8.1. What is meant by the shear strength of soils? Solution 8.1 Shear strength of a soil is its internal resistance to shearing stresses.

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1 8.1. What is meant by the shear strength of soils? Solution 8.1 Shear strength of a soil is its internal resistance to shearing stresses.

2 8.2. Some soils show a peak shear strength. Why and what type(s) of soil do so? Solution 8.2 Peak shear strength results from the tendency of some soils to dilate (expand). These soils are generally dense (e.g. dense sands and overconsolidated clays) and the confining stresses are not large enough to suppress dilation.

3 8.3. What is critical state for soils? Solution 8.3 Critical state is a condition reached when a soil attains a constant shear stress to normal effective stress ratio at a constant volume when sheared at large strains.

4 8.4. Which friction angle, peak or critical state, is more reliable? Why? Solution 8.4 Critical state is more reliable. It is unaffected by the normal effective stress and the dilation capacity of the soil.

5 8.5. Which failure criterion is used to interpret the results from a direct shear test? Why? Solution 8.5 Coulomb s criterion. The soil is sheared along a pre-determined failure plane.

6 8.6. Can you draw a Mohr s circle using the data from a direct shear test? Explain your answer. Solution 8.6 No. The stresses on the vertical planes are unknown.

7 8.7. Which failure criterion is used to interpret triaxial test results for long term loading condition? What is basis for this criterion? Solution 8.7 Mohr-Coulomb failure criterion. The basis of this criterion is that a soil will fail when the maximum stress obliquity is attained.

8 8.8. Which failure criterion is used to interpret triaxial test results for short term loading condition? What is basis for this criterion? Is this criterion used for clays or sand or both? Justify your answer. Solution 8.8 Tresca s failure criterion. The basis of this criterion is that the soil will fail at one-half the maximum principal stress difference. This criterion is used for clays under undrained condition.

9 8.9. What is soil cohesion and is it the same as the undrained shear strength? Explain your answer. Solution 8.9 No. Cohesion in the a measure of the intermolecular forces. The undrained shear strength is a measure of the shearing strength of soils (essentially fine-grained soils) when drainage of porewater is prevented.

10 8.10. Why does a sample need to be saturated to interpret the results from triaxial undrained tests? Solution 8.10 Because air in the voids can collapse or move within the soil resulting in a change in soil volume. In the undrained test, the soil volume is intended to be constant.

11 8.11. The confining pressure on a loose saturated sand under groundwater is 100 kpa. The sand is shaken by a seismic event. What is the value of the maximum excess porewater pressure that can develop in the sand? What is the corresponding effective stress? Solution 8.11 Maximum excess porewater pressure = 100 kpa The effective stress = 0. The sand mass will fluidize (be like a viscous liquid).

12 8.12. The confining pressure on a dense (relative density = 85%) saturated sand under groundwater is 100 kpa. Shearing stresses are applied to this sand. Would the excess porewater pressure increase or decrease as a result of the shearing? What is the minimum porewater pressure that can develop in this sand? Justify your answer. Solution 8.12 The excess porewater pressure is expected to increase initially and then decrease as the peak shear stress is attained. The assumption is that the effective confining pressure is not large enough to suppress the dilation tendency of the dense sand. The minimum porewater pressure is the vapour pressure of water (-99 kpa).

13 8.13. The normal and shear stresses at critical state on a horizontal sliding (failure) plane for a sand is 100 kpa and 57.7 kpa respectively. (a) Which failure criterion is best used to determine the friction angle of this sand? Justify your answer. (b) Determine the friction angle. Solution 8.13 (a) Coulomb s failure criterion. This criterion applies to soils that fail on a predermined failure plane, which in this case is the horizontal plane. (b) From equation (8.1) tan f cs = t cs = ( s n ) = f f cs = tan -1 (0.577) = 30 o

14 8.14 The following results were obtained from three direct shear (shear box) tests on a sample of sandy clay. The cross section of the shear box is 50 mm 50 mm Normal force (N) Shearing force (N) Which failure criterion is appropriate to interpret this data set? Justify your answer. (b) Plot a graph of normal force versus shear force for the data given. (c) Determine the critical state friction angle. (d) Is the soil dilatant? (e) Determine the friction angle at a normal force of 100 lb. Is this a peak or critical state friction angle? If this angle is a peak friction angle, what is the value of the dilation angle? Solution 8.14 (a) Coulomb s failure criterion. This criterion applies to soils that fail on a predermined failure plane, which in the direct shear test is the horizontal plane. (b) (c) The critical state friction angle (see graph) is From equation (8.1) P 580 cs tan tan 23.5 P x cs 1 0 z f (d) The soil is dilatant because all the consecutive points do not line on an approximate straight line through the origin. The first two data points lie way off from this line. (e) The friction angle at a normal force of 446 N is a peak friction angle. P 1 x p p tan tan 31.8 P 446 p at 446N z f o o o

8.15 The results of a direct shear test on a dense sand using a vertical force is 200 N are shown in the table below. Determine, and. The sample area is 65 mm x 65 mm and the sample height is 20 mm.

