基于极限分析上限方法的海底斜坡稳定性评价
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摘要
极限平衡法仍是当前海底斜坡稳定性的主要工程评价方法,但该法只能给出稳定性分析的近似解答。基于极限分析运动学定理,假定海底斜坡发生对数螺线型滑移破坏模式,将滑体有效自重和简化波浪力等以外荷载形式叠加引入到虚功率方程中,与潜在滑动面上由黏聚力产生的内能耗散率相平衡,建立考虑一阶简化波浪效应的海底斜坡上限解法;利用多变量无导数求极值的逐级迭代方法与最优化技术,结合抗剪强度折减思想,求解波浪加载下不同时刻的海底斜坡稳定性与相应的临界破坏机构,并针对典型算例开展有限元数值解的验证。进而联合采用数值法与上限解,探讨波高、波长、水深等波浪参数对海底斜坡稳定性与滑动机制的影响。结果表明,本文提出的上限解与数值解吻合较好,获得的安全系数与破坏模式等符合一般规律,为波浪作用下海底斜坡的稳定性评价提供了新的途径。
Currently,the limit equilibrium method(LEM)has been one of the most popular approaches to assess the seafloor stability.But still,the method has some limitations and only the approximate solutions can be obtained.To achieve the true solution,the upper bound approach based on kinematic theorem of limit analysis incorporating a log-spiral rotational failure mechanism,is established to solve the stability of submarine slopes,in which the simplified linear wave loading is considered,and the external work rates produced by the effective self-gravity of sliding body and the wave-induced pressure on the seafloor slope are equal to the internal energy dissipation rates yielded by the cohesion along the critical sliding surface(CSS).The safety factor(FS)and the corresponding CSS at different time under waves are obtained by combining multivariate stepwise iterative method without derivative and the mathematically optimal technique with strength reduction method(SRM).And,typical example is introduced to carry out the verification of the finite element numerical solution.On the basis of these,the effect of wave parameters such as wave length,wave height and water depth on the slope stability and failure mechanism are discussed.Calculation results show that the FSs and the corresponding CSSs obtained by the upper bound approach agreet well with the numerical solutions,and are also consistent with the general rules.The proposed approach provides a new path for the analysis of seafloor stability.
Currently,the limit equilibrium method(LEM)has been one of the most popular approaches to assess the seafloor stability.But still,the method has some limitations and only the approximate solutions can be obtained.To achieve the true solution,the upper bound approach based on kinematic theorem of limit analysis incorporating a log-spiral rotational failure mechanism,is established to solve the stability of submarine slopes,in which the simplified linear wave loading is considered,and the external work rates produced by the effective self-gravity of sliding body and the wave-induced pressure on the seafloor slope are equal to the internal energy dissipation rates yielded by the cohesion along the critical sliding surface(CSS).The safety factor(FS)and the corresponding CSS at different time under waves are obtained by combining multivariate stepwise iterative method without derivative and the mathematically optimal technique with strength reduction method(SRM).And,typical example is introduced to carry out the verification of the finite element numerical solution.On the basis of these,the effect of wave parameters such as wave length,wave height and water depth on the slope stability and failure mechanism are discussed.Calculation results show that the FSs and the corresponding CSSs obtained by the upper bound approach agreet well with the numerical solutions,and are also consistent with the general rules.The proposed approach provides a new path for the analysis of seafloor stability.
引文
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[10]刘红军,张民生,贾永刚,等.波浪导致的海床边坡稳定性分析[J].岩土力学,2006,27(6):986-990.Liu Hongjun,Zhang Minsheng,Jia Yonggang,et al.Analysis of seabed stability under wave loading[J].Rock and Soil Mechanics,2006,27(6):986-990.
[11]邵广彪,冯启民,王华娟.海底缓坡场地地震侧移数值分析方法[J].岩土力学,2006,27(9):1401-1406.Shao Guangbiao,Feng Qimin,Wang Huajuan.A method for numerical analysis of earthquake induced lateral displacements of submerged gentle slope[J].Rock and Soil Mechanics,2006,27(9):1401-1406.
