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# Craig's Soil Mechanics 7th Edition

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140 Stresses and displacements The results of a test using the Menard pressuremeter are represented by a plot of corrected pressure ( p) against volume (V ) as shown in Figure 5.4(a). On this plot a linear section occurs between pressures pi and pf. The value pi is the pressure necessary to achieve initial contact between the cell and the borehole wall and to recompress soil disturbed or softened as a result of boring. The value pf is the pressure corresponding to the onset of plastic strain in the soil. Eventually a limit pressure ( p1) is approached at which continuous expansion of the borehole cavity would occur. A ‘creep’ curve, obtained by plotting the volume change between the 30 and 120 s readings against the corresponding pressure, may be a useful aid in fixing the values pi and pf, significant breaks occurring at these pressures. The datum or reference pressure for the interpretation of pressuremeter results is a value ( p0) equal to the in-situ total horizontal stress in the soil before boring. Originally this value was assumed to be equal to pi but the use of a pre-formed borehole means that the soil is being stressed from an unloaded condition, not from the initial undisturbed state; consequently the value of p0 should be greater than pi. (It should be appreciated that it is normally very difficult to obtain an independent value of in-situ total horizontal stress.) The reference volume V0 (corresponding to the pressure p0) is taken to be the initial volume of the borehole cavity over the test length. At any stage during a test the volume V, corresponding to the pressure p, is referred to as the current volume. Figure 5.4 Pressuremeter test results. Elasticity and plasticity 141 Alternatively the results of a pressuremeter test can be represented by plotting corrected pressure against the circumferential strain ("c) at the borehole wall. The circumferential strain is given by the ratio of the increase in radius of the borehole cavity (�r) to the radius at the reference state (r0). The relationship between current volumetric strain and circumferential strain is �V V ¼ 1� ð1þ "cÞ�2 (Shear strain (�) is equal to twice circumferential strain.) Marsland and Randolph [11] proposed a procedure, using the p�"c plot, for the determination of p0, applicable to soils such as stiff clays which exhibit essentially linear stress–strain behaviour up to peak strength. The linear section of the p�"c plot should terminatewhen the shear stress at the boreholewall is equal to the (peak) undrained strength of the clay, i.e. when the pressure becomes equal to ( p0 þ cu). The value of cu is determined using Equation 5.7, for which a value of the reference volume V0 is required. The method involves an iterative process in which estimates of p0, and hence V0, are made and the corresponding value of cu determined until the point representing ( p0 þ cu) corresponds with the point on the plot at which significant curvature begins, as shown in Figure 5.4(b). The value of the limit pressure ( p1) can be determined by plotting pressure against the logarithm of current volumetric strain and extrapolating to a strain of unity, representing continuous expansion, as shown in Figure 5.4(c). An analysis of the expansion of the borehole cavity during a pressuremeter test was presented by Gibson and Anderson [6], the soil being considered as an elastic–perfectly plastic material. Within the linear section of the p�V plot the shear modulus is given by G ¼ V dp dV ð5:4Þ where dp/dV is the slope of the linear section and V is the current volume of the borehole cavity. However, it is recommended that the modulus is determined from an unloading–reloading cycle to minimize the effect of soil disturbance. In the case of saturated clays it is possible to obtain the value of the undrained shear strength (cu), by iteration, from the following expression: p1 � p0 ¼ ln G cu � � þ 1 � cu ð5:5Þ In modern developments of the pressuremeter the measuring cell is expanded directly by gas pressure. This pressure and the radial expansion of the rubber mem- brane are recorded by means of electrical transducers within the cell. In addition, a pore water pressure transducer is fitted into the cell wall such that it is in contact with the soil during the test. A considerable increase in accuracy is obtained with these pressuremeters compared with the original Menard device. It is also possible to adjust the cell pressure continuously, using electronic control equipment, to achieve a con- stant rate of increase in circumferential strain (i.e. a strain-controlled test), rather than to apply the pressure in increments (a stress-controlled test). 142 Stresses and displacements Some soil disturbance adjacent to a borehole is inevitable and the results of pressuremeter tests in pre-formed holes can be sensitive to the method of boring. The self-boring pressuremeter was developed to overcome this problem and is suitable for use in most types of soil; however, special insertion techniques are required in the case of sands. This device, illustrated in Figure 5.3(b), is jacked slowly into the ground and the soil is broken up by a rotating cutter fitted inside a cutting head at the lower end, the optimum position of the cutter being a function of the shear strength of the soil. Water or drilling fluid is pumped down the hollow shaft to which the cutter is attached and the resulting slurry is carried to the surface through the annular space adjacent to the shaft; the device is thus inserted with minimal disturbance of the soil. The only correction required is for the pressure required to stretch the membrane. A ‘push-in’ penetrometer has also been developed for insertion below the bottom of a borehole, for use particularly in off-shore work. This pressuremeter is fitted with a cutting shoe, a soil core passing upwards inside the device. The membrane of a pressuremeter may be protected against possible damage (particularly in coarse soils) by a thin stainless steel sheath with longitudinal cuts, designed to cause only negligible resistance to the expansion of the cell. Results from a strain-controlled test in clay using the self-boring pressuremeter are of the form shown in Figure 5.4(d), the pressure ( p) being plotted against the circum- ferential strain ("c). Use of the self-boring pressuremeter overcomes the difficulty in determining the initial in-situ total horizontal stress; because soil disturbance is minimal the pressure at which the membrane starts to expand (referred to as the ‘lift-off’ pressure) should be equal to p0, as shown in Figure 5.4(d). The value of the shear modulus is given by the following equation, derived in a later analysis by Palmer [13], in which no assumption is made regarding the stress–strain characteristics of the soil. For expansion of a borehole cavity at small strains it was shown that G ¼ 1 2 dp d"c ð5:6Þ The modulus should be obtained from the slope of an unloading–reloading cycle as shown in Figure 5.4(d), ensuring that the soil remains in the ‘elastic’ state during unloading. Wroth [20] has shown that, in the case of a clay, this requirement will be satisfied if the reduction in pressure during the unloading stage is less than 2cu. For a saturated clay the undrained shear strength (cu) can also be obtained from the following equation derived from the analysis of Gibson and Anderson: p ¼ p1 þ cu ln �V V � � ð5:7Þ where �V/V is the current volumetric strain. It should be noted that Equation 5.7 is relevant only after the plastic state has been reached in the soil (i.e. when pf < p < p1). The plot of p against ln (�V/V) should become essentially linear for the final stage of the test as shown in Figure 5.4(c), and the value of cu is given by the slope of the line. Elasticity and plasticity 143 In Palmer’s analysis it