高速公路桥隧过渡段力学行为与动力响应研究
|
摘要
随着高速公路的建设逐渐进入山岭重丘区,桥梁隧道工程也日益增多。桥隧过渡工程最显著的特点是相互连接的桥梁与隧道之间存在着相互影响,桥梁、隧道和周边岩体受到的扰动更多,其力学行为更为复杂。但是,目前国内外对桥隧过渡工程的研究十分有限,如何对‘施工过程中进行优化,以及如何分析车辆荷载对桥隧过渡段结构的动力作用都是值得关注的问题。针对以往研究中的不足,本文建立室内相似模型,首次利用室内试验研究了桥隧连接工程在重复行车荷载下围岩及结构的应力应变特征,及疲劳损伤。随后利用数值模拟手段,研究了桥隧结构在周期行车荷载下的动力响应。随后根据桥隧连接处存在沉降差异的特点,推导了重载汽车通过沉降差异处的振动方程,并建立相应的隧道振动响应方程,以此求得隧道在车辆冲击荷载下的动力响应。以室内试验,数值模拟及理论分析等手段研究桥隧过渡结构在行车荷载作用下力学行为与动力响应,在此基础上分别针对隧道边仰坡的参数反演,稳定性分析以及隧道施工围岩的力学行为进行了研究,阐明了隧道围岩在施工过程中的力学行为变化,为桥隧过渡段的设计施工提供了理论依据。最后结合现场试验,将本文研究成果与实际测试结果进行对比,验证了本文的理论计算的正确性。本文获得的具体研究成果有如下几点：
(1)在确定试验材料和试验方案的基础上,研究了不同工况下桥隧过渡段施工过程中,隧道围岩压力变化情况,洞口附近围岩及边仰坡土体的稳定性。在此基础上,研究了不同工况下桥隧邻接工程在后期运营阶段,汽车荷载及其冲击作用下,桥、隧结构各关键部位及洞口土体的受力、变形、位移和沉降情况,及工程中常见的病害机理。
(2)利用有限元软件MIDAS-GTS,建立了桥隧过渡段的三维数值计算分析,并根据车辆动荷载的大小与时变规律,施加动力荷载。通过桥隧过渡段的围岩衬砌应力,位移的比对分析,研究车速与桥隧过渡段的不同形式对其稳定性的影响.对两种不同的基础形式在动荷载作用下的动力反应进行对比,分析提出合理的桥隧搭接过渡段结构形式,为方案比选提供理论依据。
(3)在桥台与隧道衬砌的连接处,两者之间的沉降差异使车辆通过桥隧过渡段时对路面产生冲击作用。考虑车体自身的纵向转动与倾覆,车辆通过桥隧连接段的过程视为一定初始条件下的受迫振动,根据D'Alembert原理,建立了三自由度与五自由度下,车辆与路面的动力耦合计算模型并给出其振动方程。并利用Laplace变换,对该系统的动力响应进行分析,求得各车轮冲击力随时间的变化规律。为了研究上述冲击荷载对隧道断面的动力效应,将根据已有两相饱和介质Green函数,利用Lamb积分公式,结合隧道断面特征,以解析积分法推导了矩形和圆形断面隧道在上述衰减动力荷载下的振动反应,并研究了该荷载作用于隧道底部任意位置时的隧道振动位移反应表达式闭合解、反应时程曲线、瞬态和稳态的振动形态。
(4)为了获取隧道的边仰坡物理力学参数,采用位移反分析技术对其进行研究。分别针对层状以及均质边坡,分别提出了基于模糊数学以及测斜曲线分析的反分析技术,并给出其目标函数。结合工程实例,计算了的目标函数的敏感度,证明其有效性。根据参数反演的结果,利用FLAC3D软件,利用多滑动面技术,分析隧道边仰坡的稳定性。
(5)利用有限差分软件FLAC3D建立桥隧过渡段计算模型,分别模拟了不同围岩级别下,桥隧搭接段与邻接段的围岩应力、围岩塑性区、洞周位移及地表位移规律。并比较了不同施工方法(台阶法,侧壁导坑,CRD法)对围岩稳定性的影响,并对扩大基础与桩基础条件下,桥隧邻接段围岩以及桩体自身应力应变规律进行研究,为施工方案的选择提供指导。
With the construction of highway in the mountainous areas, the number of bridge and tunnel engineering increases day by day. The significant characteristic of the bridge-tunnel connection section is the mutual influence between the connecting bridge and tunnel. What's more, the bridge, tunnel and rock are disturbed frequently and mechanical behavior is more complex. However, the research on bridge-tunnel connection section is quite limited. According to the disadvantage in the previous research, a simulation test was modeled using similarity theorem. The characteristic of strain and stress and the fatigue damage for bridge-tunnel connection section under repeated traffic loading is studied, especially the surrounding rock and the construction. And the dynamic response of bridge-tunnel connection section under vehicular load in1or2periods is analyzed by numerical simulation. Because of the differential settlement at the junction of bridge and tunnel, the vibration equation of heavy duty vehicles passing the bridge-tunnel connection section is derived. And the vibration response equation of tunnel rock is established, the vibration response of surrounding rock under vehicles is obtained. After studying the mechanical behavior and vibration response under vehicles load by similar simulation test, numerical simulation and theoretical analysis, in the presented study, the back analysis and the stability analysis of the slope and is studied and the mechanical behavior of the tunnel surrounding rock is analyzed. Finally, with the field test, the research result and the actual results is compared to prove the correctness of the theoretical calculation. The main research content is as following:
(1) The static force calculated model of bridge-tunnel connection section is built by Finite difference method software FLAC3D, the surrounding rock stress, plastic zone, side wall displacements and surface displacement of bridge-tunnel connection section under different rock grade is calculated. And, the influence of construction method (steps method, CRD method and siding head method) to surrounding rock stability is studied. What's more, with the spread foundation and pile foundation, the stress and strain of surrounding rock and foundation is researched for guidance to the construction and design.
(2) Using the finite element software MIDAS-GTS, the3-D dynamic calculated model of bridge-tunnel connection section is built and the dynamic load is applied by the size and time-dependent deformation of vehicle load. With obtaining the surrounding rock, linking stress and displacement, the stability of bridge-tunnel connection section is researched by various vehicle and different construction type. Comparing the dynamic response of two type of foundation under dynamic load, the reasonable foundation is presented for the theory basis of the project design.
(3) On the basis of the experiment material and program, the tunnel surrounding rock stress distribution, the stability of tunnel portal and side and face upward slope in construction progress under different construction condition are studied. What's more, considering the vehicle load and dynamic load, the stress, deformation, displacement and settlement of the key position of the construction and tunnel portal soil is studied. The common disease mechanism is also researched.
(4) For obtaining the physical and mechanical parameters heading slope, the displacement back analysis technology is applied. Aiming at layered and homogeneous slope, the back analysis method is proposed based on fuzzy mathematics and inclination curve features characteristic analysis, and the objective function is presented. With the practice engineering, the effectiveness of method is proved by calculated objective function sensibility. Using the intensive parameter, the slope stability is analyzed with multi slide surface technology with FLAC3D.
(5) Settlement difference occurs at the joint between bridge and tunnel, making impact action to tunnel-bridge section when vehicle passes, has significant influence to comfortableness of vehicle driving and the whole tunnel construction. Considering the rotation and overturn in longitudinal direction, the process of vehicle passing tunnel-bridge section is regarded as the forced oscillation with certain initial condition, by which the calculate model of man-vehicle-road is built under D'Alembert principle and vibration equation is given. What's more, by Laplace transform, the acceleration of driver and the impact force to road is solved. And these magnitudes variation with time can be obtained. Finally, the influence factor to the impact is studied, to provide the theory basis of reduce the damage by impact loading result from settlement difference. For studying the above impact loading dynamic effect to tunnel section, with Green function and Lamb integral formula, combining the tunnel section features, the vibration response of rectangle and circle tunnel under the damping dynamic loading is derived by analytical integral method. And the closed solutions of vibration displacement response under impact or harmonic loads acting on inside of saturated soil tunnel, the travel time history of elastic wave and the transient and ordinary modes of vibration were obtained when the loading is in any position at the bottom of tunnel.
