Anura3D質點法探討國道三號3.1K邊坡破壞歷程

Post-failure Simulation of Freeway No.3 3.1K Landslide in Taiwan Using MPM Code Anura3D

賴宜群(Yi-Chun Lai)

指導教授 ： 葛宇甯

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001587

摘要

邊坡安全一直是大地工程領域重要的課題之一，邊坡災害將人們的生命及財產暴露於危險當中，在台灣，降雨、地震及人為因素等造成之邊坡災害更是不勝枚舉。隨著數值方法的發展，其已被廣泛應用於邊坡防護之設計與分析上，其中又以極限平衡法(Limit Equilibrium Analysis, LEA)和有線元素法(Finite Element Method, FEM)最為常見，然而，傳統數值方法中的網格畸變是對於大變形量分析上的主要限制，因此傳統數值方法僅適用於釐清初始破壞階段或者相對小的變形問題。

邊坡破壞後之情形及可能受滑動影響的潛勢範圍逐漸成為大家關注的核心議題之一，因此質點法(Material Point Method, MPM)於1994年由Sulsky等人提出，以克服模擬大變形問題時受網格畸變的限制。質點法和一些同樣用於模擬大變形問題之數值方法最大的不同之處在於其結合大地工程中之組成律及運用牛頓運動定律來模擬大變形下之破壞及破壞過程中的動態行為，因此，質點法可以視為合尤拉法則(Eulerian Approach)及拉格朗日法則(Lagrangian Approach)於一身之適合模擬大變形問題的進階版有線元素法。

本研究首先運用Anura3D質點法軟體，從乾土性質之單相度-單質點(one-phase single-point)到飽和土壤雙相度-單一質點(two-phase single-point)進行一些案例及試驗驗證。接著，運用大地工程學會之總結報告、現地調查及試驗室試驗等相關資料進而模擬國道三號3.1K邊坡破壞案例，選取之分析剖面為大地工程學會所判斷之沿著滑動方向的關鍵長剖面，並利用邊坡破壞前與破壞後之數值地形模型(Digital Terrain Model, DTM)作為模型幾何建置依據及分析結果之滑動距離及堆積情況之比對。國道三號3.1K邊坡破壞被歸類為順向坡破壞，導致該邊坡破壞事件發生之主因為雨水長期經由上部砂岩(SS)中的節理及垂直裂縫入滲，雨水長年累積於不透水頁岩層(SH)上面之砂頁岩互層(SS/SH)中，導致其軟化。本研究根據前人利用Stabl 5.0、Plaxis2D及Flac3D之數值分析結果(廖洪鈞等，2011、2012及2013)，對砂頁岩互層(SS/SH)進行凝聚力(C)和摩擦角(φ)之強度折減以模擬地下水位上升對其之軟化效應。

質點法提供完整之邊坡破壞過程模擬，故破壞過程中的動態行為也可有進一步理解，研究結果顯示該剖面於地錨完全失效之情況下，當砂頁岩互層(SS/SH)軟化至C=0 kPa、φ=10°時，整體破壞導致的滑動距離及堆積情形最吻合破壞後之數值地形模型，邊坡破壞歷程約歷時18~20秒，其滑動速率最高可超過每秒12公尺，這也解釋了災害當下邊坡於極短時間內覆蓋住國道南向線及北向線，並導致四輛汽車連同五位用路人受到波及掩埋。

相較於其他數值方法，質點法可以廣泛運用於許多大變形問題，大地材料組成律之適用性亦能提供更進一步對於觸發破壞之機制的探討與掌握及了解破壞過程中應力-應變關係，因此質點法算是滿適合應用於大地領域之數值方法。藉由此論文研究，對於一些利用質點法獲得到的邊坡災害歷程中關鍵的時間點及相關討論，這些概念可以作為未來邊坡破壞之安全指標，且可納入國土規畫以減低災害所導致的相關損失。

關鍵字

質點法 ； MPM ； Material Point Method ； Anura3D ； 大變形 ； 國道三號3.1K邊坡破壞 ； 破壞後分析 ； 動態過程

並列摘要

Slope stability is always an important issue in geotechnical engineering, landslides can put human life and property in danger. In Taiwan, due to the climate change, people often suffer from rainfall-induced landslide, furthermore, earthquake and artificial factors may also be the possible triggers. Therefore, many numerical methods have been proposed to contribute in disaster reduction. Started from original design of slope protection to analyze the possible critical state of the slope. The traditional geotechnical analyses, such as Limit Equilibrium Analysis (LEA) and Finite Element Method (FEM), are two of the analytical techniques commonly used for slope stability assessment nowadays. However, due to the limitation of mesh distortion, these traditional methods are not capable of simulating large deformation problems. Only the behaviors at pre-failure stage and with small deformation failure can be clarified.

