial volume of the soil, V,. The 216 8 PORE PRESSURE PARAMETERS pore pressure parameters computed from the experimental results are the average tangent B or D parameters. The re- sults indicate that the tangent B and D parameters are a function of the stress state in the soil and the degree of saturation of the soil. In general, the pore pressure param- eters increase as the total stress on the soil increases. 8.3.6 Experimental Measurements of the a Parameter Figure 8.40 presents two sets of experiments where the a parameter was measured on two compacted soils under isotropic loading (Bishop, 1961a). The CY parameter is the ratio of the matric suction change, d(u, - uw), to the net isotropic pressure change, d(u3 - u,). This is in accor- dance with the definition of the CY parameter given in Eq. (8.129). The first test is on a shale compacted at a water content slightly above optimum water content. The a parameter was initially about 0.6, and decreased as the net isotropic pressure increased, as shown in Fig. 8.40(a). The second test is on a boulder clay compacted slightly below optimum water content. The a pameter started with a value of about 0.1, and also decreased with increasing net isotropic pressures, as illustrated in Fig. 8.40(b). In other words, the change in matric suction due to a change in net isotropic pressure becomes insignificant at high total stresses or low matric suctions. CHAPTER 9 Shear Strength Theory Many geotechnical problems such as bearing capacity, lat- eral earth pressures, and slope stability are related to the shear strength of a soil. The shear strength of a soil can be related to the stress state in the soil. The stress state vari- ables generally used for an unsaturated soil are the net nor- mal stress, (u - u,), and the matric suction, (u, - uw), as explained in Chapter 3. This chapter describes how. shear strength is formulated in terms of the stress state variables and the shear strength parameters. Techniques for measur- ing the shear strength parameters in the laboratory are out- lined in Chapter 10. The application of the shear strength equation to different types of geotechnical problems is pre- sented in Chapter 11. A brief historical review of the shear strength theory and attempts to measure relevant soil properties is given in this chapter prior to formulating the shear strength equation. The shear strength test results discussed in the review are selected from the many references on this subject. The se- lection of research papers for reference is based primarily upon whether or not the researcher used proper procedures and techniques for the measurement or control of the pore pressures during the shearing process. The two commonly performed shear strength tests are the triaxial test and the direct shear test. The theory associated with various types of triaxial tests and direct shear tests for unsaturated soils are compared and discussed in this chapter. Measurement techniques and related equipment are described in Chapter 10. A theoretical model for predicting the strain rate re- quired for testing unsaturated soils is also presented. The shear strength equation for an unsaturated soil is pre- sented, both in analytical and graphical forms. Both forms of presentations assist in visualizing the changes which oc- cur when going from unsaturated to saturated conditions and vice versa. The possibility of nonlinearity in the shear strength failure envelope is discussed. Various possible methods for handling the nonlinearity are outlined. Soil specimens which are “identical” in their initial con- ditions are required for the determination of the shear strength parameters in the laboratory. If the strength pa- rameters of an undisturbed soil are to be measured, the tests should be performed on specimens with the same geolog- ical and stress history. On the other hand, if strength pa- rameters for a compacted soil are being measured, the specimens should be compacted at the same initial water content and with the same compactive effort. The soil can then be allowed to equalize under a wide range of applied stress conditions. It is most impottant to realize that soils compacted at different water contents, to different densi- ties, are “different” soils. In addition, the laboratory test should closely simulate the loading conditions that are likely to occur in the field. Various stress paths that can be simulated by the triaxial and the direct shear tests are de- scribed in Chapters 9 and 10. 