# One-Dimensional Creep Consolidation Model for Peat Soil
## 2 Materials and Methods
### Viscoelasticplastic Constitutive Relation of Peat Soil
When the load is less than the pre-consolidation pressure, the elastic and time-independent plastic strains increase with the increase in \(\ln\sigma_{z}^{\prime}\) at a relatively low rate (\(\kappa\), \(\zeta\)). The strain in the primary and secondary consolidation stages of the low organic peat soil also have a linear relationship with \(\ln\sigma_{z}^{\prime}\). When the load is greater than the pre-consolidation pressure, the strain change law of the low organic peat soil is consistent with that of the other peat soils. At this time, the strain modulus of the peat soil increases significantly, and its slope is represented by \(\kappa^{\prime}\), \(\zeta^{\prime}\). Therefore, the elastic strain can be expressed as follows:  
\[\epsilon_{z}^{e}=\epsilon_{z0}^{e}+\kappa\ln(\frac{\sigma_{z}^{\prime}}{ \sigma_{zref}^{\prime}}) \tag{8}\]  
where \(\sigma_{zref}^{\prime}\) is the reference effective stress (kPa). When the load is less than the pre-consolidation pressure, it is considered as the initial effective stress \(\sigma_{z0}^{\prime}\); and when the load is greater than the pre-consolidation pressure, it is considered as the pre-consolidation stress \(\sigma_{z0}^{\prime}\);  
\(\epsilon_{z0}^{e}=\) strain value when \(\sigma_{z}^{\prime}=\sigma_{zref}^{\prime}\);  
\(\kappa=\) slope of \(\epsilon_{z}^{e}\sim\ln\sigma_{z}^{\prime}\). When the load is greater than the pre-consolidation pressure, \(\kappa\) is considered as \(\kappa^{\prime}\). The time-independent plastic strain can be expressed as follows:  
Figure 7:0  
Figure 7:1 Strain versus stress curve at primary and secondary consolidation stages. where \(\varepsilon_{z0}^{sp}=\) strain value at \(\sigma_{z}^{\prime}=\sigma_{zref}^{\prime}\);  
\(\zeta=\) slope of \(\varepsilon_{z}^{sp}\sim\ln\sigma_{z}^{\prime}\). When the load is greater than the pre-consolidation pressure, \(\zeta\) is considered as \(\zeta^{\prime}\). According to Equations (8) and (9), the time-independent elastic-plastic strain can be expressed as Equation (10). The strain diagram of the peat soil is shown in Figure 7:2  
Figure 7:3  
Figure 7:4  
Generally, the viscous strain of soft soil is calculated according to the secondary consolidation coefficient in the \(d-\log t\) curve. For peat soil, the viscous strain rate is the strain rate of the tertiary consolidation stage and can be expressed as Equation (12). Figure 7:5  
Figure 7:6  
where \(\varepsilon_{z}^{tp}=\) viscous strain;  
\(\eta=\) slope of the strain curve \(\varepsilon_{z}\sim t\) in the tertiary consolidation stage (viscous strain stage), as shown in Figure 11;  
\(t_{ref}=\) reference time for the onset of viscous strain (min);  
\(t_{e}=\) creep duration, that is, the equivalent time (min). Therefore, the modified nonlinear rheological model of the peat soil can be expressed as shown in Figure 7:7  
Figure 7:8 Schematic diagram of viscous strain curve. Figure 7:9 Elastic-plastic strain curve. Figure 11 shows that the viscous strain of the peat soil grows at a stable low rate for a long time, and its creep rate hardly changes. Therefore, the difference between the nonlinear rheological model of the peat and the soft soils is that its viscous strain rate (\(\dot{\epsilon}_{tz}^{tp}\)) may be equal to the viscous strain rate (\(\dot{\epsilon}_{tzref}^{tp}\)) of the normal consolidation line, that is, \(\dot{\epsilon}^{tp}\geq\dot{\epsilon}_{ref}^{tp}\) on the upper side of the normal consolidation line, with \(\dot{\epsilon}^{tp}\leq\dot{\epsilon}_{ref}^{tp}\) on the lower side, as shown in \[\epsilon_{z}=\epsilon_{z}^{e}+\epsilon_{z}^{sp}+\epsilon_{z}^{tp} \tag{3}\]0  
According to Equations (3)-(13), the viscoelastic-plastic constitutive equation for the peat soil is as follows:  
\[\epsilon_{z}=\epsilon_{z}^{e}+\epsilon_{z}^{sp}+\epsilon_{z}^{tp} \tag{3}\]1  
Equation (14) is the deformation calculation formula for peat soil, which was obtained based on the timeline model proposed by [PERSON] and [PERSON].