[12]王刚,张建民.波浪作用下某防沙堤的动力固结有限元分析[J].岩土力学,2006,27(4):555-560.Wang Gang,Zhang Jianmin.Dynamic consolidation finite element analysis of a sediment-protecting dyke under ocean wave loading[J].Rock and Soil Mechanics,2006,27(4):555-560.
[13]许文锋,车爱兰,王治,等.地震荷载作用下海底滑坡特征及其机理[J].上海交通大学学报,2011,45(5):782-786.Xu Wenfeng,Che Ailan,Wang Zhi,et al.Destruction characteristic of seabed landslide during earthquake motion and its mechanism[J].Journal of Shanghai Jiaotong University,2011,45(5):782-786.
[14]Chen W F.Limit analysis and soil plasticity[M].Plantation:J Ross Publishing,2007.
[15]Viratjandr C,Michalowski R L.Limit analysis of submerged slopes subjected to water drawdown[J].Canadian Geotechnical Journal,2006,43(8):802-812.
[16]Nian T K,Chen G Q,Luan M T,et al.Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils[J].Canadian Geotechnical Journal,2008,45(8):1092-1103.
[17]郭代培.两种方法模拟波浪荷载对岩质边坡作用的比较[C]//第三届全国水工岩石力学学术会议论文集.上海:同济大学出版社,2010:1-5.Guo Daipei.Comparison of two ways to simulate the effect on wave load on rock slope[C]//Third National Hydraulic Rock Mechanics Conference Proceedings.Shanghai:Tongji University Press,2010:1-5.
[18]Zienkiewicz O C,Humpheson C,Lewis R W.Associated and non-associated visco-plasticity and plasticity in soilmechanics[J].Geotechique,1975,25(4):671-689.
[19]郑宏,李春光,李焯芬,等.求解安全系数的有限元法[J].岩土工程学报,2002,24(5):626-628.Zheng Hong,Li Chunguang,Lee Chackfan,et al.Finite element method for solving the factor of safety[J].Chinese Journal of Geotechnical Engineering,2002,24(5):626-628.
[20]刘敏,刘博,年廷凯,等.线性波浪加载下海底斜坡失稳机制的数值分析[J].地震工程学报,2015,37(2):415-421.Liu Min,Liu Bo,Nian Tingkai,et al.Numerical analysis of the failure mechanism of submarine slopes under linear loading[J].China Earthquake Engineer Journal,2015,37(2):415-421.
[2]Locat J,Lee H J.Submarine landslides:advances and challenges[J].Canadian Geotechnical Journal,2002,39(1):193-212.
[3]Mosher D C,Moscardelli L,Shipp R C,et al.Submarine mass movements and their consequences[M].Amsterdam:Netherlands Springer,2010.
[4]Leynaud D,Mienert J,Nadim F.Slope stability assessment of the Helland Hansen area offshore the mid-Norwegian margin[J].Marine Geology,2004,213(1):457-480.
[5]孙永福,董立峰,蒲高军,等.风暴潮作用下黄河水下三角洲斜坡稳定性研究[J].工程地质学报,2006,14(5):582-587.Sun Yongfu,Dong Lifeng,Pu Gaojun,et al.Stability analysis of slopes in the subaqueous delta of the Yellow River under storm wave loading[J].Journal of Engineering Geology,2006,14(5):582-587.
[6]胡光海,刘振夏,房俊伟.国内外海底斜坡稳定性研究概况[J].海洋科学进展,2006,24(1):130-136.Hu Guanghai,Liu Zhenxia,Fang Junwei.A review of submarine slope stability studies at home and abroad[J].Advances in Marine Science,2006,24(1):130-136.