9.1 HISTORY OF SHEAR STRENGTH The shear strength of a saturated soil is described using the Mohr-Coulomb failure criterion and the effective stress concept (Terzaghi, 1936). (9.1) where rff = shear stress on the failure plane at failure c’ = effective cohesion, which is the shear strength intercept when the effective normal stress is equal to zero (ar - uw)i = effective normal stress on the failure plane at failure uff = total normal stress on the failure plane at failure uwf = pore-water pressure at failure 9‘ = effective angle of internal friction. T~ = c‘ + (af - tan 4‘ Equation (9.1) defines a line, as illustrated in Fig. 9.1 The line is commonly referred to as a failure envelope. This envelope represents possible combinations of shear stress and effective normal stress on the failure plane at failure. The shear and normal stresses in Eq. (9.1) are given 217 218 9 SHEAR STRENGTH THEORY t Failure envelope: T~~ = c‘ + (ul - u,h tan 4’ 7 0 Effective normal stress, (a - u,) Figure 9.1 Mohr-Coulomb failure envelope for a saturated soil. the subscript “J” The ‘7’’ subscript within the brackets refers to the failure plane, and the “f” subscript outside of the brackets indicates the failure stress condition. One subscript ‘7’’ is given to the pore-water pressure to indi- cate the failure condition. The pore-water pressure acts equally on all planes (i.e., isotropic). The shear stress de- scribed by the failure envelope indicates the shear strength of the soil for each effective normal stress. The failure en- velope is obtained by plotting a line tangent to a series of Mohr circles representing failure conditions. The slope of the line gives the effective angle of internal friction, 4’, and its intercept on the ordinate is called the effective cohe- sion, c’. The direction of the failure plane in the soil is obtained by joining the pole point to the point of tangency between the Mohr circle and the failure envelope (see Chapter 3). The tangent point on the Mohr circle at failure represents the stress state on the failure plane at failure. The use of effective stresses with the Mohr-Coulomb failure criterion has proven to be satisfactory in engineer- ing practice associated with saturated soils. Similar at- tempts have been made to find a single-valued effective stress variable for unsaturated soils, as explained in Chap- ter 3. If this were possible, a similar shear strength equa- tion could be proposed for unsaturated soils. However, in- creasing evidence supports the use of two independent stress state variables to define the stress state for an unsat- urated soil, and consequently the shear strength (Matyas and Radhakrishna, 1968, Fredlund and Morgenstern, 1977). Numerous shear strength tests and other related studies on unsaturated soils have been conducted during the past 30 years. This section presents a review of studies related to the shear strength of unsaturated soils. Similar to satu- rated soils, the shear strength testing of unsaturated soils can be viewed in two stages. The first stage is prior to shearing, where the soils can be consolidated to a specific set of stresses or left unconsolidated. The second stage in- volves the control of drainage during the shearing process. The pore-air and pore-water phases can be independently maintained as undrained or drained during shear. In the drained condition, the pore fluid is allowed to completely drain from the specimen. The desire is that there be no excess pore pressure built up during shear. In other words, the pore pressure is externally controlled at a con- stant value during shear. In the undrained condition, no drainage of pore fluid is allowed, and changing pore pres- sures during shear may or may not be measured. It is im- portant, however, to measure or control the pore-air and pore-water pressures when it is necessary to know the net normal stress and the matric suction at failure. The stress state variables at failure must be known in order to assess the shear strength of the soil in a fundamental manner. Many shear strength tests on unsaturated soils have been performed without either controlling or measuring the pore- air and pore-water pressures during shear. In some cases, the matric suction of the soil has been measured at the be- ginning of the test. These results serve only as an indicator of the soil shear strength since the actual stresses at failure are unknown. A high air entry disk with an appropriate air entry value should be used when measuring pore-water pressures in an unsaturated soil. The absence of a high air entry disk will limit the possible measurement of the difference between the pore-air and pore-water pressure to a fraction of an atmosphere. The interpretation of the results from shear strength tests on unsaturated soils becomes ambiguous when the stress state variables at failure are not known. The following literature review is grouped into two cate- gories. The first category is a review of shear strength tests where there has been adequate control or measurement of the pore-air and pore-water pressures. The second cate- gory is a review of shear strength tests on unsaturated soils where there has been inadequate control or measmment of pore pressures during shear. 