Cyclic Shear Tests: Dynamic Properties 143 describes that the rate of generation of excess pore water pressure affected significantly by frequency of cyclic loading. The loading frequency of 1 Hz shows lesser rate of generation of excess pore water pressure compared to other frequency.
Fig. 5.37 Variations of ru and shear strain with loading frequency for N = 1
Fig. 5.38 Variations of ru with number of loading cycles at different loading frequencies
Cyclic Shear Tests: Dynamic Properties 144 from strain-controlled tests conducted at different γ (considering only first cycle, N = 1) and from stress-controlled tests conducted for different CSR (considering all hysteresis cycles, N = 1-40). Fig. 5.39 presents the variations in shear modulus with γ obtained from both strain- controlled and stress-controlled approach. It is seen that the results follow similar degradation pattern with minimal difference from each other. Fig. 5.40 shows the variations in damping ratio (D#) with γ obtained from both stress-controlled and strain-controlled approach. It can be noted that D# attains the peak magnitude at γ ≈ 1% from both the approaches. From the results of damping ratio variations, it can be concluded that the damping ratio varies with similar trend form both strain and stress-controlled approach, and hence the dynamic soil properties can be evaluated by both the approaches. However, due to asymmetry in hysteresis loop after few loading cycles, the stress-controlled approach misrepresents the precise estimation of dynamic properties. In such condition, strain-controlled approach can give accurate dynamic properties for any constant shear strain amplitudes. Beyond the peak shear strain of 1%, a significant reduction in damping ratio is observed at higher strain levels which are noticeably different from that observed in the damping ratio curves from earlier studies (Seed and Idriss, 1970;
Iwasaki et al., 1978; Kokusho, 1980; Seed et al., 1986; Vucetic and Dobry, 1991; Stokoe et al., 1995; Govindaraju, 2005; Kirar and Maheswari, 2013). It should be noted that, for the earlier studies, tests were conducted up to strain levels of about 1% only by strain-controlled approach.
Very few researchers have provided the experimental evidence of estimated damping ratio beyond 1% shear strain based on strain-controlled approach which followed a similar trend as obtained in the present study (Kiku and Yoshida, 2000; Brennan et al., 2005; Mashiri, 2014;
Matasovic and Vucetic, 1993).
Cyclic Shear Tests: Dynamic Properties 145
Fig. 5.39 Variation of shear modulus obtained from strain- and stress-controlled excitations
Fig. 5.40 Variation of damping ratio obtained from strain- and stress-controlled excitations
TESTS ON DRY COHESIONLESS SOIL
Strain-controlled cyclic triaxial tests were conducted on dry cohesionless soil (DBS) specimens.
A typical plot of input and output of DBS specimen at an axial strain of 0.20% subjected to f = 1 Hz for 40 cycles and effective confining pressure (σʹc) of 100 kPa is presented in Fig. 5.41.
Fig. 5.41a depicts the applied axial strain on to the specimen. Fig. 5.41b shows the variation of
0.01 0.1 1 10
0 10 20 30 40 50 60
Strain-controlled
, f = 1 Hz N = 1
'c = 100kPa Dr = 60%
Stress-controlled
CSR = 0.1 0.4, f = 1 Hz
Shear modulus (MPa)
Shear strain (%)
0.01 0.1 1 10
0 10 20 30 40
Stress-controlled
CSR = 0.1 0.4, f = 1 Hz
c = 100 kPa Dr = 60%
Damping ratio (%)
Shear strain (%) Strain-controlled
f = 1 Hz N = 1
Cyclic Shear Tests: Dynamic Properties 146 deviator stress with number of cycles, which is responsible for the increase in stiffness due to particle rearrangement in each loading-unloading cycle. Fig. 5.41c shows the pore water pressure variation; since the soil is dry, the development of excess PWP will be zero. Fig. 5.41d shows the stress path variation because of zero pore water pressure. Fig. 5.41e shows the hysteresis loop during cyclic loading reflects the dissipation of energy only due to friction associated with movement of the sand particles.
Fig. 5.41 (a-d) Typical test results of DBS at ε = 0.20%, f = 1 Hz and σʹc = 100 kPa e
c d
a b
Cyclic Shear Tests: Dynamic Properties 147
Fig. 5.42 (a-j) Typical shear stress-shear strain plot for SBS at different γ for initial two cycles at Dr = 60%, σʹc = 100 kPa and f = 1 Hz
Fig. 5.42(a-j) presents the hysteresis loops for initial two cycles obtained from the strain- controlled CT tests conducted on DBS at different peak shear strain levels. It is seen that the
a c
d e
g h i
f
j
b
Cyclic Shear Tests: Dynamic Properties 148 hysteresis loops becomes gradually asymmetric with increasing peak shear strain, similar to the SBS tests. Beyond γ = 0.15%, the 1st cycle hysteresis loop is observed to be asymmetric, as can be noted from the stark dissimilarity in shear stress magnitude in compression and tension side (Fig. 5.42d-j). Thus, in the present study, only the 1st cycle of loading and the corresponding hysteresis loop has been chosen for the evaluation of dynamic properties, as described in section 5.3.1.
Effect of shear strain and confining pressure on dynamic shear properties
The variation of shear modulus and damping ratio of DBS for 1st loading cycle are presented in Fig. 5.43 and Fig. 5.44, respectively. Fig. 5.43 reflects the rapid decrease of shear modulus with the increase of shear strain amplitudes (γ), and increase in the same with the increase of confining pressure at any particular shear strain amplitude.
Fig. 5.43 Variation of shear modulus of DBS with shear strain at different σʹc from strain- controlled tests
Fig. 5.44 indicates that the soil damping is strongly influenced by both the shear strain amplitude and effective confining pressure. It shows the variations in damping ratio of DBS
Cyclic Shear Tests: Dynamic Properties 149 with shear strain using symmetrical (D) and modified (D#) approach. It has been observed that D# is significantly higher than D and exhibits an asymptotic trend. The damping ratio (D) exhibits non-conventional behaviour beyond shear strain of 1%. From the scatter plot of D and D# at σ′c = 50 kPa, 100 kPa and 150 kPa, it can be stated that the effect of σ′c is not significant over the tested range of shear strain. Therefore, an average line was plotted for practical purposes. It can be observed that for DBS, D# is greater than D. The difference between D# and D is around 20-40% in between the range of shear strain 0.15%-0.50% and this difference increase more than 100% with the increase of shear strain beyond 0.50% (Fig. 5.44).
Fig. 5.44 Variation of damping ratio of DBS with shear strain at different σʹc from strain- controlled tests