The post-failure stage and run-off process of landslide is becoming the core issue nowadays. To conquer the difficulty in the constraint of deformation, Material Point Method (MPM) was proposed for simulating large deformation problems (Sulsky et al., 1994). Different to other methods which also have the ability of handling large deformation in the simulation, MPM can be considered as the extended version of FEM with the benefit of its geotechnical based feature. It is also a particle based method with the material is represented by many Lagrangian material points passing through the Eulerian mesh which combines both Eulerian and Lagrangian Approaches. The large deformation failure and kinematics can be performed by MPM based on geotechnical constitutive models and the Newton’s law of motion.

The thesis focuses on the failure reversion of the Freeway No.3 3.1K Landslide in Taiwan, in 2010, by means of MPM code Anura3D. Besides this, some applications used as the validation by using one-phase single-point and fully dynamic and coupled two-phase single-point formulations. With the sufficient in-situ investigation reported in the forensic report of the Freeway No.3 3.1K Landslide by Taiwan Geotechnical Society, the laboratory experiments and the Digital Terrain Model (DTM) at initial state of the excavated dip slope and post-failure stage were adopted in geometry/stratum building and result comparison in the research. The strength reduction in the alternation of sandstone and shale layer (SS/SH) which caused the landslide tragedy was due to the water accumulation above the impermeable shale layer (SH) from rainfall infiltrating through the vertical cracks and jointing in sandstone layer (SS). The reduction in cohesion (C) and friction angle (φ) represents both strength softening and raising of groundwater table. The determination of the softening degree in SS/SH layer in MPM model is based on the numerical analyses results done in Stabl 5.0, Plaxis2D, Flac3D (Liao and Lee, 2011; Liao et al., 2012; Liao et al., 2013).

The MPM provides the complete process of landslide in simulation, thus, the kinematics during the failure can also be obtained. The result shows that with no anchor remained after the landslide in the critical section of the studied slope, as SS/SH layer reduced to C=0 kPa, φ=10° has the best agreement with the post-failure topography in run-off distance and deposition. The landslide duration lasts around 18~20 s, but the maximum run-off velocity can reach to more than 12 m/s. The sliding mass covers both the southbound and northbound lanes in a short period of time, this may explain how this rapid landslide could burry four vehicles and lead to five deaths on April 25th, 2010.

Comparing to other numerical methods, MPM can be applied to large deformation problems to clarify the post-failure stage, and thanks to the adoption of geotechnical based constitutive models in this method, the stress-strain relations from the initial stage to post-failure stage and the triggering mechanism may possibly be captured. Therefore, it is a geoengineering-friendly numerical algorithm which can be applied to variety of fields. In this study, with understanding the critical timings of landslide by MPM, this concept can be provided as important index on slope failure and national spatial planning for disaster reduction.

並列關鍵字

MPM ； Material Point Method ； Anura3D ； large deformation ； Freeway No.3 3.1K Landslide ； post-failure ； kinematics

參考文獻

Abe, K., S. Nakamura, H. Nakamura and K. Shiomi (2017). “Numerical Study on Dynamic Behavior of Slope Models Including Weak Layers from Deformation to Failure Using Material Point Method”. Soils and Foundations, vol. 57, No.2, pp. 155-175.

Bandara, S., A. Ferrari and L. Laloui (2016). “Modelling Landslides in Unsaturated Slopes Subjected to Rainfall Infiltration Using Material Point Method”. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 40, pp. 1358-1380.

Bishop, A. W. and L. Bejurum (1960). “The Relevance of the Triaxial Test to the Solution of Stability Problems” Proceeding, ASCE Research Conference on Shear Strength of Cohesive Soils, pp. 437-501.

Ceccato, F. and P. Simonini (2017). “Numerical Based Design of Protection Systems Against Landslides”. Conference Paper.

Ceccato, F., P. Simonini and A. Rohe (2014). “Simulation of Slope Failure Experiment with the Material Point Method”. Conference Paper.