Calculation of the freeze wall thickness under high external loads

Abstract

In practice, the required thickness of freeze walls (FWs) is typically calculated using formulas based on the Mohr–Coulomb (MC) strength criterion. However, applying such formulas to determine FW thickness in water-saturated rocks at great freezing depths may lead to significant errors due to the nonlinearity of the failure envelope of Mohr’s circles. This study analyzes the functional form of nonlinear relationships between the maximum shear stress (corresponding to the failure state) and the mean normal stress for various rock types. A classification of rocks (sand, clay, siltstone) is proposed based on the functional form of the approximating formulas representing the nonlinear failure envelope of Mohr’s circles. A numerical solution was obtained for the limit stress state of an FW in siltstone at –6 °C under varying external loads applied to the outer wall of the FW. This solution was compared with the classical solution by S. S. Vyalov; as a result, we have identified the conditions and boundaries within which classical FW thickness formulas, based on the linear MC criterion, remain valid. A new formula was derived for determining FW thickness under external load with taking into account the nonlinear behavior of the failure envelope of Mohr’s circles.