# Static Properties of Kaolinite Samples from Different Structures and the Influence of Strain Rate
## 4 Determination of Strain Rate and Experimental Details
### Shear Strength Formula Considering the Influence of Strain Rate  
#### 5.3.1 Strain Rate Sensitivity Parameter  
[PERSON] and [PERSON] [33] statistically analysed the effects of the strain rate on the shear strength of various clays and concluded that the undrained shear strength of clay increases with the strain rate. For every order-of-magnitude increase in strain rate, the undrained shear strength increased by approximately 10%. They summarised an empirical formula for the shear strength (Equation (6)), where the reference strain rate was 1%/h. \[\frac{S_{u}}{S_{u,\varepsilon=1\%}}=1+0.1\log\dot{\epsilon} \tag{6}\]  
where \(\dot{\epsilon}\) is the strain rate, \(S_{u}\) is the undrained shear strength corresponding to this strain rate, and \(S_{u,\varepsilon=1\%}\) is the undrained shear strength corresponding to a strain rate of 1%/h. [PERSON] et al. [34] conducted a series of triaxial undrained shear tests on Boston blue clay with over-consolidation ratios ranging from 1 to 8 and strain rates ranging from 0.05%/h to 50%/h. They concluded that the strain rate has a major impact on the shear strength in triaxial undrained shear tests and introduced a strain rate sensitivity parameter (\(\rho\)). \[\rho=\left[\Delta S_{u}\big{/}S_{u0}\right]/\Delta\mathrm{lg}\dot{\epsilon}_ {a} \tag{7}\]  
where \(\Delta S_{u}\) is the increase in the shear strength, \(S_{u0}\) is the undrained shear strength value obtained at the reference strain rate, and \(\dot{\epsilon}_{a}\) is the strain rate. By combining Equations (6) and (7), we can obtain the formula for the shear strength by considering the effect of the strain rate,  
\[S_{u2}-S_{u1}=\rho\cdot S_{u1}\cdot\mathrm{lg}[\epsilon_{2}/\epsilon_{1}] \tag{8}\]  
Figure 12: Deviatoric stress–axial-strain relationships: (**a**) flocculated and (**b**) dispersed samples. where \(\varepsilon_{1}\) represents a certain strain rate, \(S_{u1}\) represents the corresponding shear strength at that strain rate, \(\varepsilon_{2}\) represents another strain rate, and \(S_{u2}\) represents the corresponding shear strength at that strain rate. Within a certain range, the relationship between the shear strengths corresponding to any two strain rates is linear. The slope of the line represents the strain rate sensitivity parameter (\(\rho\)). It is worth noting that some scholarly research indicates that when the strain rate is below a certain threshold value (approximately 0.01%/min), further reduction in the strain rate does not lead to a decrease in strength; however, other scholars did not observe the same phenomenon when their experiments reached similar conditions. The effect of the overconsolidation ratio on the strain rate parameter does not exhibit a clear pattern, and this formula is applicable to normally consolidated clay [35]. [PERSON] [36] conducted triaxial undrained shear tests on structured and destroyed samples of Grande-Balene (G-B) clay and Olag clay at various strain rates to obtain the shear strengths of un-disturbed and re-moulded clays at different strain rates. Combining this finding with the shear strength data of the two structured kaolin samples at different strain rates, the relationship between the shear strength and strain rate for different types of clay is shown in Figure 13. The stronger the structure of the clay, the higher its shear strength, and the relationship between the shear strength and strain rate aligns with Equation (8). The data for the six lines in the figure exhibit relatively low dispersion results. The slope of the straight lines in the figure represents the strain rate sensitivity parameter (\(\rho\)) of the clay. The strain rate sensitivity parameters of the six samples are summarised in Table 6. The results show that the structure has an impact on the strain rate sensitivity parameters, and the extent of this impact varies among different types of clay. These findings suggest that both structure and strain rate influence shear strength.