Tunnel Failure Evolution and System Reliability Analysis Based on the β-unzipping Method

Abstract

The structural failure of a tunnel is a process that evolves from local damage to overall destruction. The system reliability analysis method can be useful for analyzing the evolutionary law of local structural failure. In many complex stress environments, the structural performance function may be very complicated or even impossible to solve. This paper establishes a response surface function to represent the implicit tunnel performance function. The reliability of the shear capacity of a tunnel is considered. The critical parts and critical failure paths of the tunnel system are determined using the β-unzipping method. Failure evolution is analyzed to obtain the failure process of the tunnel system. Different failure modes are shown under different cases. Based on the partial failure probability and impact on the tunnel system, the risk levels of the critical parts at each stage of the failure history are evaluated. Therefore, the tunnel failure tree model obtained by combining the response surface method and β-unzipping method plays an important role in tunnel reliability evolution, and can evaluate tunnel safety comprehensively.

Series–Parallel System Analysis and Reliability Research of Grid Structures Considering Adaptive Dynamic Bounding Threshold

“…The nodes (3,4) are connected with the ends of the first-level constraint bars, which are regarded as the second-level constraint node. The member 5 ⃝ between the nodes (3, 4) represents the second-level constraint bars. The members ( 6 ⃝, 7 ⃝, 8 ⃝, 9 ⃝) are connected with the second-level constraint nodes and away from the supports, which are the third-level constraint bars.…”

“…The members ( 6 ⃝, 7 ⃝, 8 ⃝, 9 ⃝) are connected with the second-level constraint nodes and away from the supports, which are the third-level constraint bars. The intersection points (5,6) of the third-level constraint bars are the third-level constraint nodes, and the component ➉ between the third-level constraint nodes is the third-level constraint bar. (2) The divided constraint levels are sorted from high to low into levels one, two, and three.…”

“…Therefore, for any node, as long as it is constrained by any two bars with different constraint directions, it can be guaranteed to be completely constrained. Taking the second-level constraint node 3 as an example, the node is connected with first-level constraint members ( 1⃝, 2 ⃝), a second-level constraint member 5 ⃝, and third-level constraint members ( 6 ⃝, 7 ⃝). In order to verify the conclusion that the low-level constraint member cannot constrain the high-level constraint member, the five bars are removed one by one, and only two bars are retained each time to be connected to the second-level constraint node 3.…”

“…Song et al [4] relied on subjective experience to identify the first two failure stages using the β-unzipping method for structural damage. Yang et al [5] judged the failure of the structure through subjective experience. When the minimum reliability index of a certain stage is greater than 3, it is considered as structural failure.…”

“…In recent years, many researchers have paid attention to the selection of the bounding threshold, studied the selection criteria of the bounding threshold, and achieved good results. When identifying the failure path, Yang et al [5] used the difference in failure probability of several special bars in each stage as the boundary threshold and set different selection ranges according to the different failure probabilities of the member, which improved the accuracy of selecting the failure member. Liu et al [11] proposed an adaptive dynamic bounding threshold method which can automatically adjust the bounding threshold according to the reliability index of the bar.…”