(1)在确定试验材料和试验方案的基础上,研究了不同工况下桥隧过渡段施工过程中,隧道围岩压力变化情况,洞口附近围岩及边仰坡土体的稳定性。在此基础上,研究了不同工况下桥隧邻接工程在后期运营阶段,汽车荷载及其冲击作用下,桥、隧结构各关键部位及洞口土体的受力、变形、位移和沉降情况,及工程中常见的病害机理。
(2)利用有限元软件MIDAS-GTS,建立了桥隧过渡段的三维数值计算分析,并根据车辆动荷载的大小与时变规律,施加动力荷载。通过桥隧过渡段的围岩衬砌应力,位移的比对分析,研究车速与桥隧过渡段的不同形式对其稳定性的影响.对两种不同的基础形式在动荷载作用下的动力反应进行对比,分析提出合理的桥隧搭接过渡段结构形式,为方案比选提供理论依据。
(3)在桥台与隧道衬砌的连接处,两者之间的沉降差异使车辆通过桥隧过渡段时对路面产生冲击作用。考虑车体自身的纵向转动与倾覆,车辆通过桥隧连接段的过程视为一定初始条件下的受迫振动,根据D'Alembert原理,建立了三自由度与五自由度下,车辆与路面的动力耦合计算模型并给出其振动方程。并利用Laplace变换,对该系统的动力响应进行分析,求得各车轮冲击力随时间的变化规律。为了研究上述冲击荷载对隧道断面的动力效应,将根据已有两相饱和介质Green函数,利用Lamb积分公式,结合隧道断面特征,以解析积分法推导了矩形和圆形断面隧道在上述衰减动力荷载下的振动反应,并研究了该荷载作用于隧道底部任意位置时的隧道振动位移反应表达式闭合解、反应时程曲线、瞬态和稳态的振动形态。
(4)为了获取隧道的边仰坡物理力学参数,采用位移反分析技术对其进行研究。分别针对层状以及均质边坡,分别提出了基于模糊数学以及测斜曲线分析的反分析技术,并给出其目标函数。结合工程实例,计算了的目标函数的敏感度,证明其有效性。根据参数反演的结果,利用FLAC3D软件,利用多滑动面技术,分析隧道边仰坡的稳定性。
(5)利用有限差分软件FLAC3D建立桥隧过渡段计算模型,分别模拟了不同围岩级别下,桥隧搭接段与邻接段的围岩应力、围岩塑性区、洞周位移及地表位移规律。并比较了不同施工方法(台阶法,侧壁导坑,CRD法)对围岩稳定性的影响,并对扩大基础与桩基础条件下,桥隧邻接段围岩以及桩体自身应力应变规律进行研究,为施工方案的选择提供指导。
With the construction of highway in the mountainous areas, the number of bridge and tunnel engineering increases day by day. The significant characteristic of the bridge-tunnel connection section is the mutual influence between the connecting bridge and tunnel. What's more, the bridge, tunnel and rock are disturbed frequently and mechanical behavior is more complex. However, the research on bridge-tunnel connection section is quite limited. According to the disadvantage in the previous research, a simulation test was modeled using similarity theorem. The characteristic of strain and stress and the fatigue damage for bridge-tunnel connection section under repeated traffic loading is studied, especially the surrounding rock and the construction. And the dynamic response of bridge-tunnel connection section under vehicular load in1or2periods is analyzed by numerical simulation. Because of the differential settlement at the junction of bridge and tunnel, the vibration equation of heavy duty vehicles passing the bridge-tunnel connection section is derived. And the vibration response equation of tunnel rock is established, the vibration response of surrounding rock under vehicles is obtained. After studying the mechanical behavior and vibration response under vehicles load by similar simulation test, numerical simulation and theoretical analysis, in the presented study, the back analysis and the stability analysis of the slope and is studied and the mechanical behavior of the tunnel surrounding rock is analyzed. Finally, with the field test, the research result and the actual results is compared to prove the correctness of the theoretical calculation. The main research content is as following:
(1) The static force calculated model of bridge-tunnel connection section is built by Finite difference method software FLAC3D, the surrounding rock stress, plastic zone, side wall displacements and surface displacement of bridge-tunnel connection section under different rock grade is calculated. And, the influence of construction method (steps method, CRD method and siding head method) to surrounding rock stability is studied. What's more, with the spread foundation and pile foundation, the stress and strain of surrounding rock and foundation is researched for guidance to the construction and design.
(2) Using the finite element software MIDAS-GTS, the3-D dynamic calculated model of bridge-tunnel connection section is built and the dynamic load is applied by the size and time-dependent deformation of vehicle load. With obtaining the surrounding rock, linking stress and displacement, the stability of bridge-tunnel connection section is researched by various vehicle and different construction type. Comparing the dynamic response of two type of foundation under dynamic load, the reasonable foundation is presented for the theory basis of the project design.
(3) On the basis of the experiment material and program, the tunnel surrounding rock stress distribution, the stability of tunnel portal and side and face upward slope in construction progress under different construction condition are studied. What's more, considering the vehicle load and dynamic load, the stress, deformation, displacement and settlement of the key position of the construction and tunnel portal soil is studied. The common disease mechanism is also researched.
(4) For obtaining the physical and mechanical parameters heading slope, the displacement back analysis technology is applied. Aiming at layered and homogeneous slope, the back analysis method is proposed based on fuzzy mathematics and inclination curve features characteristic analysis, and the objective function is presented. With the practice engineering, the effectiveness of method is proved by calculated objective function sensibility. Using the intensive parameter, the slope stability is analyzed with multi slide surface technology with FLAC3D.
(5) Settlement difference occurs at the joint between bridge and tunnel, making impact action to tunnel-bridge section when vehicle passes, has significant influence to comfortableness of vehicle driving and the whole tunnel construction. Considering the rotation and overturn in longitudinal direction, the process of vehicle passing tunnel-bridge section is regarded as the forced oscillation with certain initial condition, by which the calculate model of man-vehicle-road is built under D'Alembert principle and vibration equation is given. What's more, by Laplace transform, the acceleration of driver and the impact force to road is solved. And these magnitudes variation with time can be obtained. Finally, the influence factor to the impact is studied, to provide the theory basis of reduce the damage by impact loading result from settlement difference. For studying the above impact loading dynamic effect to tunnel section, with Green function and Lamb integral formula, combining the tunnel section features, the vibration response of rectangle and circle tunnel under the damping dynamic loading is derived by analytical integral method. And the closed solutions of vibration displacement response under impact or harmonic loads acting on inside of saturated soil tunnel, the travel time history of elastic wave and the transient and ordinary modes of vibration were obtained when the loading is in any position at the bottom of tunnel.
引文
[1]李冬生,马志富,许占良,等.长昆线桥隧过渡设计研究[J].铁道工程学报.2011(12)：69-73.
[2]王树仁,张海清,慎乃齐.穿越采空区桥隧工程危害效应分析及对策[J].解放军理工大学学报(自然科学版).2009(5)：492-496.
[3]郭建湖.高低不平顺条件下高速铁路桥-隧过渡段路基的动力特性[J].铁道科学与工程学报.2008(4)：7-13.
[4]郑光,许强,杜宇本.高陡岩质桥隧工程边坡稳定性评价及工程支护措施[J].成都理工大学学报(自然科学版).2011(4)：430-437.