9.1 HISTORY OF SHEAR STRENGTH 219 The concept of "strain" is used in presenting triaxial test results in the form of stress versus strain curves. Stress and strain concepts are discussed in detail in Chapters 3 and 12, respectively. Normal strain is defined as the ratio of the change in length to the original length. When a soil specimen is subjected to an axial normal stress, the normal strain in the axial direction can be defined as follows (Fig. 9.2): (100) (9.2) ey = axial normal strain in the ydirection ex- Lo = original length of the soil specimen L = final length of the soil specimen. A series of direct shear tests on unsaturated fine sands and coarse silts were conducted by Donald (1956). The tests were performed in a modified direct shear box, as shown in Fig. 9.3(a). The pore-air and pore-water pres- sures were controlled during shear. The top of the direct shear box was exposed to the atmosphere in order to main- tain the pore-air pressure, u,, at atmospheric pressure, 101.3 kPa (i.e., zero gauge pressure). The pore-water pressure, u,, was controlled at a negative value by apply- ing a constant negative head to the water phase. The spec- imen was placed in contact with the water in the base of the shear box through use of a colloidon membrane. The water in the base of the shear box was then connected to a constant head overflow tube at a desired negative gauge pressure [Fig. 9.3(b)]. The pore-water pressure could be reduced to approximately zero absolute before cavitation occurred in the measuring system. The soil specimens were consolidated under a total stress of approximately 48 kPa, with a uniform initial density. The desired negative pore-water pressure was applied for several hours in order for the specimens to reach equilib- Lo - L Lo = - where pressed as a percentage I"" + Figure 9.2 Strain concept used in the triaxial test. A /Colloidon membranes II Sintered bronze1 Plastic tube (4 To LTXcuum I u Constant head overflow tube (b) Figure 9.3 Modified direct shear equipment for testing soils un- der low matric suction. (a) Modified direct shear box with a col- loidon membrane; (b) system for applying a constant negative pore-water pressure (from Donald, 1956). rium. The specimens were then sheared at a rate of 0.071 mm/s. The results from four types of sand are presented in Fig. 9.4. The shear strength at zero matric suction is the strength due to the applied total stress. As the matric suc- tion is increased, the shear strength increases to a peak value and then decreases to a fairly constant value. As long as the specimens were saturated, the strengths of the sands appeared to incmse at the same rate as for an increrise in total stress. Once the sands desaturated, the rate of increase in strength decreased, and in fact, the strength decreased when the suction was increased beyond some limiting value. The U.S. Bureau of Reclamation has performed a num- ber of studies on the shear strength of unsaturated, com- pacted soils in conjunction with the construction of earth fill dams and embankments (Gibbs et al. 1960; Knodel and Coffey, 1966; Gibbs and Coffey, 1969). Undrained triaxial tests with pore-air and pore-water pressure measurements were perfarmed. The pore-air pressure, u,, was measured through the use of a coarse ceramic disk at one end of the specimen. The pore-water pressure, u,, was measured at the other end of the specimen through the use of a high air entry disk. The pore-air and pore-water pressures were measured during the application of an isotropic pressure, a3, and subsequently during the application of the deviator stress, (a, - u3). The pore-air pressure measurements agreed closely with the pore-air pressure predictions using Hilf s analysis (Chapter 8). 220 25 - 20 - __ - e m Medium Frankston sand E 10- I r 9 SHEAR STRENGTH THEORY I I I I I 8- Ff-f-: Graded Frankston sand - __ - ~ 8 Matric suction, (u, - u,) (kPaJ (a) 25 20 f 15 3 : 10 I - t .c ln 5 0 Matric suction, (u, - u,J (kPa) (C) Figure 9.4 Results of direct shear tests on sands under low matric suctions (modified from Don- ald, 1956). No attempt was made to relate the measured shear strength to the matric suction, (u, - u,). Rather, two sets of shear strength parameters were obtained by plotting two Mohr-Coulomb envelopes. The first envelope was tangent to Mohr circles plotted using the (a - u,) stress variables [i.e., Eq. (9. l)]. The second envelope was tangent to Mohr circles plotted using the (a - u,) stress variables. Figure 9.5 presents typical plots of two envelopes used to plot the shear strength data. The pore pressure measurements for undrained triaxial test no. 3 were presented in Chapter 8. The two failure envelopes indicated that there is a greater difference in their cohesion intercepts than in their friction angles. An extensive research program on unsaturated soils was conducted at Imperial College, London, in the late 1950's and early 1960's. At the Research Conference on the Shear Strength of Cohesive Soils, Boulder, CO, Bishop et al. (1960) proposed testing techniques and presented the re- sults of five types of shear strength tests on unsaturated soils. The types of tests were: 1) consolidated drained, 2) consolidated undrained, 3) constant water content, 4) un- drained, and 5) unconfined compression tests. These are P 400r Specimen No. 1 v) $ 100 r 200 400 600 800 Stress variable, (a - u. ) (kPa) (a) 0 400 : 300 g- 200 c ; 100 0) c mo 200 400 600 800 0 Stress variable, (a - u,) (kPa) (b) Figure 9.5 Two procedures used by the U.S. Bureau of Recla- mation to plot their shear strength data. (a) Failure envelope based on the (a - u,,) stress variables; @) failure envelope based on the (a - u,,,) stress variables (from Gibbs and Coffey, 1969). [...]