Nonlinear compression

Nonlinear Compression Deformation 

1.1 Modulus Degradation

The following figure shows the modulus degradation of unstructured clays and uncemented sands. The generalized form may be given as (Fahey & Carter, 1993):

       (32)

Where,

q is the deviator stress,

qult is the strength of soil

Figure 8 Monotonic Modulus Reduction Curves from (a) Static Torsional and Triaxial Shear Data on Clays and Sands, and (b) Using Modified Hyperbolic Expression Proposed by Fahey & Carter (1993, after Mayne et al., 2007)

Mayne et al. (2007) suggested that values of f=1 and g=0.3±0.1 be used as reasonable first-order estimates for unstructured clays and uncemented materials. Eq. (26) can be rewritten as

       (33)

The could be expressed in various forms as

               (34)

Where,

σz is the induced vertical stress by footing pressure, q;

(σz)ult  is the induced vertical stress under ultimate bearing capacity, qult.

1.2 Poisson's ratio

If shear wave velocity (Vs) and compressive wave velocity (Vp) data is available, Poisson's ratio can be calculated based on the following equation.

       (35)

If Vs and Vp are not available, geotechnical engineers usually rely on tabulated values such as those in the following table (Coduto, 2010).

* Adapted from Kulhawy, et al., 1983

The variation of Poisson's ratio with the parameter DR is shown in the following figure.

Figure 9 Poisson's ratio

For sandy soil, 

               (36)

For clayey soil,

               (37)

Where, 

               (38)

       (39)

       (40)

For sandy soil, DR is the relative density of the soil. For clayey soil, DR can be simply considered as a parameter.

1.3 Compression Deformation

       (41)

               (42)

are calculated from Eqs. (9), (10), and (11) or (17), (18), and (20). is calculated from Eqs. (31), (32), or (33).

1.4 Stiffness based on SPT, CPT and Vs data

Shear modulus at small strain is determined by 

       (43)