Elastic Analysis of Nonhomogeneous Frozen Wall under Nonaxisymmetric Ground Stress Field and in State of Unloading

The mechanical analysis of frozen walls is a cornerstone technology of artificially frozen ground. The mechanical response of frozen walls is affected by heterogeneity, excavation unloading, uneven ground pressure, and the characteristics of surrounding rock. However, these factors are rarely taken into full consideration in existing analysis models. To address this shortfall, this study presents a plane-strain model that considers the inhomogeneity of frozen walls, the unloaded state of the frozen-wall inner edge, and the nonuniform ground stress field (abbreviated as “IF model”). The solution of the IF model is based on the superposition of thin concentric cylinders under two types of contact conditions: complete contact and smooth contact, and its validity is tested by a finite-element calculation. The calculation indicates that the excavation reduces the radial force and increases the tangential force between the frozen wall and the surrounding earth mass; the ground principal stress is rotated after the excavation. If the radial unloading equals the tangential unloading at the inner edge of the frozen wall, the response of the radial stress differs from that of the tangential stress at the outer edge of the frozen wall. The circumferential stress and the radial displacement at the inner edge correlate linearly with the nonuniform coefficient of the ground press and the unloading ratio. If the nonuniform coefficient is relatively small, the inner edge of the frozen wall may incur tensile damage. Compared with the model of a homogeneous frozen wall (abbreviated as “HF model”), which has a uniform temperature distribution, the absolute value of the circumferential stress is lower (higher) for the IF model where the temperature is above (below) average. When the frozen wall is relatively thick, the circumferential stress of the inner edge of the frozen wall is lower for the IF model than for the HF model. The percent reduction is 8.12%∼9.32% for rock freezing and 13.41%∼18.03% for soil freezing. The IF model proposed herein thus reflects the characteristics of frozen walls and surrounding rock more clearly and accurately than the HF model and obtains stress states closer to the reality. Therefore, the IF model is recommended for the design and construction of frozen walls