[5]明祖涛,游振兴,张届.高速铁路桥隧沉降预测模型的研究[J].测绘通报.2011(8)：17-19.
[6]张喜刚,徐国平,刘高.公路桥隧工程风险评估[J].公路交通科技.2010(11)：73-77.
[7]孙广臣,傅鹤林,巢万里.桥隧邻接工程多源损伤室内模型试验研究[J].中南林业科技大学学报.2011(11)：157-165.
[8]赵峰,夏永旭,许东.桥隧相接隧道明洞稳定性研究[J].公路.2009(12).
[9]李勇,丁浩.桥隧相接条件下超大断面隧道的设计[J].地下空间与工程学报.2006(3)：416-419.
[10]付宏平,陈光金,刘海江.桥隧过渡工程整体施工独立控制网建网方案探讨[J].铁道标准设计.2012(4)：9-12.
[11]吴昊,罗敖.山区高速公路桥隧连接段交通事故成因分析[J].山西建筑.2010(31)：267-268.
[12]王飞.山区高速公路桥隧过渡技术的研究与应用[J].交通标准化.2008(11)：124-127.
[13]张剑.山区高速铁路隧道间桥隧连接结构探讨[J].铁道工程学报.2011(8)：62-67.
[14]向明航,郑罡,曾嵩.山区公路桥隧结合段风险影响因素分析[J].西部交通科技.2012(1)：54-59.
[15]叶茂.铁路客运专线桥隧过渡段桥式方案的选择[J].城市道桥与防洪.2010(5)：39-41.
[16]陈列.武广客运专线桥隧过渡地段混凝土简支箱形梁施工方案[J].铁道工程学报.2007(10)：40-43.
[17]王树仁,张海清,慎乃齐等.下伏采空区桥隧工程变形及受力响应特征分 析[J].岩石力学与工程学报.2009(6)：1144-1151.
[18]许曦,朱建军,刘庆元.长大桥隧工程的GPS跨障碍高程控制[J].中国公路学报.2004(4)：77-81.
[19]刘光磊,宋二祥,刘华北等.饱和砂土地层中隧道结构动力离心模型试验[J].岩土力学.2008(8)：2070-2076.
[20]方林,蒋树屏,林志,等.穿越断层隧道振动台模型试验研究[J].岩土力学.2011(9)：2709-2713.
[21]左宇军,马春德,朱万成,等.动力扰动下深部开挖洞室围岩分层断裂破坏机制模型试验研究[J].岩土力学.2011(10)：2929-2936.
[22]李育枢,李天斌,王栋,等.黄草坪2-#隧道洞口段减震措施的大型振动台模型试验研究[J].岩石力学与工程学报.2009(6)：1128-1136.
[23]王源,刘松玉,谭跃虎,等.九华山隧道爆破施工对明城墙振动影响的监测与分析[J].岩石力学与工程学报.2007：3584-3589.
[24]徐海清,傅志峰,梁立刚,等.列车荷载作用下紧邻垂直多孔隧道环境振动分析[J].岩土力学.2011(6)：1869-1873.
[25]申玉生,高波,王英学.强震区山岭隧道洞口段结构动力特性分析[J].岩石力学与工程学报.2009：3131-3136.
[26]陈兴华编著.脆性材料结构模型试验[M].北京：水利电力出版社,1983
[27]林韵梅编著.实验岩石力学[M].北京：煤炭工业出版社,1984
[28]李鸿昌编著.矿山压力的相似模拟试验[M].徐州：中国矿业大学出版社,1993
[29]顾大钊编著.相似材料和相似模型[M].徐州：中国矿业大学出版社,1995
[30]程桦,孙钧,吕渊.软弱围岩复合式隧道衬砌模型试验研究[J].岩石力学与工程学报.1997(2)：67-75.
[31]徐志英,施善云.土与地下结构动力相互作用的大型振动台试验与计算[J].岩土工程学报.1993(4)：1-7.
[32]陈锋,蔡德钩,韩自力,等.路涵过渡段涵洞竖向压力现场试验研究[J].铁道建筑.2011(4)：49-51.
[33]黄晚清,陆阳,罗书学,等.秦沈客运专线路涵过渡段动应力测试与分析[J].西南交通大学学报.2005(2)：220-223.
[34]陈浩,任伟中,李丹,等.深埋隧道锚杆支护作用的数值模拟与模型试验研究[J].岩土力学.2011：719-724.
[35]张泉,罗强.遂渝铁路刚性路基动应力测试分析[J].铁道标准设计.2006(2)：18-20.
[36]施成华,彭立敏,王伟.铁路隧道基底破坏力学形态的试验研究[J].实验力学.2005(1)：57-64.
[37]张宏光,谢永利,杨晓华.楔型柔性搭板模型试验[J].长安大学学报(自然科学版).2005(3)：54-57.
[38]Chua K H, BalendrT et al. Groundborne vibrations due to trains in tunnels. Earthquake Engineering and Structural Dynamics,1992,21(5):445-460.
[39]Chua K H, Lo K W, et al. Building response due to subway train traffic. Journal of Geotechnical Engineering,1995,121(11):747-754.
[40]Gardien W, StUit H Q. Modeling of soil vibrations from rail way tunnels. Journal of Sound and Vibrations,2003,267:605-619.
[41]Minsili L.S, Wen Q, Xia H, Medjo Eko R. Assessment and Predietion of underground train induced vibrations and their effects on nearby building structures in Cameroon.3rd International Symposium on Environmental Vibrations:Prediction, Monitoring, Mitigation and Evaluation, Taipei, China, November 2007.
[42]Andersen L, Jones C J C. Vibration from a rail way tunnel Predicted by coupled finite element and boundary element analysis in two and three dimensions[A].Proceeding of 5th European Conference Structural Dynamics [C].Munich, Germany,2002:1131-1136
[43]Forrest J A, Hunt H E M. A three-dimensional model for calculation of train-induced ground vibration [J]. Journal of Sound and Vibration,2006, 294(1):678-705.
[44]Forrest J A, Hunt H E M. Ground vibration generated by trains in underground tunnels [J]. Journal of Sound and Vibration,2006,294(4):706-736
[45]Hussein M F M, Hunt H E M. A numerical model for calculating vibration from a railway tunnel embedded in a full-Space [J]. Journal of Sound and Vibration, 2007,305(1):401-431
[46]Stamos A A, Beskos D E.3-D seismic response analysis of long lined tunnels in half-space. Soil dynamics and Earthquake Engineering,1996,15:111-118.
[47]Stamos A A, Beskos D E. Dynamic analysis of large 3-D underground structures by the BEM. Earthquake Engineering and Engineering Vibration,1995, 1-8.
[48]Francois S, Lombaert G Degrande G. Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations. Soil dynamics and Earthquake Engineering,2005,25:839-856.
[49]Lombaert G Degrande G. Numerical modeling of free field traffic induced vibrations. Soil dynamics and Earthquake Engineering,2000,19:477-488.
[50]Wolf S. Potential low frequency ground vibration (<6.3Hz) impacts from underground LPT operations[J] Journal of Sound and Vibration,2003,267(3):651-661.
[51]Thornely R M. The prediction of vibration, ground-borne and structure-radiated noise from railways.using finite difference method-Part 1: theory [J].Proceedings of the Institute of Acoustics,2004,26(2):69-79
[52]Jones C J C, Thompson D J, Petyt M. Studies using a combined finite element and boundary element model for vibration propagation from railway tunnels [A]. Seventh International Congress on Sound and Vibration(ICSV7).
