Earthquakes - Geotechnical Engineering Investigation - page 941

Characteristic Properties of Soils under Cyclic Strain
Shear modulus G (see Table 3.26 and Figure 3.33) is the relation between shear stress and
shear strain, which occurs under small amplitudes, such as earthquake loads.
Internal damping ratio D or

(see Figure 3.33) pertains to the dissipation of energy dur-
ing cyclic loading. Shear modulus and damping are the most important characteristics
required for the analysis of most situations.
Strength and stress-strain relationships in general must be considered for large deforma-
tions such as are produced by sea-wave forces on pile-supported structures.
Poisson's ratio

λ

is required for the description of dynamic soil response, but varies
within relatively close limits and affects seismic response only slightly. It is independent
of frequency in the range of interest in earthquake engineering, and in contrast to E and
G , is insensitive to thixotropic effects. General ranges are

ν

ν 0.25 to 0.35 for cohesionless

soils and ν 0.4 to 0.5 for cohesive soils.

Soil Reaction to Dynamic Loads
Initially , cyclic loading causes partially irreversible deformations, irrespective of strain
amplitude, and load-unload stress-strain curves do not coincide.
Subsequently , after a few cycles of similar small-strain amplitudes, differences between
successive reloading curves tend to disappear and the stress-strain curve becomes a
closed loop (see Figure 3.33). This can be described by two parameters: shear modulus,
defined by the average slope, and damping ratio, defined by the ratio of the specific
enclosed areas as shown in the figure. It reflects the energy that must be fed into the soil
to maintain a steady state of free vibration.

Cyclic Shear Related to Earthquake Characteristics
Simple shear stress-strain characteristics at low strains are important in site response
analysis because the significant earthquake strain amplitudes normally do not exceed
10 4 or 10 5 , and are usually in the range of 10 1 to 10 3 . Higher strains might occur dur-
ing site response to a large earthquake, but the number of cycles at high strain amplitude
are likely to be few.
The effect of the number of cycles at low strain amplitudes is not great.
The effect of loading frequency is negligible within the range encountered in most earth-
quakes, i.e., 0.1 to 20 Hz.
Strain amplitude is the most significant characteristic. Shear modulus decreases markedly
with an increase in strain amplitude as shown in Figure 3.33 (Taylor and Larkin, 1978).

Shear Modulus and Damping Ratio
Factors Affecting Values
Main factors affecting values for shear modulus and damping ratio in all soils are shear
strain amplitude, initial effective mean principal stress, void ratio, shear stress level, and
the number of loading cycles.
Cohesive soil values are affected also by stress history (OCR), saturation degree, effective
strength parameters, thixotropy, and temperature.
Shear strain amplitude affects the shear modulus as follows:
●

Cohesionless soils : Shear modulus G decreases appreciably for amplitudes greater
than 10 -4 , below which G is nearly constant

Cohesive soils : G decreases with increase in amplitude at all levels (Faccioli and
Resendiz, 1976)

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