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# Craig's Soil Mechanics 7th Edition

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however, are the same. From Figure 4.8(e) it is apparent that the difference between maximum and ultimate stress decreases with increasing effective normal stress; therefore, if the maximum shear stress is plotted against effective normal stress for each individual test, the plotted points will lie on an envelope which is slightly curved, as shown in Figure 4.8(g). The value of �0max for each test can then be represented by a secant parameter, the value decreasing with increasing effective normal stress until it becomes equal to �0cv. The reduction in the difference between maximum and ultimate shear stress with increasing normal stress is mainly due to the correspond- ing decrease in ultimate void ratio. The lower the ultimate void ratio the less scope there is for dilation. In addition, at high stress levels some fracturing or crushing of particles may occur with the consequence that there will be less particle interlocking to be overcome. Crushing thus causes the suppression of dilatancy and contributes to the reduced value of �0max. In practice, the routine laboratory testing of sands is not feasible because of the problem of obtaining undisturbed specimens and setting them up, still undisturbed, in the test apparatus. If required, tests can be undertaken on specimens reconstituted in the apparatus at appropriate densities but the in-situ structure is then unlikely to be reproduced. Guidance on appropriate values of the parameters �0max and � 0 cv is given in certain codes of practice. In the case of dense sands it has been shown that the value of �0max under conditions of plane strain can be 4 � or 5� higher than the corresponding value obtained by conventional triaxial tests. The increase in the case of loose sands is negligible. Liquefaction Liquefaction is a phenomenon in which loose saturated sand loses a large percentage of its shear strength and develops characteristics similar to those of a liquid. It is usually induced by cyclic loading of relatively high frequency, resulting in undrained conditions in the sand. Cyclic loading may be caused, for example, by vibrations from machinery and, more seriously, by earth tremors. Loose sand tends to compact under cyclic loading. The decrease in volume causes an increase in pore water pressure which cannot dissipate under undrained conditions. Indeed, there may be a cumulative increase in pore water pressure under successive cycles of loading. If the pore water pressure becomes equal to the maximum total stress component, normally the overburden pressure, the value of effective stress will be zero, i.e. interparticle forces will be zero, and the sand will exist in a liquid state with negligible shear strength. Even if the effective stress does not fall to zero the reduction in shear strength may be sufficient to cause failure. Liquefaction may develop at any depth in a sand deposit where a critical combin- ation of in-situ density and cyclic deformation occurs. The higher the void ratio of the sand and the lower the confining pressure the more readily liquefaction will occur. The larger the strains produced by the cyclic loading the lower the number of cycles required for liquefaction. Shear strength of sands 105 4.4 SHEAR STRENGTH OF SATURATED CLAYS Isotropic consolidation If a saturated clay specimen is allowed to consolidate in the triaxial apparatus under a sequence of equal all-round pressures, sufficient time being allowed between successive increments to ensure that consolidation is complete, the relationship between void ratio (e) and effective stress (�03) can be obtained. Consolidation in the triaxial apparatus under equal all-round pressure is referred to as isotropic consolidation. The relationship between void ratio and effective stress depends on the stress history of the clay. If the present effective stress is the maximum to which the clay has ever been subjected, the clay is said to be normally consolidated. If, on the other hand, the effective stress at some time in the past has been greater than the present value, the clay is said to be overconsolidated. The maximum value of effective stress in the past divided by the present value is defined as the overconsolidation ratio (OCR). A normally consolidated clay thus has an overconsolidation ratio of unity; an overconsolidated clay has an overconsolidation ratio greater than unity. Overconsolidation is usually the result of geological factors, for example, the erosion of overburden, the melting of ice sheets after glaciation and the permanent rise of the water table. Overconsolidation can also be due to higher stresses previously applied to a specimen in the triaxial apparatus. The characteristic relationship between e and �03 is shown in Figure 4.9. AB is the curve for a clay in the normally consolidated condition. If after consolidation to point B the effective stress is reduced, the clay will swell or expand and the relation- ship will be represented by the curve BC. During consolidation from A to B, changes in soil structure continuously take place but the clay does not revert to its original structure during swelling. A clay existing at a state represented by point C is now in the overconsolidated condition, the overconsolidation ratio being the effective stress Figure 4.9 Isotropic consolidation. 106 Shear strength at point B divided by that at point C. If the effective stress is again increased the consolidation curve is CD, known as the recompression curve, eventually becoming the continuation of the normal consolidation curve AB. It should be realized that a state represented by a point to the right of the normal consolidation curve is impossible. Undrained strength In principle, the unconsolidated–undrained triaxial test enables the undrained strength of the clay in its in-situ condition to be determined, the void ratio of the specimen at the start of the test being unchanged from the in-situ value at the depth of sampling. In practice, however, the effects of sampling and preparation result in a small increase in void ratio. Experimental evidence (e.g. Duncan and Seed [10]) has shown that the in-situ undrained strength of saturated clays is significantly anisotropic, the strength depending on the direction of the major principal stress relative to the in-situ orienta- tion of the specimen. Thus, undrained strength is not a unique parameter. When a specimen of saturated clay is placed on the pedestal of the triaxial cell the initial pore water pressure is negative due to capillary tension, total stresses being zero and effective stresses positive. After the application of all-round pressure the effective stresses in the specimen remain unchanged because, for a fully saturated soil under undrained conditions, any increase in all-round pressure results in an equal increase in pore water pressure (see Section 4.7). Assuming all specimens to have the same void ratio and composition, a number of unconsolidated–undrained tests, each at a different value of all-round pressure, should result, therefore, in equal values of principal stress difference at failure. The results are expressed in terms of total stress as shown in Figure 4.10, the failure envelope being horizontal, i.e. �u ¼ 0, and the shear strength is given by �f ¼ cu. It should be noted that if the values of pore water pressure at failure were measured in a series of tests then in principle only one effective stress circle, shown dotted in Figure 4.10, would be obtained. The circle representing an unconfined compression test would lie to the left of the effective stress circle in Figure 4.10 because of the negative pore water pressure in the specimen. The unconfined strength of a clay is due to a combination of friction and pore water suction. If the best common tangent to the Mohr circles obtained from a series of tests is not horizontal then the inference is