[53]Degrande G, Othman R, Othman Ret al. A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element-boundary element formulation[J] Journal of Sound and Vibration, 2006,293(3-5):645-666
[54]Andersen L, Jones C J C. Coupled boundary and finite element analysis of vibration from railway tunnels-a comparison of two- and three-dimensional models[J]. Journal of Sound and Vibration,2006,293:611-625
[55]王其昌,蔡成标,罗强,等.高速铁路路桥过渡段轨道折角限值的分析[J].铁道学报.1998(3)：110-114.
[56]高新强,仇文革.新型铁路隧道门洞口段结构受力特征现场试验研究[J].岩石力学与工程学报.2005(12)：2155-2159.
[57]李亮,张丙强,杨小礼.高速列车振动荷载下大断面隧道结构动力响应分析[J].岩石力学与工程学报.2005(23)：4259-4265.
[58]彭立敏,施成华,黄娟,等.列车荷载作用下隧道铺底结构疲劳寿命分析[J].铁道学报.2007(1)：82-85.
[59]秦旗,梁波,韩仙华.地震荷载下无碴轨道桩网路基的动力响应分析[J].兰州交通大学学报.2008(3)：33-36.
[60]赵明阶,刘绪华,敖建华,等.隧道顶部岩溶对围岩稳定性影响的数值分析[J].岩土力学.2003(3)：445-449.
[61]郭军,王明年,谭忠盛,等.大跨浅埋黄土隧道中系统锚杆受力机制研究[J].岩土力学.2010(3)：870-874.
[62]施成华,雷明锋,彭立敏,等.桥隧过渡结构静动力特性影响因素分析[J].中南大学学报(自然科学版).2011(4)：1085-1091.
[63]翟婉明,王少林.桥梁结构刚度对高速列车—轨道—桥梁耦合系统动力 特性的影响[J].中国铁道科学.2012(1)：19-26.
[64]Hisatake M, Hieda Y.2008 Three-dimensional back-analysis method for the mechanical parameters of the new ground ahead of a tunnel face[J], Tunneling and Underground Space Technology,23(4):373-380.
[65]Ghorbani M, Sharifzadeh M.2009 Long term stability assessment of Siah Bisheh powerhouse cavern based on displacement back analysis method[J]. Tunneling and Underground Space Technology,24(5):574-583.
[66]Cai M, Morioka H, Kaiser P K, et al.2007 Back-analysis of rock mass strength parameters using AE monitoring data[J]. International Journal of Rock Mechanics and Mining Sciences,44(4):538-549.
[67]Yang C, Wu Y H, Hon T. A no-tension elastic-plastic model and optimized back-analysis technique for modeling nonlinear mechanical behavior of rock mass in tunneling[J]. Tunneling and Underground Space Technology,2010,25(3):279-289.
[68]Wu J, Tsai P. New dynamic procedure for back-calculating the shear strength parameters of large landslides [J]. Engineering Geology Reconnaissance of Extreme Natural Disasters of Morakot Typhoon, Taiwan,2011,123(1-2):129-147.
[69]Sonmez H, Ulusay R, Gokceoglu C. A practical procedure for the back analysis of slope failures in closely jointed rock masses [J]. International Journal of Rock Mechanics and Mining Sciences,1998,35(2):219-233
[70]Styles T D, Coggan J S, Pine R J. Back analysis of the Joss Bay Chalk Cliff Failure using numerical modeling [J]:Engineering Geology,2011,120(1-4):81-90.
[71]Jiang J C, Yamagami T. A new back analysis of strength parameters from single slips. Computers and Geotechnics[J],2008.35(2):286-291
[72]Fakhimi A, Salehi D, Mojtabai N. Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project [J]. Tunneling and Underground Space Technology,2004,19(1):57-67.
[73]Shang Y J Cai J. G. Hao W. D.et al. Intelligent back analysis of displacements using precedent type analysis for tunneling [J]. Tunneling and Underground Space Technology.2002.17(4):381-389
[74]Yu Y. Zhang B. Yuan H. An intelligent displacement back-analysis method for earth-rockfill dams. Computers and Geotechnics [J].2007.34(6):423-434
[75]Zhang L Q, Yue Z Q, Yang Z F. A displacement-based back-analysis method for rock mass modulus and horizontal in situ stress in tunneling-Illustrated with a case study. Tunnelling and Underground Space Technology [J]. 2006.21(6):636-649
[76]Maier G, Jurina.L, Podolak.K. On model identification problem in rock mechanics[C]. Proc Symp on the Structural Foundations on Rock. Capri: 1977:257-261.
[77]Gioda G. Indirect identification of the average elastic characteristics of rock masses[C]. Proc Int Conf on Structural Foundations on Rock.Sydney,1980,.1:65-73.
[78]Arai R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior [J]. Soil and Foundations,1984,24(1):95-108.
[79]Sakurai S, Abe S. A design approach to dimensioning underground openings[C]. Pros 3rd Int Conf Numerical Methods in Geomechanics. Aachen,1979, 649-661.
[80]Sakurai S and Takeuchi K. Back analysis of measured displacements of tunnels[J]. Rock Mechanics and Rock Engineering,1983,16:173-180.
[81]Sakurai S, Deeswasmongkol N, Shiji M. Back analysis for determining material characteristics in cut slope [J].Int Symposium on Engineering in complex Rock Fonnations, Beijing, Nov,1986.
[82]晏同珍,杨顺安,方云.滑坡学[M].武汉,中国地质大学出版社,2000.
[83]杨志法等.有限元法图谱[M].北京,科学出版社,1988.
[84]杨林德,朱合华,冯紫良等.岩土工程问题的反演理论与工程实践[M].北京：科学出版社,1998.
[85]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学.1996,6：29-34.
[86]王芝银,杨志法,王思敬.岩石力学位移反演分析回顾及进展田力学进展.1998,4：488-498
[87]Zhang L L, Zhang J, Zhang L M. Back analysis of slope failure with markov chain monte carlo simulation[J]. Computers and Geotechnics.2010,37(7-8):905-912
[88]邓建辉,丰定祥,葛修润.多介质边坡弹性模量位移反分析模型及优化方法[J].岩土力学与工程学报,1997,19(3)：22-27.
[89]杜景灿.加权位移反演法确定岩体结构面的力学参数[J].岩土工程学报,1999,21(2)：209-216.
[90]吉林,赵启林,冯兆祥,等.软弱夹层与结构面的力学参数反演[J].水利学报.2003(11)：107-111.
[91]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学.2006(5)：795-798.
[92]孙志彬,杨小礼,黄阜.基于模糊数学和粒子群算法的边坡参数反分析[J].华南理工大学学报(自然科学版).2011(6)：137-141.
[93]赵衡,刘晓明.桥头跳车引起的路面受力计算分析[J].公路交通科技.2005(5)：59-62.
[94]刘萌成,黄晓明,陶向华.桥台后高填方路堤工后沉降影响因素分析[J].交通运输工程学报.2005(3)：36-40.
[95]高燕希,张军,张起森.软弱地基桥台台背填筑EPS的结构分析[J].中国公路学报.2003(3)：28-31.
[96]王亦麟.软土地基桥头跳车处理探讨[J].公路交通科技.2000(1)：30-32.
[97]王虎,胡长顺,王秉纲.连续配筋混凝土路面动荷响应分析[J].工程力学.2001(5)：119-126.
[98]邓学钧,黄晓明,沈伟新.弹性层状体系的动力响应分析[J].土木工程学报.1995(3)：9-16.
[99]俞建荣,陈荣生,金志强.半刚性基层与刚性面层联结状态对刚性路面荷载应力的影响析[J].岩土工程学报.1996(4)：37-42.
[100]陶向华,黄晓明.人-车-路相互作用三质量车辆模型分析[J].交通运输工程学报.2004(3)：11-15.
[101]周华飞,蒋建群.刚性路面在运动车辆作用下的动力响应[J].土木工程学报.2006(8)：117-125.