15 8.15 The results of a direct shear test on a dense sand using a vertical force is 200 N are shown in the table below. Determine, and. The sample area is 65 mm x 65 mm and the sample height is 20 mm. In the P cs p table, x, z, and P x are the horizontal and vertical displacements and horizontal (shear) force, respectively. Solution Peak Critical state Horizontal load (N) Horizontal displacement (mm) Figure P8.15a

16 p Figure P8.15b The peak shear force is about 178 N and occurs when the horizontal displacement is about 6.6 mm. The vertical displacement just after the peak shear force is achieved remains approximately constant. The critical shear force is about 159 N (Note: At this shear force the soil volume remains approximately constant.). You can use force instead of stress in the equations below because the area is the same for shear and normal forces. 178 p 200 p at 45 lb 1 p 1 o tan tan 41.7 n 159 cs cs 1 o tan tan 38.5 n f f o o o Using the horizontal displacement versus the vertical displacement graph, the average slope for which the soil is dilating is a approximately tan -1 [(0 {-0.26})/(6 2)] = 3.7 o which is 0.5 o (about 16%) greater than the calculated value. This difference is reasonable in comparing experimental and theoretical derived values for this test.

17 8.16 An unconfined, undrained compression test was conducted on a compacted clayey sand classified as SC. The sample size was 38 mm in diameter 76 mmlong. The peak axial force recorded was 230 N, and the sample shortened by 2 mm. (a) Which failure criterion is appropriate to interpret the test data? (b) Determine the undrained shear strength. Solution 8.16 (a) The Tresca s failure criterion. (b) Diameter D m; length H 0.076m; axial displacement = ΔH o = m o r o 2 A m H o 1 1 H s u p o Pz 0.23 p 98.7kPa 2A o 2 2

The results at peak and critical states are shown in the table below. (a) Which failure criterion is appropriate to interpret this data set? Justify your answer.

18 8.17 CU triaxial tests were carried out according to ASTM standards on a sample of a clay classified as CH. The sample was isotropically consolidated using a cell pressure of 400 kpa before the axial displacements were incrementally applied. The results at peak and critical states are shown in the table below. (a) Which failure criterion is appropriate to interpret this data set? Justify your answer. (b) Draw Mohr s circles (total and effective stresses) for the test. (c) Calculate the peak and critical state friction angles and show these angles on the Mohr-circles. (d) Calculate the undrained shear strengths at peak and at critical state and show them on the Mohr-circles. (e) Determine the inclination of angle of the failure plane to the plane on which the major principal effective stress acts at peak shear stress. Solution 8.17 (a) For effective stress conditions, the friction angle is determined using the Mohr-Coulomb s failure criterion. For the total stress condition, the Tresca s failure criterion is used to determine the undrained shear strength. (b) See Table below for values to plot Mohr-circles. Peak effective stress Critical state effective stress Peak total stress Critical state total stress (c) (d) su = 1-3 )/2 kpa Peak 193 Critical state 162

19 p 29.4 (e) p= o o o

20 8.18 A CU test on a stiff, overconsolidated clay was carried out according to ASTM standards at a constant cell pressure of 90 kpa. The peak deviatoric stress recorded was 294 kpa. The corresponding excess porewater pressure was kpa. (a) Calculate the friction angle. Is this the critical state friction angle? Explain your answer. (b) Calculate the undrained shear strength. SOLUTION 8.18 (a) Peak The peak deviatoric stress was reported. Thus, the friction angle is not the critical state friction angle. (b) (su)p = 1-3 )/2 kpa Peak 147

8.19 CU tests were conducted on three samples of a compacted clay. Each sample was saturated before shearing.

Calculate (a) the friction angle and indicate if this is for peak or critical state, (b) the undrained shear strength for each test, and

Solution 8.19 (a) The average friction angle = 25.

21 8.19 CU tests were conducted on three samples of a compacted clay. Each sample was saturated before shearing. The results, when no further change in excess porewater pressure or deviatoric stress occurred, are shown in the table below. Calculate (a) the friction angle and indicate if this is for peak or critical state, (b) the undrained shear strength for each test, and (c) draw Mohr s circle of total and effective stress for each test and compare your results to those calculated in (a) and (b). Solution 8.19 (a) The average friction angle = 25.7 o (critical state ) (b) See table above (c) Mohr s circles of total and effective stress Total stress is shown by the light line and effective stress by the dark line. Because the porewater pressure is small the total and effective stresses are approximately equal. 26 o

8.19 A CU triaxial test was carried out on a silty clay that was isotropically consolidated using a cell pressure of 90 kpa. The following data were obtained.