[7]王立忠,缪成章.慢速滑动泥流对海底管道的作用力研究[J].岩土工程学报,2008,30(7):982-987.Wang Lizhong,Miao Chengzhang.Pressure on submarine pipelines under slowly sliding mud flows[J].Chinese Journal of Geotechnical Engineering,2008,30(7):982-987.
[8]顾小芸.海底边坡稳定分析方法综述[J].力学进展,1989,19(1):50-59.Gu Xiaoyun.Overview of analysis method of submarine slope stability[J].Advances in Mechanics,1989,19(1):50-59.
[9]刘晓丽,窦锦钟,英姿,等.波致海底缓倾角无限坡滑动稳定性计算分析[J].海洋学报,2015,37(3):99-105.Liu Xiaoli,Dou Jinzhong,Ying Zi,et al.Computational analysis of waves induced angled infinite slope sliding[J].Haiyang Xuebao,2015,37(3):99-105.
[10]刘红军,张民生,贾永刚,等.波浪导致的海床边坡稳定性分析[J].岩土力学,2006,27(6):986-990.Liu Hongjun,Zhang Minsheng,Jia Yonggang,et al.Analysis of seabed stability under wave loading[J].Rock and Soil Mechanics,2006,27(6):986-990.
[11]邵广彪,冯启民,王华娟.海底缓坡场地地震侧移数值分析方法[J].岩土力学,2006,27(9):1401-1406.Shao Guangbiao,Feng Qimin,Wang Huajuan.A method for numerical analysis of earthquake induced lateral displacements of submerged gentle slope[J].Rock and Soil Mechanics,2006,27(9):1401-1406.
[12]王刚,张建民.波浪作用下某防沙堤的动力固结有限元分析[J].岩土力学,2006,27(4):555-560.Wang Gang,Zhang Jianmin.Dynamic consolidation finite element analysis of a sediment-protecting dyke under ocean wave loading[J].Rock and Soil Mechanics,2006,27(4):555-560.
[13]许文锋,车爱兰,王治,等.地震荷载作用下海底滑坡特征及其机理[J].上海交通大学学报,2011,45(5):782-786.Xu Wenfeng,Che Ailan,Wang Zhi,et al.Destruction characteristic of seabed landslide during earthquake motion and its mechanism[J].Journal of Shanghai Jiaotong University,2011,45(5):782-786.
[14]Chen W F.Limit analysis and soil plasticity[M].Plantation:J Ross Publishing,2007.
[15]Viratjandr C,Michalowski R L.Limit analysis of submerged slopes subjected to water drawdown[J].Canadian Geotechnical Journal,2006,43(8):802-812.
[16]Nian T K,Chen G Q,Luan M T,et al.Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils[J].Canadian Geotechnical Journal,2008,45(8):1092-1103.
[17]郭代培.两种方法模拟波浪荷载对岩质边坡作用的比较[C]//第三届全国水工岩石力学学术会议论文集.上海:同济大学出版社,2010:1-5.Guo Daipei.Comparison of two ways to simulate the effect on wave load on rock slope[C]//Third National Hydraulic Rock Mechanics Conference Proceedings.Shanghai:Tongji University Press,2010:1-5.
[18]Zienkiewicz O C,Humpheson C,Lewis R W.Associated and non-associated visco-plasticity and plasticity in soilmechanics[J].Geotechique,1975,25(4):671-689.
[19]郑宏,李春光,李焯芬,等.求解安全系数的有限元法[J].岩土工程学报,2002,24(5):626-628.Zheng Hong,Li Chunguang,Lee Chackfan,et al.Finite element method for solving the factor of safety[J].Chinese Journal of Geotechnical Engineering,2002,24(5):626-628.
[20]刘敏,刘博,年廷凯,等.线性波浪加载下海底斜坡失稳机制的数值分析[J].地震工程学报,2015,37(2):415-421.Liu Min,Liu Bo,Nian Tingkai,et al.Numerical analysis of the failure mechanism of submarine slopes under linear loading[J].China Earthquake Engineer Journal,2015,37(2):415-421.