[102]刘俊卿,刘超,赵洪金.横观各向同性刚性路面体系静动力分析[J].长安大学学报(自然科学版).2010(2)：48-52.
[103]张军辉,王鹏,黄晓明.软土地基上高速公路加宽工程的数值分析[J].公路交通科技.2006(6)：32-35.
[104]颜可珍,夏唐代,黄立葵.双参数粘弹性地基无限长板的瞬态动力响应分析[J].岩石力学与工程学报.2005(24)：4576-4580.
[105]颜可珍,吴罗成,朱向平.移动荷载作用下弹性半空间土体的动力响应[J].建筑科学与工程学报.2011(4)：30-34.
[106]周华飞,蒋建群,张土乔.移动荷载下Kelvin地基上无限长梁的稳态响应[J].浙江大学学报(工学版).2004(10)：91-96.
[107]蒋建群,周华飞,张土乔.移动荷载下Kelvin地基上无限大板的稳态响应[J].浙江大学学报(工学版).2005(1)：28-33.
[108]蒋建群,周华飞,张土乔.移动荷载下粘弹性地基上无限大板的稳态响应[J].中国公路学报.2006(1)：6-11.
[109]曹志刚,蔡袁强,徐长节.移动车辆荷载作用下路面的动力响应[J].浙江 大学学报(工学版).2009(4)：777-781.
[110]张洪亮,胡长顺,许伟清.移动荷载作用下柔性路面的动力响应[J].长安大学学报(自然科学版).2005(5)：6-10.
[111]赖国麟.桥头跳车防治措施的研究报告之附件二—关于桥头搭板沉降坡差容许值的建议.东南大学运输工程研究所.
[112]张洪亮.路桥过渡段车路动力学分析及容许差异沉降研究[D].长安大学博士论文,2005.
[113]Biot M A. General Theory of Three-Dimensional ConsolidationJ]. J. Appl.Phys.,1941,12:155-164
[114]Biot M A.Theory of Elastic Wave in a Fluid-Saturated Porous Solid, I.Low-Frequency Range [J].J. Acoust. Soc. Am.,1956a,28:168-178
[115]Biot M A. Theory of Elastic Wave in a Fluid-Saturated Porous Solid, II.Low-Frequency Range [J].J. Acoust. Soc. Am.,1956b,28:179-191
[116]Biot M A. Mechanics of Deformation and Acoustic Propagation in Porous Media [J].J. Appl. Phys.,1962,33(4):1482-1498
[117]Boer D. Theory of Porous media:highlights in the historical development and current state [M].Berlin:Spring-Verlag,2000.
[118]Truesdell C, Toupin R A. The classical Field Theories [J].In Handbuch der physic, Spring, Berlin3(1)
[119]Green A E, Naghdi P M. A Dynamic Theory of interacting Continua[J].Int J. Engng. Sci.,1965,3:231-241
[120]Bowen R.M.混合物理论[M].江苏科技出版社,1983
[121]Bo wen R M, Reinicke K M. Plane Progressive Waves in a Binary Mixture of Linear Elastic Materials [M].J. Appl.Mech.,1978,45:493-499
[122]Atkin R J, Craine R E. Continuum Theories of Mixtures:Basic Theory and Historical Development[J].Q. J. Appl. Math.,1978,45:209-244
[123]Atkin R J, Craine R E. Continuum Theory of Mixture:Application[J].J. Inst. Maths. Appls,1976,17:153-207
[124]Plona T J. Observation of a second bulk compressional wave in porous mediumat ultrasonic frequencies[J].Appl. Phys. Lett,1980,36:259-261
[125]Berryman J G. Confirmation of Biot's Theory [J].Appl. Phys. Lett,1980, 37:382-384
[126]丁伯阳.含裂隙介质受压破裂前的地震波特性的综合实验研究与理论分析[J].西北地震学报,1983,5(5)：21-33
[127]Stoll R D. Sediment Acoustics[J].Berlin:Spring-Verlag,1989
[128]Burridge P. Vargas C A. The fundamental solution in dynamic poroelasticity[J].Geophys. R. astr. Soc,1979,58:61-82
[129]Auriault J L. Bome L. Dynamics of porous saturated media. Checking of the generalized law of darcey[J]. Acoust. soc. Am,1985,77:2012-2023
[130]Kazi-Aoual M N. Bonnet G. Green's functions in an infinite transversely isotropic saturated poroelastic medium[J].Acoust. Soc. Am.,1988,84:1883-1889
[131]Paul S. On the Disturbance Produced in a Semi-Infinite Poroelastie Medium by a Surface Load[J]. Pure. Appl. Geophys.,1976,114:615-627
[132]Philippacopoulos A J. Lamb's problem for fluid-saturated porous media [J]. Bull Seism, Soc. Am,1988,78(2):908-923
[133]Norris A N. Radiation from a point source and scattering theory in afluid-saturated porous solid [J]. J. Acoust. Soc. Am.,1985,77:2012-2023
[134]Kayrfia A M. Banerjee, P. K. Fundamental solutions of biot's equations ofdynamic poroelasticity [J]. Int. J. Engng. Sci.,1993,31(5):817-830
[135]Chen J. Time domain function solution to Boit's complete equations of dynamic poroelasticity. Part Ⅰ:Two-Dimensional Solution[J]. Int. J. Solid Struct, 1994b,3 (10):1447-1490
[136]Chen J. Time domain function solution to Boit's complete equations of dynamic poroelasticity part Ⅱ:Three-Dimensional Solution [J].Int. J. Solid. Struct, 1994,3(2):169-202
[137]丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用[J].地球物理学报,1999,42(6)：800-808
[138]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2)：234-241
[139]丁伯阳,孟凡丽,胡敏云.两相饱和介质的弹性位错震源矢量与静态位移场[J].地震学报,2002,14(3)：251--258
[140]丁伯阳,樊良本,孟凡丽.两相饱和介质半无限空间位错位移场[J].地球物理学报,2003,46(3)：408-414
[141]Garg S K. Wave propagation effects in a fluid-saturated porous solid [J]Journal of Geophysical Research,197.1,76:7947-7962
[142]Garg S K. Good A. J. Compressional waves in fluid-saturated elastic prous media[J]. Journal of Applied Physics,1974,45:1968-1974
[143]Garg S K. Dynamics of gas-fluidized beds [J]. Journal of Applied Physics, 1975,46:4493-4500
[144]Chen B F. Hung T K. Hydrodynamic pressure of water and sediment onrigid dam [J]. J. Eng. Mech. ASCE,1993,7(119):1411-1433
[145]Ghaboussi J. Variational formulation of dynamics of fluid saturated porous elastic solids.1972,98:947-963
[146]Ghaboussi J. Wilson E L. Finite element for rock joints and interfaces[J]. J. Soil Mech. Div,ASCE,1973,99(10):833-848
[147]Zienkiewicz O C. Shiomi T. Dynamic behaviour of saturated porous media-the generalized Biot formulation and its numerical solution [J]. Int. J. Num. Anal. Mech. Geomech,1984,8:71-96
[148]Johnson L R. Green's function for lamb's problem [J]. Geophys. J. R. Astron. Soc.,1974,37:99-131
[149]Kobayashi S. Nishimmra N. Green's tensors for elastichalf-spaces-application of boundary integral equation method [J]. Memoirs fac. Eng. Kyoto. Univ, 1980,42:228-241
[150]Manolis G D. Dynamic response of lined tunnels by anisoparametric boundary element method [J]. Comp. Meth. Appl. Mech. Eng.,1983,36:291-307
[151]李德寅,王邦楣,林亚超.结构模型试验[M].北京：科学出版社,1996.3
[152]王涛.桩—土相互作用影响的模型试验研究[J].岩土力学,2008,29(6)：1589-1593
[153]王戍平.破碎围岩隧道的模拟试验研究[D].杭州：浙江大学,2004
[154]裘伯永,盛兴旺,乔建东等.桥梁工程[M].北京：中国铁道出版社,2000,12
[155]董昌周,杨建辉,胡挺.公路隧道模型试验相似材料试验研究[J].现代隧道技术.2010(1)：11-16.
