# Spatiotemporal Mechanical Effects of Framework-Slope Systems Under Frost Heave Conditions
## 2 Experimental  
### Engineering Background  
The study is based on a slope reinforcement project located in Xinjiang, China. As shown in Figure 1, the slope has a height of 20 m and the local soil freezes at approximately \(-1\)\({}^{\circ}\)C. The average surface temperature during the winter half-year is around \(-20\)\({}^{\circ}\)C. The initial reinforcement scheme adopts a frame-anchor system using C30-grade concrete and HRB400-grade steel bars for the anchors. The spacing between adjacent anchors is 2 m. The elastic moduli of the concrete, anchor rods, and anchor grout body are 3 \(\times\)\(10^{4}\) MPa, 3.5 \(\times\)\(10^{5}\) MPa, and 3 \(\times\)\(10^{4}\) MPa, respectively. The anchor borehole diameter is 150 mm, and each anchor is 10 m long. The horizontal beams and vertical columns of the frame structure have design widths of 550 mm and 500 mm, respectively, with 2 m spacing between frame units.  
This slope, located in the hinterland of the Eurasian continent, is primarily composed of silty clay and features a typical temperate continental semi-humid climate. The landslide area exhibits mid-low mountain topography with distinct climatic variations, with concentrated summer rainfall influenced by monsoons and deep seasonal snow cover in winter driven by the Siberian High. This climatic pattern aligns with regions sharing comparable slope frost heave classifications--including Kazakhstan,  
Figure 1: Conceptual model of the frame-anchored slope used for THM numerical simulation.  
Asia adjacent to Xinjiang, and northwestern/northeastern China--making it a widespread engineering concern. Geological surveys confirm that the area belongs to a typical seasonal freeze-thaw cycle zone. The study area spans the Kunes River's third terrace, the Aiken Daban structural denudation platform, and the Xiaoyuludus Basin transition zone. Quaternary sediments are predominantly fluvio-pluvial silty clay, with in situ tests indicating a natural moisture content of w = 12.6%, frost heave rates of 3-12%, and a Class III frost heave classification [23].  
This project employed ZY-FLJ-200 axial force meters to dynamically monitor anchor rod axial forces during slope deformation. Monitoring points were installed on anchor rods near the slope crest and toe. These instruments offer advantages including stable performance, high sensitivity, and excellent waterproofing, with an operating temperature range of \(-\)45 to +60 \({}^{\circ}\)C. The configuration and installation are shown in Figure 2. The field monitoring equipment is also installed as shown in Figure 2. Axial force on anchor rods can be calculated using Equation (1).  
\[p_{2}=K_{2}\big{[}\big{(}F_{1}^{\prime}+F_{2}^{\prime}+F_{3}^{\prime}\big{)}/3- \big{(}F_{0}^{\prime}+F_{0}^{\prime}\big{)}/3\big{]}+b_{1}(T_{i}-T_{0})+B_{2} \tag{1}\]  
where \(p_{2}\) is the axial force acting on the anchor bolt; \(K_{2}\) is the instrument calibration coefficient; \(b_{1}\) and \(B_{2}\) are the temperature correction coefficient and computation correction value of the load cell, respectively; \(F_{1}^{\prime}\), \(F_{2}^{\prime}\), \(F_{3}^{\prime}\), and \(F_{0}^{\prime}\) are the measured values of the load cell and the average value of a single reference-equivalent measurement, respectively; \(T_{i}\) and \(T_{0}\) are the measured temperature and the reference temperature of the load cell, respectively.