
Craig's Soil Mechanics 7th Edition
Pré-visualização50 páginas
(as illustrated in Example 4.3). Figure 4.12 Correction factor for undrained strength measured by the vane test. (After Bjerrum [5].) Table 4.1 Undrained strength classification Stiffness state Undrained strength (kN/m2) Hard >300 Very stiff 150–300 Stiff 75–150 Firm 40–75 Soft 20–40 Very soft <20 110 Shear strength Tangent parameters c0 and �0 apply only to a relatively small stress range. The tangent value of �0 is likely to be lower than the critical-state value. Caution is required in the use of the c0 parameter, especially at low stress levels where it would represent a significant proportion of shear strength. If the critical-state value of �0cv is required for a heavily overconsolidated clay then, if possible, tests should be performed at stress levels that are high enough to define the critical-state envelope, i.e. specimens should be consolidated at all-round pressures in excess of the preconsolidation value. Alterna- tively, an estimated value of �0cv can be obtained from tests on normally consolidated specimens reconsolidated from a slurry. Effective stress parameters can also be obtained by means of drained triaxial tests (or direct shear tests). Clays under drained conditions behave as frictional materials. The rate of strain must be slow enough to ensure full dissipation of excess pore water pressure at any time during application of the principal stress difference. Total and effective stresses will thus be equal throughout the test. The rate of strain must again be related to the permeability of the clay. The volume change taking place during the application of the principal stress difference must be measured in the drained test so that the corrected cross-sectional area of the specimen can be calculated. Typical test results for specimens of normally consolidated and overconsolidated clays are shown in Figure 4.14. In consolidated–undrained tests, axial stress and pore water pressure are plotted against axial strain. For normally consolidated clays, axial stress reaches an ultimate value at relatively large strain, accompanied by increase in pore water pressure to a steady value. For overconsolidated clays, axial stress increases to a peak value and then decreases with subsequent increase in strain. However, it is not usually possible to reach the ultimate stress due to excessive specimen deformation. Pore water pressure increases initially and then decreases, the higher the overconsolidation ratio the greater the decrease. Pore water pressure may become negative in the case of heavily overconsolidated clays as shown by the dotted line in Figure 4.14(b). In drained tests, axial stress and volume change are plotted against axial strain. For normally consolidated clays an ultimate value of stress is again reached at relatively high strain. A decrease in volume takes place during shearing and the clay hardens. For over- consolidated clays a peak value of axial stress is reached at relatively low strain. OC NC φcv σ′ τ ′ Figure 4.13 Failure envelopes for normally consolidated (NC) and overconsolidated (OC) clays. Shear strength of saturated clays 111 Subsequently, axial stress decreases with increasing strain but, again, it is not usually possible to reach the ultimate stress in the triaxial apparatus. After an initial decrease, the volume of an overconsolidated clay increases prior to and after peak stress and the clay softens. For overconsolidated clays the decrease from peak stress towards the ultimate value becomes less pronounced as the overconsolidation ratio decreases. In practical situations, if the stress in a particular soil element becomes equal to the peak shear strength, any further increase in strain will result in a reduction in strength. Consequently, additional stress will be transferred to adjacent elements, perhaps resulting in peak strength being also reached in these elements. A sequence of pro- gressive failure could thus be set in train within a soil mass. Therefore, unless it is certain that strains throughout the soil mass will remain less than that corresponding to peak strength, it is necessary to use the critical-state strength in design. Figure 4.14 Typical results from consolidated–undrained and drained triaxial tests. 112 Shear strength Stress paths The successive states of stress in a test specimen or an in-situ element of soil can be represented by a series of Mohr circles or, in a less confusing way, by a series of stress points. The curve or straight line connecting the relevant stress points is called the stress path, giving a clear representation of the successive states of stress. Stress paths may be drawn in terms of either effective or total stresses. The horizontal distance between the effective and total stress paths is the value of pore water pressure at the stresses in question. In general, the horizontal distance between the two stress paths is the sum of the pore water pressure due to the change in total stress and the static pore water pressure. In the normal triaxial test procedure the static pore water pressure (us) is zero. However, if a triaxial test is performed under back pressure, the static pore water pressure is equal to the back pressure. The static pore water pressure of an in-situ element is the pressure governed by the water table level. The effective and total stress paths (denoted by ESP and TSP, respectively) for the triaxial tests represented in Figure 4.14 are shown in Figure 4.15, the coordinates being 1⁄2 (� 0 1��03) and 1⁄2 (�01þ�03) or the total stress equivalents. The effective stress paths terminate on the modified failure envelope. All the total stress paths and the effective stress paths for the drained tests are straight lines at a slope of 45�. The detailed shape of the effective stress paths for the consolidated–undrained tests depends on the clay in question. The effective and total stress paths for the drained tests coincide, provided no back pressure has been applied. The dotted line in Figure 4.15(c) is the effective stress path for a heavily overconsolidated clay in which the pore water pressure at failure (uf) is negative. The hydraulic triaxial apparatus This apparatus, developed by Bishop and Wesley [4], is shown diagrammatically in Figure 4.16. The chamber containing the soil specimen is similar to a conventional triaxial cell; however, the pedestal is connected by a ram to a piston in a lower pressure chamber, the vertical movement of the ram being guided by a linear bearing. Rolling seals are used to accommodate the movement of the ram in both chambers. Axial load is applied to the specimen by increasing the pressure in the lower chamber. Standard constant pressure systems can be used but preferably with a motorized drive arrangement to control the rate of pressure increase. Although the axial load on the specimen can be calculated from a knowledge of the pressures in the two chambers, the mass of the ram and apparatus dimensions, it is preferable to measure the load directly by means of a load cell above the specimen. A cross-arm mounted on the ram passes through the slots in the side of the apparatus (the section of the apparatus containing the linear bearing being open to atmosphere); vertical rods attached to the ends of the cross-arm operate against dial gauges (or transducers), enabling the change in length of the specimen to be measured. The slots in the side of the apparatus also accommodate the pore pressure and drainage connections from the pedestal. The potential of the apparatus can be fully exploited by means of an automatic system controlled by a computer. The apparatus enables a wide range of stress paths, reproducing in-situ stress changes, to be imposed on the specimen. Shear strength of saturated clays 113 Example 4.1 The following results were obtained from direct shear tests on specimens of a sand