[156]丁浩,蒋树屏,陈林杰.公路隧道外水压力的相似模型试验研究[J].公路交通科技.2008(10)：99-104.
[157]曾开华,许家雄,张国锋.深部巷道破坏过程相似模拟实验研究[J].金属矿山.2011(9)：44-48.
[158]董昌周,曲晨.隧道围岩体相似材料试验研究[J].浙江科技学院学报.2011(6)：499-502.
[159]张强勇,李术才,郭小红,等.铁晶砂胶结新型岩土相似材料的研制及其应用[J].岩土力学.2008(8)：2126-2130.
[160]凌建明,王伟,邬洪波.行车荷载作用下湿软路基残余变形的研究[J].同济大学学报(自然科学版).2002(11)：1315-1320.
[161]张曦,唐益群,周念清,等.地铁振动荷载作用下隧道周围饱和软黏土动力响应研究[J].土木工程学报.2007(2)：85-88.
[162]崔正翔,嵇正毓.地铁隧道振动对地面环境影响预测的探讨[J].噪声与振动控制.1996(1)：9-14.
[163]刘维宁,夏禾,郭文军.地铁列车振动的环境响应[J].岩石力学与工程学报.1996：586-593.
[164]王逢朝,夏禾,张鸿儒.地铁列车振动对邻近建筑物的影响[J].北方交通大学学报.1999(5)：45-48.
[165]由广明,刘维宁.交叠车站与区间隧道列车振动对环境的影响[J].北京交通大学学报.2005(4)：40-44.
[166]雷震宇,周顺华,许恺.列车动荷载对下立交结构的影响分析[J].岩石力学与工程学报.2004(20)：3536-3540.
[167]翟辉,刘维宁.地铁列车引起的低频地表响应及减振措施研究[J].都市快轨交通.2005(4)：116-120.
[168]张玉娥.地铁区间隧道列车振动响应测试与数值分析[D].兰州铁道学院学位论文.
[169]王祥秋,杨林德,周治国.列车振动荷载作用下隧道衬砌结构动力响应特性分析[J].岩石力学与工程学报,2006,25(7)：246-249.
[170]李德武,高峰,韩文峰.列车振动下隧道基底合理结构形式的研究[J].岩石力学与工程学报,2004,23(13)：2292-2297.
[171]李德武,高峰.隧道仰拱对列车振动影响的研究[J].铁道学报,1999,21(4).
[172]Burk M, Kingsbury H B. Response of Poro elastic Layers to Moving Loads[J]. Int. J. Solid Struct,1984,20:499-511.
[173]Siddharthan R, Zafir Z, Norris, GM. Moving Load Response of Layered Soil. I. Formulation [J]. J. Eng. Mech,1993,119:2052-2071.
[174]Biot M A. Mechanics of deformation and acoustic propagation in porous media [J]. J. App 1. phys,1962,33:1482-1498.
[175]Biot M A. Theory of propagation of elastic wave in a fluid satue rated soil[J]. Acoust. Soc. Amer.,1956,28:168-178.
[176]丁伯阳,党改红,袁金华. Green函数对饱和土隧道内集中荷载作用振动位移反应的计算[J].振动与冲击,2009,11：101-112.
[177]Ding B Y, Meng F L, Hu M Y. The source vector and static displacement field by elastic dislocation on the two-phase saturated medium [J]. Acta Seismologica Sinica,2001,14(3):251-258.
[178]Miao T D, Zhu J J, Ding B Y. Essay on constitutive relation of wave propagation in saturated porous media [J]. Acta Mechanica Sinica,1995,27 (5):536-543.
[179]丁伯阳,宋新初,袁金华.饱和土隧道内集中荷载作用下振动位移反应的Green函数解答[J].工程力学,2009,6：154-155.
[180]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2)：234-241
[181]Fakhimi A, Salehi D, Mojtabai N. Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project[J]. Tunnelling and Underground Space Technology.2004,19(1):57-67.
[182]Yazdani M, Sharifzadeh M, Kamrani K, et al. Displacement-based numerical back analysis for estimation of rock mass parameters in Siah Bisheh powerhouse cavern using continuum and discontinuum approach[J]. Tunnelling and Underground Space Technology.2012,28(0):41-48.
[183]Deng J H, Lee C F. Displacement back analysis for a steep slope at the three gorges project site[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(2):259-268
[184]陈鹏,杨小礼,黄阜.浅埋三孔隧道围岩位移场解析解研究[J].铁道科学与工程学报,2011,32(1)：87～90.
[185]姜功良.浅埋软土隧道稳定性极限分析[J].土木工程学报,1998,31(5)：65～72.
[186]谢骏,刘纯贵,于海勇.双平行圆形隧道稳定的塑性极限分析上限解[J].岩石力学与工程学报,2006,25(9)：1835～1841.
[187]杨小礼,王作伟.非线性破坏准则下浅埋隧道围岩压力的极限分析[J].中南大学学报(自然科学版),2010,41(1)：299～302.
[188]靳晓光,刘伟,郑学贵.小净距偏压公路隧道开挖顺序优化[J].公路交通科技,2005,22(8)：61-64.
[189]刘伟,靳晓光,陈少华.高速公路小净距隧道合理净距的探讨[J].地下空间,2004,24(3)：380-385.
[190]刘艳青,钟世航,卢汝绥.小净距并行隧道力学状态的试验研究[J].岩石力学与工程学报,2000,19(9)：590-594.
[191]庄宁,廖少明等.大跨度小净距群洞隧道施工方案优化研究[J].地下空间与工程学报,2007,3(1)：96-100.
[192]孙元国,李文江,朱永全.客运专线小净距隧道施工效应的数值模拟分析 [J].石家庄铁道学院学报(自然科学版),2007,20(3)：6-14.
[193]舒志乐,刘保县,李月.偏压小净距隧道围岩压力分析[J].地下空间与工程学报,2007,3(3)：430-433.
[194]曹林,胡居义,黎冬林.小净距公路(双洞)隧道围岩破坏模式研究[J].2007,18(3)：65-69.
[195]王作伟.非线性破坏准则下浅埋隧道围岩压力的上限分析[D].中南大学,2010.
[196]李树忱,李术才,徐帮树.隧道围岩稳定分析的最小安全系数法[J].岩土力学,2007,28(3)：549-554.
[197]张黎明,郑颖人,王在泉,等.有限元强度折减法在公路隧道中的应用探讨[J].岩土力学,2007,28(1)：97-101.
[198]喻言,柳群义,冯德山.隧道岩体稳定性的非线性单元安全系数分析[J].中南大学学报(自然科学版),2010,41(3)：1085-1089.
[199]陈鹏,吴责,杨小礼.三孔小净距隧道围岩安全系数分析[J].湖南文理学院学报(自然科学版),2011,11(2)：55-58.
[200]刘小文,张功.强度折减应用于隧道群整体稳定性分析的判据比较[J].南昌大学学报(工科版),2010,18(2)：154-157.
[201]周小波,龙绪健.基于强度折减理论的软弱围岩隧道坍方机理分析[J].中外公路,2011,22(5)：197-200.
[202]张红,郑颖人,杨臻,等.黄土隧洞安全系数初探[J].地下空间与工程学报,2009,19(2)：297-306.
[203]陈建锋.三台阶法在软弱围岩隧道开挖施工中的应用探讨[J].中国西部科技,2010,25(26)：16-17.
