Journal: Computers and Geotechnics

Authors: Xuegang Pan; Jinqing Jia.

Affiliation: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology

      This study proposes a surrogate model-based method for time-dependent reliability analysis of anchor-reinforced slope systems (ARSS). By incorporating composite failure modes, variability of geotechnical materials, and corrosion effects as uncertainty factors, the method overcomes the limitations of traditional system reliability analysis methods. The system failure probability is defined as the sum of the products of the combined probability of local anchor failure and the conditional probability of slope failure under the corresponding conditions. The time-dependent system reliability of the bearing capacity of anchored slopes, which degrades over time due to corrosion effects, is also calculated. The results show that the ARSS has a certain degree of redundancy. However, due to stress redistribution effects, local anchor failure significantly increases the probability of failure of the remaining anchors and the slope. The failure of adjacent anchors and anchors located in the middle-lower part of the slope has a more significant impact. Although the system failure probability is mainly determined by non-anchor failure events, ignoring local anchor failure may lead to non-conservative results. The anchors initially have strong corrosion resistance. However, over time, corrosion significantly reduces their bearing capacity, leading to an almost fourfold increase in the probability of slope failure. This study highlights the importance of considering local anchor failure, variability of geotechnical materials, and corrosion effects in the long-term reliability assessment of anchor support systems. These considerations contribute to improving the safety and sustainability of geotechnical engineering practices.

Fig. 1 Geometry and reinforcement layout of anchored soil slope

Fig. 2 Displacement contours of slope without anchor reinforcement

Fig. 3 Displacement contours of ARSS when a single layer of anchors fails (φ = 20, c = 20 kPa): (a) all anchors working; (b) layer A1 fails; (c) layer A2 fails; (d) layer A3 fails; (e) layer A4 fails; (f) layer A5 fails

Fig. 4 Root mean square error of axial force and safety factor of anchors under various conditions

Fig. 5 Comparison of RSM predicted values with numerical results under various anchor conditions: (a) F2* and (b) Fs

Fig. 6 Comparison of conditional probabilities of failure without anchors calculated by MCS and FORM

Fig. 7 Variation of anchor stability force with service time

Fig. 8 Time-dependent system failure probability of ARSS

      This study proposes a method to evaluate the time-dependent system reliability of anchor-reinforced rock slope systems (ARSS), considering the impact of local soil or anchor failure on slope stability. The method focuses on analyzing uncertainty factors such as corrosion effects, geotechnical variability, and different failure mechanisms. Finally, the method is applied to a practical engineering case and compared with the calculation results of other evaluation methods.

(1) The instability of ARSS is classified into mutually independent events, which are composed of different combinations of anchor failures. Based on the total probability theorem, the system failure probability is expressed as the sum of the products of the local anchor failure probability and the conditional probability of slope failure for these events. By considering the time-dependent reduction of anchor support capacity due to corrosion, the time-dependent system reliability of the slope can be calculated. This method considers the influence of composite failure modes and corrosion degradation on the failure probability of anchored slopes without the need to calculate correlation coefficients between multiple failure modes.

(2) As a complex composite system, the anchor-reinforced rock slope support system (ARSS) exhibits diverse and interdependent failure modes. Local failure of anchors or rock/soil leads to stress redistribution within the slope. Failure of adjacent layers is more likely to cause a simultaneous decrease in support capacity in the affected area, forming a larger unstable zone and thus endangering the overall stability of the slope. The key layers located in the middle-lower part of the slope (such as A1, A2, and A3) contribute significantly to overall stability, while the upper and lower layers (such as A4 and A5) have relatively less influence.

(3) The ARSS has a certain degree of redundancy, but multi-layer failure significantly increases the probability of instability, with the cumulative effect of adjacent layer failure being the most pronounced. Without layer failure, the probability of overall slope failure is only 1.241%. When one, two, or all key layers fail, the probability of slope instability increases to 16.924%, 51.107%, and 95.943%, respectively.

(4) The probability of ARSS system failure depends on the probability of local anchor failure and the conditional probability. The likelihood of slope instability is evaluated under the occurrence of these events. When the probability of multi-layer instability events is low, their contribution to the overall probability of slope instability is minimal. Therefore, a high conditional probability of slope instability under specific conditions does not necessarily mean a high overall probability of system instability. The probability of system instability is mainly determined by the case without layer instability. However, ignoring local layer instability may lead to non-conservative calculation results.

(5) Corrosion not only reduces the bearing capacity of anchors but also increases the risk of slope instability. Although anchors have strong corrosion resistance in the early stage, over time, the cumulative effect of corrosion significantly weakens their bearing capacity, almost quadrupling the probability of slope instability. Therefore, long-term slope stability assessment should incorporate corrosion modeling and prediction. Effective anti-corrosion measures should be taken to extend the service life of anchors, more accurately predict future instability risks, and improve the overall stability of slopes. In summary, this study comprehensively investigates the stability of anchor cable support systems using system reliability analysis methods, providing valuable insights and guidance for engineering practice and academic research. Future research can further expand these results to provide stronger support for improving the safety and reliability of slope reinforcement engineering.

Xuegang Pan, Jinqing Jia. Time-dependent system reliability analysis of anchor-reinforced slopes based on surrogate models. Computers and Geotechnics 184 (2025) 107257