# One-Dimensional Creep Consolidation Model for Peat Soil
## 2 Materials and Methods
### Viscoelasticplastic Constitutive Relation of Peat Soil  
[PERSON] and [PERSON] [26] and [PERSON] and [PERSON] [11] proposed the theory of using equivalent time to calculate viscous strain. However, due to the particularity of the deformation process of peat soil, the deformation parameters of peat soil are not applicable to the timeline theory. Therefore, the stress and strain of the peat soil were analyzed here. The consolidation process of peat soil can be divided into the primary consolidation stage of elastic deformation, the secondary consolidation stage of plastic deformation (can  
Figure 6: Rebound deformation of 100 kPa load test group. Figure 7: Ratio of rebound deformation to deformation at the primary consolidation stage. be divided into time-independent and time-dependent parts), and the tertiary consolidation stage of viscous deformation. The strain can be expressed by Equations (3)-(5). \[\epsilon_{z}=\epsilon_{z}^{e}+\epsilon_{z}^{sp}+\epsilon_{z}^{tp} \tag{3}\]  
\[\epsilon_{z}^{sp}=\epsilon_{z}^{sp}+\epsilon_{z}^{tp} \tag{4}\]  
\[\epsilon_{z}^{cp}=\epsilon_{z}^{e}+\epsilon_{z}^{sp} \tag{5}\]  
where \(\epsilon_{z}^{e}\) = elastic strain (recoverable strain after unloading);  
\(\epsilon_{z}^{sp}\) = time-independent plastic strain (unrecoverable strain unaffected by loading time);  
\(t_{z}^{tp}\) = viscous strain (unrecoverable strain affected by loading time);  
\(\epsilon_{z}^{sp}\) = viscoplastic strain (unrecoverable strain after unloading);  
\(\epsilon_{z}^{sp}\) = time-independent elastic-plastic strain. The elastic strain of the peat soil primarily occurred in the primary consolidation stage because the skeleton of the soil was destroyed in the tertiary consolidation stage, and the elastic strain was not equal to the rebound. Therefore, the elastic strain was calculated by accumulating the strain in the primary consolidation stage, as shown in Equation (6) and Figure 8.  
\[\epsilon_{z}^{e}=\sum_{i=1}^{n}\epsilon_{zi}^{e} \tag{6}\]  
where \(\epsilon_{z}^{e}\) = elastic strain;  
\(\epsilon_{z}^{e}\) = elastic strain of the \(i\)-th load. The secondary consolidation stage of the peat soil produces plastic strain, including time-independent plastic strain and time-dependent plastic strain (viscous strain). The time-independent plastic strain was calculated using the strain accumulation method. The rate of viscous strain (\(R_{ter}\)) is the slope of the stress-strain curve during the third consolidation stage. According to Figure 5, \(R_{ter}\) changed insignificantly with time during the loading process. Therefore, the time-independent plastic strain can be calculated by subtracting the viscous strain from the strain in the secondary consolidation stage, as expressed in Equation (7). \[\epsilon_{zi}^{sp}=\epsilon_{zzi}-R_{ter,i}\big{(}T_{sec,i}-T_{pri,i}\big{)} \tag{7}\]  
where \(\epsilon_{zi}^{sp}\) = time-independent plastic strain of the \(i\)-th load;  
\(\epsilon_{zzi}\) = strain in secondary consolidation stage of the \(i\)-th load;  
\(R_{ter,i}\) = viscous strain rate of the \(i\)-th load (/min);  
\(T_{pri,i}\) = completion time of the primary consolidation stage for the \(i\)-th load (min);  
\(T_{sec,i}\) = completion time of the secondary consolidation stage for \(i\)-th load (min). Figure 9 shows the strain curves of the peat, highly organic peaty soil, and medium organic peaty soil. The consolidation process of low organic peaty soil is divided into two stages when the load is less than the pre-consolidation pressure. At this time, the strain is  
Figure 8: Schematic of strain accumulation curve. divided into the strains in the primary and secondary consolidation stages. When the load is greater than the pre-consolidation pressure, it is divided into three stages [27]. Therefore, the strains in low organic peaty soils must be discussed separately. Figure 9 shows that both the elastic and time-independent plastic strains of the peat soil exhibit a two-stage linear relationship with \(\ln\sigma_{z}^{\prime}\).