# Compound Instability Effect and Countermeasures of Pit-in-Pit in Collapsible Loess Strata
## 2 Instability Mechanism
### Characteristics of Collapsible Loess Degraded by Water  
Loess exhibits relatively high shear strength in a dry environment. However, when exposed to water, its shear strength decreases. The most important factors affecting the change in the soil shear strength are the weakening of cementation and the change of pores [35], as shown in Figure 4. The undisturbed loess structure was transformed by leaching, which provided favorable conditions for disintegration caused by water infiltration. The presence of matric suction further accelerates this infiltration, causing the pore pressure inside the soil to rapidly increase until disintegration occurs [36].  
For foundation pit engineering, when rainfall or groundwater begins to infiltrate the foundation pit soil, the soil strength is reduced to a critical value and instability failure will occur, as shown in Figure 4. At the same time, for unsaturated loess, due to the influence of its compaction and structural strength [37], the shear strength index of loess has its unique properties and the strength envelope also shows a special law, which does not fully conform to the Mohr-Coulomb criterion [38].  
According to [PERSON]'s analysis of the undrained shear test data of collapsible loess, the envelope line of unsaturated loess is not straight, but a broken line composed of two straight lines and the turning point of the broken line is related to the structural strength [38]. The \(\sigma_{c}\) is the normal stress at the critical point of structural strength and the two sections represent different structures and deformation forms of unsaturated loess. The front section maintains its original structure with small failure strain, while the latter section experiences significant structural changes and a loss of strength. The shear strength of collapsible undisturbed loess is expressed by a sectional line as follows:  
\[\tau=\left\{\begin{array}{ll}\sigma\mathrm{tg}\varphi_{1}+c&\sigma<\sigma_ {c}\\ \sigma_{c}\mathrm{tg}\varphi_{1}+(\sigma-\sigma_{c})\mathrm{tg}\varphi_{2}+c &\sigma>\sigma_{c}\end{array}\right. \tag{1}\]  
The shear strength of soil is not only related to the properties of soil, but also to the drainage conditions, shear rate, stress state, stress history, and many other factors during the test, among which the most important are the drainage conditions during the test. According to the principle of effective stress, the effective stress strength parameter should  
Figure 4: Deterioration mechanism of loess immersed in water and instability engineering of foundation pit.  
be obtained from \(\tau_{f}=c^{\prime}+\sigma^{\prime}\tan\varphi^{\prime}\). Figure 5 shows the soil shear strength index obtained by [PERSON] through the triaxial CU test. The data obtained from the test are fitted through spline functions, in which the soil shear strength index also changes with the change in the water content \(w\), the cohesion index, and \(c\) decrease with the increase in the water content, but the friction angle and effective friction angle fluctuate with the change in the water content.  
Numerous studies and reports on loess have confirmed that for loess in different regions, the change in the shear strength index is different [39; 40], but all change with the water content, which is determined by the essential characteristics of loess. The general expression of the soil shear strength index is as follows:  
\[(c,\varphi)=f(w) \tag{2}\]