# Compound Instability Effect and Countermeasures of Pit-in-Pit in Collapsible Loess Strata
## 2 Instability Mechanism
### Complex Stress System of Pit-in-Pit Structure  
Foundation pit engineering has strong practicality and particularity in the construction process; it needs to constantly monitor and analyze and dynamically adjust the project [28]. In this section, the complex stress system of pit-in-pit is analyzed theoretically based on  
Figure 1: Foundation pit disaster in loess area [27].  
Figure 2: Typical structure of pit-in-pit.  
classical earth pressure theory [29]. Figure 2 shows the complex stress system of the pit-in-pit structure, where the \(w\) is the distance between the inner pit and the outer pit, the \(h\) is the depth of the inner pit, and the \(b\) is the width of the inner pit. At this time, the overall stress state of the foundation pit becomes complicated and the soil pressure of the outer pit needs to be calculated by finite element software [30]. In the process of foundation pit excavation, as the soil is removed, the load on it is reduced, which will cause the soil at the bottom of the pit to produce an upward displacement tendency. If the excavation of the internal foundation pit continues, it will cause a change in the stress field and displacement field. Meanwhile, as the foundation pit system is in such a complex stress system, there is a great risk of settlement in the adjacent areas and on the surface caused by unloading.  
Before the excavation of the foundation pit, the lateral earth pressure distribution curve of the soil was \(OA\) and the static lateral pressure coefficient was \(K_{0}\)n. After the excavation of the foundation pit, the actual lateral earth pressure distribution curve became \(BA^{\prime}\). Due to the influence of unloading, the soil below the bottom of the pit is in a super-consolidated state. At this time, the static earth pressure coefficient increases to \(K_{0}\), where the \(K_{0}=K_{0}\)OCR\({}^{\beta}\). The excavation of a pit within a pit will cause the earth pressure acting on the pit within a pit retaining body to develop from the static lateral earth pressure distribution curve \(BA^{\prime}\) to the active earth pressure curve [31]. When designing the retaining structure of a pit within a pit, if the stress path change is not considered but it is believed that the earth pressure develops from the curve \(BA^{\prime\prime}\) to the active earth pressure curve like in ordinary foundation pits, the magnitude of the earth pressure will be seriously underestimated. Thus, a complex stress system architecture involving the interaction of internal and external foundation pits is constructed, as shown in Figure 3.  
At the same time, for the finite soil pressure in the pit, the angle between the failure plane and the horizontal plane is no longer the fixed value in the classical Rankine and Coulomb soil pressure theory \(45^{\circ}-\varphi/2\). It is a function of the soil mechanical properties, the distance between the inner pit and the outer pit envelope, and the width and depth of the pit in the calculated depth [32]. The above characteristics determine the complexity of the calculation of the force in the pit and the sensitivity of the parameters. When the pit in the pit is excavated in a special stratum, the complexity of the system will be further amplified [33], so the compound instability effect of the pit in the collapsibility loess stratum needs to be discussed separately [34].  
Figure 3: Pit-in-pit complex stress system.