22 8.19 A CU triaxial test was carried out on a silty clay that was isotropically consolidated using a cell pressure of 90 kpa. The following data were obtained. (a) Plot the deviatoric (axial) stress against axial strain and excess porewater pressure against axial strain. (b) Determine the undrained shear strength and the friction angle. Are these critical state or peak values? Justify your answer. Solution 8.20 (a) (b) These are critical state values as the axial stress and excess porewater pressures are approximately constant.

23 8.21 The results of an ASTM standard UU test on a sample of a stiff clay classified as CL is (σ 1 - σ 3) p = 70 kpa. The initial size of the sample was 38 mm x 76 mm long and it compressed by 2 mm. Determine s u. Solution 8.21 su = 1-3 )/2 = 70/2 = 35 kpa

8.22 Plot the corrected N value (N 1,60), the bulk unit weight and friction angle with depth for the data given in Figure 3.16. Solution 8.

24 8.22 Plot the corrected N value (N 1,60), the bulk unit weight and friction angle with depth for the data given in Figure Solution 8.22 The answers to this question depend on your interpretation of the test data and the empirical constants used. However, your answers should be about +-20% of the results given below.

26 8.23 Plot the undrained shear strength with depth for the CPT results shown in Figure Solution 8.23 The answers to this question depend on your interpretation of the test data and the empirical constants used. However, your answers should be about +-20% of the results given below. Make a composite diagram identifying soil layers. Use the empirical equation in Table 8.9 to make estimated of the undrained shear strength. Since no data was given regarding the physical parameters (e.g. plasticity index) of the soils, a conservative value of N k = 19 (Table 8.9) is used. A unit weight of 18 kn/m 3 is assumed as the average unit weight of the soil. The tables below show the estimated results.

28 8.24 You are in charge of designing a retaining wall. What laboratory tests would you specify for the backfill soil? Give reasons. Solution 8.24 The backfill for retaining walls are generally coarse-grained soils. The following tests are required. 1. Grain size to classify the soil. 2. Standard Proctor Compaction test to obtain maximum dry unit weight and optimum water content for specifications during construction. 3. Direct simple shear (DSS) test on the soil compacted to maximum dry unit weight and optimum water content to obtain the friction angle because the stress condition in the backfill of a long retaining wall is plane strain. If DSS apparatus is not available then substitute direct shear test. The soil should be sheared until the critical state is obtained. A simple angle of repose test can be done to compare with the critical state friction angle obtained from the test. The two results should be similar.

8.25 Solution 8.25 (a) 26.7 o Critical state is a reasonable assumption since the shears strains are large, the deviatoric stress and the porewater pressure are approximately constant.

29 8.25 Solution 8.25 (a) 26.7 o Critical state is a reasonable assumption since the shears strains are large, the deviatoric stress and the porewater pressure are approximately constant. (b) See table above From the test s u s u cs ic zo cs ic s u 3sin ' cs Ro zo 3 sin ' cs 2 cs ic 3 max 140 where R o 4 35 Table cs ic 3 o 0.8 o s u 3sin ' cs Ro 3sin o 3 sin ' cs 2 3 sin s u 3 The test ratio, reasonable. (c ) Recommended strength values. cs ic, is about 12% less than the theoretical estimated value. The test results appear o o Long term loading: ' 26.7 ( Use 26 ) Short term: s u = 27.5 kpa (Use 27 kpa) cs

Solution 8.26 (a) (b) The shear strength parameters are the friction angles and the undrained shear strengths. These values are tabulated using a spreadsheet.

31 Solution 8.26 (a) (b) The shear strength parameters are the friction angles and the undrained shear strengths. These values are tabulated using a spreadsheet. You can get the same results by finding the angles subtended by the tangents and the x-axis (friction angles) of the Mohr circles shown above. The undrained shear strength for each Mohr circle is the maximum value of. (c) and (d)the confining effective stress in the field is higher than the maximum cell (effective) pressure applied to the test samples. The peak friction angle is expected to decrease if a cell (effective) pressure of 300 kpa were to be used on a test sample. For a preliminary assessment, a friction angle less than 26.6 degrees will be recommended for long term loading. However, an actual value is speculative. Consequently, the shear strength parameters for design cannot be recommended with confidence. (e) Yes. Re-testing should be done. The soil should be incrementally consolidated to a cell pressure at least to 300 kpa (= current effective confining pressure) x OCR (= overconsolidation ratio) and then unloaded incrementally to 300 kpa. The shearing phase of the CU test should then be conducted to large shear strains (> 15%) or until a constant deviatoric stress and constant porewater pressure is

32 achieved. The porewater pressure must be measured continuously.

SHEAR STRENGTH OF SOIL

Soil Failure Criteria SHEAR STRENGTH OF SOIL Knowledge about the shear strength of soil important for the analysis of: Bearing capacity of foundations, Slope stability, Lateral pressure on retaining structures,