... a failure criterion for unsaturated soils may 9.2 FAILURE ENVELOPE FOR UNSATURATED SOILS 350 2 g m 227 t 300 250 6 6 200 -E5’ 150 Strain limit 100 -m 8 Strain, t 50 P Figure 9.17 Strain limit used as a failure criterion 0 Axial strain, t, (%) (a) ther research is needed to establish the most appropriate failure criteria for unsaturated soils 9.2.2 Shear Strength Equation 5 10 15 20 The shear strength... consistently equal to or less than 4 ‘, as indicated in Table 9.1, for soils from various geographic locations Net normal stress, (a- u.) Figure 9.18 Extended Mohr-Coulomb failure envelope for unsaturated soils 9.2 FAILURE ENVELOPE FOR UNSATURATED SOILS 229 Table 9.1 Experimental Values of r$b 4’ 4b 15. 8 24.8 18.1 9.6 27.3 21.7 37.3 28 .5 20.3 C’ Soil Type (Pa) Compacted shale; w = 18.6% (degrees) (degrees)... the shear strength equation for an unsaturated soil is an extension of the shear strength equation for a saturated soil For an unsaturated soil, two stress state variables are used to describe! its shear strength, while only one smss state variable [Le., effective normal stress, (u, - u,,,),] is required for a saturated soil The shear strength equation for an unsaturated soil exhibits a smooth transition... triaxial Consolidated drained triaxial Bishop et al (1960) Bishop et al (1960) Satija, (1978) 29.0 12.6 Constant drained triaxial Satija, (1978) 15. 5 28 .5 22.6 Satija, (1978) 11.3 29.0 16 .5 23.7 223 16.1 28.9 33.4 15. 3 7.4 35. 3 13.8 0.0 35. 0 16.0 25. 3 7- 25. 5 Consolidated water content triaxial Constant water content triaxial Consolidated drained direct shear Consolidated drained multistage triaxial... substituting Eq 9.2 FAILURE ENVELOPE FOR UNSATURATED SOILS 2 35 c T 5, = I-ATBc: (ATACI-~ Net normal stress, (a - ua) Figure 9.24 Relationships among the variables c, d, rp’, and $ I (9.16) for d’ and substituting (u, obtain the relationship among $, ’ for rf in order to and 4’: - u& +’, tan $’ = tan 4’ cos 4’ (9.18) The above relationships [Le., Eqs (9.13),(9. 15) , (9.17), and (9.l8)] can be used to... stress, u ( b) Figure 9.41 Use of the unconfined compressive strength, qu,to approximate the undrained shear strength, c,, for an unsaturated soil and a saturated soil (a) Relationship between q, and c, for an unsaturated soil; (b) relationship between qu and c, for a saturated soil (with negative pore-water pressures) ... parameters of the soil The initial conditions of the soil specimens must be essentially identical in order for the results to produce unique shear strength parameters for the soil Only specimens with the same geological condition and stress history should be used to define a specific set of shear strength parameten Unsaturated soil specimens are sometimes prepared by compaction In this case, the soil specimens... “identical” soil Specimens compacted at the same water content but at different dry densities, or vice versa, cannot be considered as “identical” soils, even though their classification properties the same Soils with differing density and water content conditionscan yield different shear strength parameters, and should be considered as different soils (Fig 9.13) The shear strength test is performed by... essentially equal to the effective angle of internal friction obtained from shear strength tests on saturated soil specimens The value of the + r angle for compacted soils commonly ranges from 25" to 35" , as shown in Table 9.1 The effect of compactive effort on the strength parameters, 9' and c ' , for a clayey sand is illustrated in Fig 9.29 Figure 9.30 presents the stress paths followed during consolidated... circles of the unsaturated soil specimens at failure applied total normal stress, as illustrated in Fig 9.38 - 9.3 TRIAXIAL TESTS ON UNSATURATED SOILS d 2 & 2 45 U s t r t d4 n auae _c Straight line approximation Approaching saturation r t n 0 + L-) 2 0 1 (Ill 0 3 Total normal stress, a Figure 9 3 Shear stress versus total normal stress relationship at failure for the undrained test .8 9.3 .5 Unconfined . criterion for unsaturated soils may 9.2 FAILURE ENVELOPE FOR UNSATURATED SOILS 227 350 m g 250 6 E’ 150 2 300 6 200 5 100 - - m 8 50 P 0 Axial strain, t, (%) (a) 5 10. on unsaturated soils have been conducted during the past 30 years. This section presents a review of studies related to the shear strength of unsaturated soils. Similar to satu- rated soils, . triaxial tests was per- formed by Ho and Fredlund on unsaturated soils. Undis- turbed specimens of two residual soils from Hong Kong were used in the testing program. The soils were a decom-