Stress History and In Situ Stress

At the present time, there are insufficient reliable results available to accurately predict the in situ lateral stress or stress history of coarse-grained soils from CPT results. A number of calibration chamber tests results available in clean uncemented quartz sands show that there is a unique relationship between the measured tip resistance and the effective horizontal stress, o'h (e.g., Parkin 1988; Houlsby & Hitchman 1988). While it is well known that the prepenetration state of stresses largely controls the response obtained from the CPT in sands, it is not a simple matter to extract the magnitude of in situ lateral stresses from cone data.

Elastic Modulus

The elastic modulus, E_s, of soils has also been correlated to the results of tip resistance measurements (q_c) obtained from the CPT. Most early correlations between q_c and E_s were of the general form

Figure 4.26 Updated correlation between normalized CPT tip resistance and friction angle. (From Mayne 2014.)

where

X = a constant (empirical factor)

Mitchell & Gardner (1975) compiled a large number of reported correlations, which generally show very wide scatter. Table 4.4 summarizes a number of suggestions for estimating soil modulus from CPT.

E_s in units of q_c for CPT

The use of large calibration chamber tests on reconstituted samples of sands has helped to evaluate variables that can influence correlations between soil modulus and CPT results.

Table 4.4 Some reported correlations between E_s and q_c in sands

E_s in units of q_c for CPT.

For a given sand, the ratio E/q_c is related to stress history and current stress level for sands at different relative densities. Robertson (1991) proposed that the ratio of E_s/q_c should be expressed as a function of the relative load intensity.

Because of the wide range in correlation constants that may exist between the results of in situ penetration tests and a singular value of soil modulus, it is doubtful that any method that relies on these techniques for the accuracy of settlement estimates will be of much value, other than those created by local correlations developed from full-scale field observations of performance.

Constrained Modulus

In one-dimensional compression, the tangent slope of the stress-strain curve is defined as the constrained modulus:

From elastic theory, the constrained modulus is related to the Young’s modulus and shear modulus as

Based on a series of calibration chamber tests on a dry medium to fine quartz sand, Chapman & Donald (1981) found that the initial one-dimensional constrained modulus, M, could be related to q_c. For normally consolidated conditions: the expression M = 3q_c provided a lower bound, with most data falling in the range M = 3-4 q_c. For overconsolidated specimens (with OCR < 2), the results indicated iM = 8-15 q_c with an average value of M = 12 q_c.

For a given sand, the ratio M/q_c is related to stress history and current stress level for sands at different relative densities. For both normally consolidated and overconsolidated sands, the ratio M/q_c decreases with increasing relative density, all other factors being equal. Mayne (2006) presented a compilation of test results showing a correlation between D and net tip resistance as

The value of a'. = 5 for soft to firm clays and normally consolidated sands. The global correlation between M and CPTU net tip resistance for a wide range of soils is shown in Figure 4.27.

Shear Wave Velocity and Small-Strain Shear Modulus

The small-strain shear modulus in soils may be measured using a number of field crosshole and downhole methods that are more or less considered standard techniques for dynamic testing. The shear wave velocity may also be measured directly using a seismic cone or piezocone (SCPT/SCPTU) as illustrated in Figure 4.28.

Estimates of either V_s or G_max may be obtained indirectly from CPT results through empirical correlations. G_max is obtained from V_s as

where

p = soil density

Figure 4.27 Correlation between constrained modulus and net CPTU tip resistance. (From Mayne 2006.)

Figure 4.28 Schematic of seismic CPT/CPTU.

Shear Wave Velocity and Shear Modulus from qc

Estimates of V_s and G_max in different coarse-grained soils have been suggested. Table 4.5 gives a number of reported empirical correlations. Several studies have also shown that the results of cone tests may be used to make direct estimates of G_max in coarse-grained soils. Robertson (1990) suggested a generalized approach relating G_max to normalized tip resistance that appears to be useful for estimating G_max for a wide range of soils, as shown in Figure 4.29. A similar correlation is given in Figure 4.30.

Liquefaction Potential

For over 40 years, the CPT/CPTU has been used to evaluate liquefaction potential of coarsegrained soils (Robertson &c Campanella 1985; Robertson &c Wride 1995; Stark &c Olson 1995; Idriss & Boulanger 2004; Moss et al. 2006; Juang et al. 2008). The methods generally are based on cone tip resistance, q_c or q_t, or on direct or indirect measurement of shear wave velocity (Kayabali 1996; Andrus et al. 2004). More recently, methods have also been presented incorporating CPT/CPTU friction ratio (e.g., Mola-Abasi et al. 2018). The methods are similar to approaches that use SPT N-values discussed in Chapter 2.

In general, the available methods make use of databases of CPT/CPTU results obtained at sites that experienced liquefaction and separate them from sites that did not experience liquefaction for the same seismic event. Methods are typically for earthquake with magnitude 7.5 and are based on a plot of cyclic stress ratio (CSR) that causes liquefaction and normalized cone tip resistance, as shown in Figure 4.31 for clean sands and Figure 4.32 for silty sands. The normalized tip resistance is obtained as

Table 4.5 Some reported empirical correlations between V_s and q_c for coarse-grained soils

V_s in m/s; q_c, f_s, and CT_V0 in kPa; D = depth in m; G_mJ1( in MPa.

Figure 4.29 Correlation between G_max and CPT q_c. (After Robertson 1990.)

Figure 4.30 Small strain shear modulus related to net CPTU tip resistance. (From Mayne 2006.)

where

pa = atmospheric pressure n = function of soil behavioral type (I_c)

Figure 4.31 CPT-based liquefaction potential for clean sands.

Figure 4.32 CPT-based liquefaction potential for silty sands.