[204]陈立保.三台阶法在客运专线山岭隧道软弱围岩中的推广应用[J].铁道工程学报,2008,19(12)：72-74.
[2]王树仁,张海清,慎乃齐.穿越采空区桥隧工程危害效应分析及对策[J].解放军理工大学学报(自然科学版).2009(5)：492-496.
[3]郭建湖.高低不平顺条件下高速铁路桥-隧过渡段路基的动力特性[J].铁道科学与工程学报.2008(4)：7-13.
[4]郑光,许强,杜宇本.高陡岩质桥隧工程边坡稳定性评价及工程支护措施[J].成都理工大学学报(自然科学版).2011(4)：430-437.
[5]明祖涛,游振兴,张届.高速铁路桥隧沉降预测模型的研究[J].测绘通报.2011(8)：17-19.
[6]张喜刚,徐国平,刘高.公路桥隧工程风险评估[J].公路交通科技.2010(11)：73-77.
[7]孙广臣,傅鹤林,巢万里.桥隧邻接工程多源损伤室内模型试验研究[J].中南林业科技大学学报.2011(11)：157-165.
[8]赵峰,夏永旭,许东.桥隧相接隧道明洞稳定性研究[J].公路.2009(12).
[9]李勇,丁浩.桥隧相接条件下超大断面隧道的设计[J].地下空间与工程学报.2006(3)：416-419.
[10]付宏平,陈光金,刘海江.桥隧过渡工程整体施工独立控制网建网方案探讨[J].铁道标准设计.2012(4)：9-12.
[11]吴昊,罗敖.山区高速公路桥隧连接段交通事故成因分析[J].山西建筑.2010(31)：267-268.
[12]王飞.山区高速公路桥隧过渡技术的研究与应用[J].交通标准化.2008(11)：124-127.
[13]张剑.山区高速铁路隧道间桥隧连接结构探讨[J].铁道工程学报.2011(8)：62-67.
[14]向明航,郑罡,曾嵩.山区公路桥隧结合段风险影响因素分析[J].西部交通科技.2012(1)：54-59.
[15]叶茂.铁路客运专线桥隧过渡段桥式方案的选择[J].城市道桥与防洪.2010(5)：39-41.
[16]陈列.武广客运专线桥隧过渡地段混凝土简支箱形梁施工方案[J].铁道工程学报.2007(10)：40-43.
[17]王树仁,张海清,慎乃齐等.下伏采空区桥隧工程变形及受力响应特征分 析[J].岩石力学与工程学报.2009(6)：1144-1151.
[18]许曦,朱建军,刘庆元.长大桥隧工程的GPS跨障碍高程控制[J].中国公路学报.2004(4)：77-81.
[19]刘光磊,宋二祥,刘华北等.饱和砂土地层中隧道结构动力离心模型试验[J].岩土力学.2008(8)：2070-2076.
[20]方林,蒋树屏,林志,等.穿越断层隧道振动台模型试验研究[J].岩土力学.2011(9)：2709-2713.
[21]左宇军,马春德,朱万成,等.动力扰动下深部开挖洞室围岩分层断裂破坏机制模型试验研究[J].岩土力学.2011(10)：2929-2936.
[22]李育枢,李天斌,王栋,等.黄草坪2-#隧道洞口段减震措施的大型振动台模型试验研究[J].岩石力学与工程学报.2009(6)：1128-1136.
[23]王源,刘松玉,谭跃虎,等.九华山隧道爆破施工对明城墙振动影响的监测与分析[J].岩石力学与工程学报.2007：3584-3589.
[24]徐海清,傅志峰,梁立刚,等.列车荷载作用下紧邻垂直多孔隧道环境振动分析[J].岩土力学.2011(6)：1869-1873.
[25]申玉生,高波,王英学.强震区山岭隧道洞口段结构动力特性分析[J].岩石力学与工程学报.2009：3131-3136.
[26]陈兴华编著.脆性材料结构模型试验[M].北京：水利电力出版社,1983
[27]林韵梅编著.实验岩石力学[M].北京：煤炭工业出版社,1984
[28]李鸿昌编著.矿山压力的相似模拟试验[M].徐州：中国矿业大学出版社,1993
[29]顾大钊编著.相似材料和相似模型[M].徐州：中国矿业大学出版社,1995
[30]程桦,孙钧,吕渊.软弱围岩复合式隧道衬砌模型试验研究[J].岩石力学与工程学报.1997(2)：67-75.
[31]徐志英,施善云.土与地下结构动力相互作用的大型振动台试验与计算[J].岩土工程学报.1993(4)：1-7.
[32]陈锋,蔡德钩,韩自力,等.路涵过渡段涵洞竖向压力现场试验研究[J].铁道建筑.2011(4)：49-51.
[33]黄晚清,陆阳,罗书学,等.秦沈客运专线路涵过渡段动应力测试与分析[J].西南交通大学学报.2005(2)：220-223.
[34]陈浩,任伟中,李丹,等.深埋隧道锚杆支护作用的数值模拟与模型试验研究[J].岩土力学.2011：719-724.
[35]张泉,罗强.遂渝铁路刚性路基动应力测试分析[J].铁道标准设计.2006(2)：18-20.
[36]施成华,彭立敏,王伟.铁路隧道基底破坏力学形态的试验研究[J].实验力学.2005(1)：57-64.
[37]张宏光,谢永利,杨晓华.楔型柔性搭板模型试验[J].长安大学学报(自然科学版).2005(3)：54-57.
[38]Chua K H, BalendrT et al. Groundborne vibrations due to trains in tunnels. Earthquake Engineering and Structural Dynamics,1992,21(5):445-460.
[39]Chua K H, Lo K W, et al. Building response due to subway train traffic. Journal of Geotechnical Engineering,1995,121(11):747-754.
[40]Gardien W, StUit H Q. Modeling of soil vibrations from rail way tunnels. Journal of Sound and Vibrations,2003,267:605-619.
[41]Minsili L.S, Wen Q, Xia H, Medjo Eko R. Assessment and Predietion of underground train induced vibrations and their effects on nearby building structures in Cameroon.3rd International Symposium on Environmental Vibrations:Prediction, Monitoring, Mitigation and Evaluation, Taipei, China, November 2007.
[42]Andersen L, Jones C J C. Vibration from a rail way tunnel Predicted by coupled finite element and boundary element analysis in two and three dimensions[A].Proceeding of 5th European Conference Structural Dynamics [C].Munich, Germany,2002:1131-1136
[43]Forrest J A, Hunt H E M. A three-dimensional model for calculation of train-induced ground vibration [J]. Journal of Sound and Vibration,2006, 294(1):678-705.
[44]Forrest J A, Hunt H E M. Ground vibration generated by trains in underground tunnels [J]. Journal of Sound and Vibration,2006,294(4):706-736
[45]Hussein M F M, Hunt H E M. A numerical model for calculating vibration from a railway tunnel embedded in a full-Space [J]. Journal of Sound and Vibration, 2007,305(1):401-431
[46]Stamos A A, Beskos D E.3-D seismic response analysis of long lined tunnels in half-space. Soil dynamics and Earthquake Engineering,1996,15:111-118.
[47]Stamos A A, Beskos D E. Dynamic analysis of large 3-D underground structures by the BEM. Earthquake Engineering and Engineering Vibration,1995, 1-8.
[48]Francois S, Lombaert G Degrande G. Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations. Soil dynamics and Earthquake Engineering,2005,25:839-856.
[49]Lombaert G Degrande G. Numerical modeling of free field traffic induced vibrations. Soil dynamics and Earthquake Engineering,2000,19:477-488.
[50]Wolf S. Potential low frequency ground vibration (<6.3Hz) impacts from underground LPT operations[J] Journal of Sound and Vibration,2003,267(3):651-661.
