# One-Dimensional Creep Consolidation Model for Peat Soil
## 1 Introduction  
Peat soil is a loose and water-rich aggregate of organic matter formed by the sedimentation of dead plants in swamps and lakes [1, 2] and comprises about 5-8% of the total area of the Earth. Peat soil has a high water content [3, 4], therefore, its compressibility is significantly higher than that of general soft soil [5]. The unique properties of peat soils present significant challenges in geotechnical engineering, particularly for infrastructure projects such as highways and railroads. In the process of building highways and railroads, according to the requirements of line smoothness, when the peat soil layer cannot be avoided, the shallow peat soil layer can be removed, but for the deep peat soil layer, replacement is difficult and costly. At this time, it is necessary to use stack preloading in order to reduce post-construction settlement. However, due to the unclear deformation properties and stress-strain relationships, the accuracy of settlement calculation for peat foundation is affected, which restricts engineering construction. Therefore, analyzing the settlement patterns of peat soil foundations contributes to the refinement of the soil mechanics theory, while also reducing construction costs and enhancing engineering quality. The deformation of peat soil is significantly influenced by water and organic matter [6]. [PERSON] and [PERSON] [7] categorized peat soils as amorphous and fibrous peaks and proposed that amorphous peat soil is primarily composed of colloidal particles, whereas fibrous peat soil primarily contains undecomposed plant fibers. According to this classification, [PERSON] and [PERSON] [8] proposed two constitutive models. Firstly, based on therheological model proposed by [PERSON] and [PERSON] [9], the nonlinear compression of the soil was simulated using a nonlinear spring, and the constitutive relationship of amorphous peat was established, as shown in Figure 1 and Equation (1). After the application of a load, spring P\({}_{1}\) experiences immediate compression, while, due to the existence of the Kelvin element, the compression of spring P\({}_{2}\) occurs at a more gradual pace, leading to deformation that will persist over a period of time, known as creep. Secondly, based on the pore characteristics of peat soil proposed by [PERSON] [10], [PERSON] and [PERSON] [8] used the dual Terzaghi consolidation model to simulate the macropores and micropores (Figure 2) and established the constitutive relationship of fibrous peat. \[\varepsilon(t)=\Delta\sigma[a+b(1-e^{-(\lambda/b)t})] \tag{1}\]  
where \(\Delta\sigma\) = increment in stress;  
\(t\) = time;  
\(a\) = consolidation coefficient;  
\(b\) = coefficient of secondary consolidation;  
\(\lambda/b\) = secondary consolidation rate factor. The theoretical models can describe the deformation characteristics of peat soil in the primary and secondary consolidation stages; however, it cannot accurately describe the law of strain changes with time. [PERSON] and [PERSON] [11] proposed a timeline model for clay, in which the creep strain rate was constant in the normal consolidated state. The strain exhibited a linear relationship with the logarithm of the effective stress and creep strain rate. [PERSON] [12] proposed the abc consolidation model of peat one-dimensional compression, assuming a constant relationship between the strain, the effective stress, and the creep strain rate. [PERSON] [13] proposed that the abc model is not suitable for over-consolidated soils, because the equidistant lines of over-consolidated soils are neither parallel nor linear. [PERSON] and [PERSON] [3] and [PERSON] and [PERSON] [14] proposed that peat soil conforms to the \(C_{\alpha}/C_{c}\) law, that is, the ratio of the secondary consolidation coefficient to the compression coefficient is stable, and proposed that the range for peat soil is 0.05-0.07. [PERSON] et al. [15]  
Figure 1: Rheological model of secondary consolidation [9]. Figure 2: [PERSON] and [PERSON]’s creep model of fibrous peat soil [8].