# One-Dimensional Consolidation Properties of Soft Clay under Multi-Stage Loading
## 5 Engineering Application Analysis  
The expressway is constructed on soft soil subgrade, with a thickness of 6 m. To improve the foundation, multi-staged surcharge consolidation is performed. The loading path consists of four stages: 50\(\rightarrow\)100\(\rightarrow\)150\(\rightarrow\)200 kPa. Each load is applied after the foundation appears consolidated and stable. The simplified model, shown in Figure 6, does not consider the drainage plate. According to the traditional Terzaghi theory, engineers believed that the consolidation coefficient remains constant in engineering design. They assumed that the consolidation coefficient under the initial load is the same as the consolidation coefficient throughout the entire consolidation process. In practical engineering, the consolidation coefficient can vary significantly due to factors such as consolidation stress and permeability coefficient. This paper investigates the variations in the degree of consolidation and settlement of the roadbed, calculated using [PERSON]'s one-dimensional consolidation equation, before and after applying the proposed correction. The study is based on [PERSON]'s theory of one-dimensional consolidation. Figure 7 illustrates the initial degree of consolidation calculated using the modified [PERSON] one-dimensional consolidation equation as 0. As consolidation progresses, the degree of consolidation gradually increases and eventually stabilizes when \(U_{t}=1\). However, the time taken for stabilization is significantly shorter before the modification compared to that after the modification. This is because the modified Terzaghi equation considers the influence of overburden load on consolidation stability, taking into account the decrease in pore ratio and permeability coefficient. In contrast, the traditional [PERSON] theory assumes a constant consolidation coefficient, resulting in a degree of consolidation prediction that  
Figure 6: Simplified diagram of model. is independent of the load. It is important to note that the \(U_{t}\)-\(t\) curve corresponding to different overlying loads (\(P\) = 50, 100, 150, and 200 kPa) is the same, which contradicts actual engineering observations. The relationship between load and consolidation can be observed from Figure 7. It shows that a smaller load leads to a greater degree of consolidation per unit time and a faster consolidation rate. For instance, when the degree of consolidation (\(U_{t}\)) reaches 0.95, the corresponding time required for different overlying loads (\(P\)) of 50, 100, 150, and 200 kPa is 1.23, 1.73, 2.05, and 2.63 years, respectively. Therefore, the loading time increases linearly for each level of load, and the consolidation time can be appropriately extended based on the foundation's strength to minimize post-construction settlement. In Figure 8, during the initial stage of soft foundation consolidation, the initial settlement (\(S_{ct}\)) is equal to 0. As the consolidation process progresses, \(S_{ct}\) gradually increases and eventually stabilizes at \(S_{c}\). Additionally, the settlement stability time predicted via the modified Terzaghi one-dimensional consolidation equation is greater than that predicted via the traditional Terzaghi one-dimensional consolidation equation. When the load is small (\(p\) = 50 kPa), the impact on the void ratio and permeability coefficient of a soft foundation is not significant, and the consolidation coefficient undergoes minimal change. The \(S_{t}\)-\(t\) relationship curves before and after the modification are relatively consistent. The void ratio and permeability coefficient of a soft foundation are significantly affected by a large load (\(p\) = 200 kPa). There is a large error of 0%-25% in the settlement-time relationship curve before and after correction. Hence, when the load is small, the influence of load on consolidation rate and settlement rate during the compression of a soft foundation can be disregarded.