Literature Review

Appendix 2.1: Several Empirical Correlations Reported by Kulhawy and Mayne (1990)

This appendix summarizes several empirical correlations reported by Kulhawy and Mayne (1990). Table 2.8 shows empirical correlations between standard penetration test (SPT) N-value and effective friction angle of sands, the relative density of which ranges from very loose to very dense. When the SPT N-value is less than 4, the effective friction angle is less than 28° by Peck et al. (1974) or less than 30° by Meyerhof (1956). The effective friction angle increases as the SPT N-value increases. When the SPT N-value is greater than 50, the effective friction angle is greater than 41° by Peck et al. (1974) or greater than 45° by Meyerhof (1956).

Table 2.8 Relationship between SPT N-value and effective friction angle of sand (after Kulhawy and Mayne 1990)

Table 2.9 gives an empirical correlation between cone tip resistance measured by cone penetration test (CPT) and effective friction angle of sands, the relative density of which ranges from very loose to very dense. As the cone tip resistance increases from less than 2.0 MPa to larger than 20 MPa, the effective friction angle increases from less than 30° to larger than 45°.

Table 2.9 Relationship between cone tip resistance q _c and effective friction angle of sand (after Kulhawy and Mayne 1990)

Table 2.10 summarizes the minimum and maximum of the typical dry unit weight of sands, including silty sand, clean sand, micaceous sand, and silty sand and gravel. The minimum and maximum of the dry unit weight range from 13.6 kN/m³ to 14.0 kN/m³ and from 20.0 kN/m³ to 22.9 kN/m³, respectively.

Table 2.10 Typical soil unit weight of sand (after Kulhawy and Mayne 1990)

Table 2.11 summarizes typical effective friction angles of sands. Typical effective friction angles of loose and dense uniform sands with round grains are 27.5° and 34.0°, respectively. Typical effective friction angles of loose and dense well-graded sands with angular grains are 33.0° and 45.0°, respectively. Typical effective friction angles of loose and dense sandy gravels are 35.0° and 50.0°, respectively. In addition, typical effective friction angles of loose and dense silty sands range from 27.0° to 33.0° and from 30.0° to 34.0°, respectively. For loose and dense inorganic silts, their typical effective friction angles range from 27.0° to 30.0° and from 30.0° to 34.0°, respectively.

Table 2.11 Typical values of effective friction angle of sand (after Kulhawy and Mayne 1990)

Figure 2.7 shows variation of effective friction angle of soils as a function of dry unit weight, relative density, and soil type. The effective friction angle increases as the dry unit weight and relative density increase. Figure 2.8 shows an empirical correlation between cone tip resistance $q_{c}$ measured by CPT and the effective friction angle $\phi^{\prime }$ of sands, which is a semilog regression equation

$$ \phi^{\prime } = 17.6 + 11.0\,\log \left( {\frac{{q_{c} /p_{a} }}{{\sqrt {\sigma_{v0}^{'} /p_{a} } }}} \right) $$

(2.17)

in which $\sigma_{v0}^{{^{\prime } }}$ and $p_{a}$ are vertical effective stress and standard atmospheric pressure (i.e., 0.1 MPa), respectively. Figure 2.9 shows an empirical correlation between SPT N-value (i.e., N _SPT) and undrained Young’s modulus $E_{u}^{{}}$ of clay, and it is written as

$$ E_{u}^{{}} /p_{a} = 19.3N_{\text{SPT}}^{0.63} $$

(2.18)

In Eq. (2.18), the undrained Young’s modulus $E_{u}^{{}}$ of clay is measured by pressuremeter tests.

Fig. 2.7

Relationship between the normalized dry unit weight and effective friction angle (after Kulhawy and Mayne 1990)

Fig. 2.8

Regression between normalized cone tip resistance and effective friction angle (after Kulhawy and Mayne 1990 and Wang et al. 2010)

Fig. 2.9

Regression between SPT N-value and undrained Young’s modulus of clay (after Ohya et al. 1982; Kulhawy and Mayne 1990; Phoon and Kulhawy 1999b and Wang and Cao 2013)