Analysis in terms of total stresses
Cohesive soils
If the analysis is performed in terms of total stresses, the value of the undrained cohesion cu must be reduced compared to the static case to take account of the degradation consequent to the cyclical nature of seismic stresses. Is generally neglected in favor of safety, the possible increase of the undrained strength, which can manifest in cohesive soils of high plasticity due to the high speed of application of the loads. An estimate of the reduction coefficient of the undrained strength, δcu can be obtained using the equation:
Where N is the number of load cycles induced by the earthquake and t is a parameter of degradation that can be estimated with the following relation:
The function of the cyclic shear strain γc and of the volumetric strain, the last one assessed as outlined above. The values of S and r can be estimated as a function of the plasticity index, PI and the over-consolidation ratio OCR as reported in the following table:
|
OCR=1 |
OCR=2 |
OCR=4 |
||
|---|---|---|---|---|---|
|
PI=15 |
PI=30 |
PI=50 |
PI=50 |
PI=50 |
s |
0.195 |
0.095 |
0.075 |
0.054 |
0.042 |
r |
0.600 |
0.600 |
0.495 |
0.480 |
0.423 |
Coefficients for the calculation of the cyclic degradation (Matasovic,1993)
The number of N cycles can be evaluated by calculating the number of intersections with the time axis in the time interval between the first and last exceeding of a predetermined acceleration threshold (usually equal to 0.05 g). For the cyclic shear strain γc can be used the following relation:
In which the value of the shear modulus G is determined by an iterative process from the curve (G-γ) obtained from laboratory tests and τeq is calculated with the formula discussed earlier.
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