Study on mechanism of lining cracking and distribution rule of void cracks behind lining based on XFEM

Various diseases such as lining defects, structural cracking, and water leakage are common in tunnel operation. Therefore, this paper considers the research object of the highway tunnel with typical lining defects, namely voids behind the lining. The stress distribution and crack distribution of the void behind the lining were analyzed by numerical simulation based on XFEM, and the cracking mode of the lining was studied by model test. According to the results:(1) The voids behind the tunnel lining change the stress distribution characteristics of the lining, and the lining structure within is stretched, significantly reducing the overall safety of the lining structure. Equation(2)(2) Kθ=limn→02πrσθ= cos θ2[KΙ2(1+ cos θ)−3KII2sin θ](2) With the expansion of the void range (i.e. the void toroidal range and radial length), the lining area corresponding to the void is easy to crack, and the expansion of the void range leads to the increase of the crack area, which is also verified by the model test results. Equation(3)(3) ∂Kθ∂θ|θ = θ0=0(3) A safety factor analyzes the bearing capacity of the lining structure. The safety factor of the lining area corresponding to the void is reduced, which is consistent with the results obtained by the XFEM method for the calculation of lining cracking, which proves that the XFEM method can be applied to the safety calculation of tunnel lining structure.