[51]Thornely R M. The prediction of vibration, ground-borne and structure-radiated noise from railways.using finite difference method-Part 1: theory [J].Proceedings of the Institute of Acoustics,2004,26(2):69-79
[52]Jones C J C, Thompson D J, Petyt M. Studies using a combined finite element and boundary element model for vibration propagation from railway tunnels [A]. Seventh International Congress on Sound and Vibration(ICSV7).
[53]Degrande G, Othman R, Othman Ret al. A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element-boundary element formulation[J] Journal of Sound and Vibration, 2006,293(3-5):645-666
[54]Andersen L, Jones C J C. Coupled boundary and finite element analysis of vibration from railway tunnels-a comparison of two- and three-dimensional models[J]. Journal of Sound and Vibration,2006,293:611-625
[55]王其昌,蔡成标,罗强,等.高速铁路路桥过渡段轨道折角限值的分析[J].铁道学报.1998(3)：110-114.
[56]高新强,仇文革.新型铁路隧道门洞口段结构受力特征现场试验研究[J].岩石力学与工程学报.2005(12)：2155-2159.
[57]李亮,张丙强,杨小礼.高速列车振动荷载下大断面隧道结构动力响应分析[J].岩石力学与工程学报.2005(23)：4259-4265.
[58]彭立敏,施成华,黄娟,等.列车荷载作用下隧道铺底结构疲劳寿命分析[J].铁道学报.2007(1)：82-85.
[59]秦旗,梁波,韩仙华.地震荷载下无碴轨道桩网路基的动力响应分析[J].兰州交通大学学报.2008(3)：33-36.
[60]赵明阶,刘绪华,敖建华,等.隧道顶部岩溶对围岩稳定性影响的数值分析[J].岩土力学.2003(3)：445-449.
[61]郭军,王明年,谭忠盛,等.大跨浅埋黄土隧道中系统锚杆受力机制研究[J].岩土力学.2010(3)：870-874.
[62]施成华,雷明锋,彭立敏,等.桥隧过渡结构静动力特性影响因素分析[J].中南大学学报(自然科学版).2011(4)：1085-1091.
[63]翟婉明,王少林.桥梁结构刚度对高速列车—轨道—桥梁耦合系统动力 特性的影响[J].中国铁道科学.2012(1)：19-26.
[64]Hisatake M, Hieda Y.2008 Three-dimensional back-analysis method for the mechanical parameters of the new ground ahead of a tunnel face[J], Tunneling and Underground Space Technology,23(4):373-380.
[65]Ghorbani M, Sharifzadeh M.2009 Long term stability assessment of Siah Bisheh powerhouse cavern based on displacement back analysis method[J]. Tunneling and Underground Space Technology,24(5):574-583.
[66]Cai M, Morioka H, Kaiser P K, et al.2007 Back-analysis of rock mass strength parameters using AE monitoring data[J]. International Journal of Rock Mechanics and Mining Sciences,44(4):538-549.
[67]Yang C, Wu Y H, Hon T. A no-tension elastic-plastic model and optimized back-analysis technique for modeling nonlinear mechanical behavior of rock mass in tunneling[J]. Tunneling and Underground Space Technology,2010,25(3):279-289.
[68]Wu J, Tsai P. New dynamic procedure for back-calculating the shear strength parameters of large landslides [J]. Engineering Geology Reconnaissance of Extreme Natural Disasters of Morakot Typhoon, Taiwan,2011,123(1-2):129-147.
[69]Sonmez H, Ulusay R, Gokceoglu C. A practical procedure for the back analysis of slope failures in closely jointed rock masses [J]. International Journal of Rock Mechanics and Mining Sciences,1998,35(2):219-233
[70]Styles T D, Coggan J S, Pine R J. Back analysis of the Joss Bay Chalk Cliff Failure using numerical modeling [J]:Engineering Geology,2011,120(1-4):81-90.
[71]Jiang J C, Yamagami T. A new back analysis of strength parameters from single slips. Computers and Geotechnics[J],2008.35(2):286-291
[72]Fakhimi A, Salehi D, Mojtabai N. Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project [J]. Tunneling and Underground Space Technology,2004,19(1):57-67.
[73]Shang Y J Cai J. G. Hao W. D.et al. Intelligent back analysis of displacements using precedent type analysis for tunneling [J]. Tunneling and Underground Space Technology.2002.17(4):381-389
[74]Yu Y. Zhang B. Yuan H. An intelligent displacement back-analysis method for earth-rockfill dams. Computers and Geotechnics [J].2007.34(6):423-434
[75]Zhang L Q, Yue Z Q, Yang Z F. A displacement-based back-analysis method for rock mass modulus and horizontal in situ stress in tunneling-Illustrated with a case study. Tunnelling and Underground Space Technology [J]. 2006.21(6):636-649
[76]Maier G, Jurina.L, Podolak.K. On model identification problem in rock mechanics[C]. Proc Symp on the Structural Foundations on Rock. Capri: 1977:257-261.
[77]Gioda G. Indirect identification of the average elastic characteristics of rock masses[C]. Proc Int Conf on Structural Foundations on Rock.Sydney,1980,.1:65-73.
[78]Arai R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior [J]. Soil and Foundations,1984,24(1):95-108.
[79]Sakurai S, Abe S. A design approach to dimensioning underground openings[C]. Pros 3rd Int Conf Numerical Methods in Geomechanics. Aachen,1979, 649-661.
[80]Sakurai S and Takeuchi K. Back analysis of measured displacements of tunnels[J]. Rock Mechanics and Rock Engineering,1983,16:173-180.
[81]Sakurai S, Deeswasmongkol N, Shiji M. Back analysis for determining material characteristics in cut slope [J].Int Symposium on Engineering in complex Rock Fonnations, Beijing, Nov,1986.
[82]晏同珍,杨顺安,方云.滑坡学[M].武汉,中国地质大学出版社,2000.
[83]杨志法等.有限元法图谱[M].北京,科学出版社,1988.
[84]杨林德,朱合华,冯紫良等.岩土工程问题的反演理论与工程实践[M].北京：科学出版社,1998.
[85]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学.1996,6：29-34.
[86]王芝银,杨志法,王思敬.岩石力学位移反演分析回顾及进展田力学进展.1998,4：488-498
[87]Zhang L L, Zhang J, Zhang L M. Back analysis of slope failure with markov chain monte carlo simulation[J]. Computers and Geotechnics.2010,37(7-8):905-912
[88]邓建辉,丰定祥,葛修润.多介质边坡弹性模量位移反分析模型及优化方法[J].岩土力学与工程学报,1997,19(3)：22-27.
[89]杜景灿.加权位移反演法确定岩体结构面的力学参数[J].岩土工程学报,1999,21(2)：209-216.
[90]吉林,赵启林,冯兆祥,等.软弱夹层与结构面的力学参数反演[J].水利学报.2003(11)：107-111.
[91]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学.2006(5)：795-798.
[92]孙志彬,杨小礼,黄阜.基于模糊数学和粒子群算法的边坡参数反分析[J].华南理工大学学报(自然科学版).2011(6)：137-141.
[93]赵衡,刘晓明.桥头跳车引起的路面受力计算分析[J].公路交通科技.2005(5)：59-62.
[94]刘萌成,黄晓明,陶向华.桥台后高填方路堤工后沉降影响因素分析[J].交通运输工程学报.2005(3)：36-40.
[95]高燕希,张军,张起森.软弱地基桥台台背填筑EPS的结构分析[J].中国公路学报.2003(3)：28-31.
[96]王亦麟.软土地基桥头跳车处理探讨[J].公路交通科技.2000(1)：30-32.
[97]王虎,胡长顺,王秉纲.连续配筋混凝土路面动荷响应分析[J].工程力学.2001(5)：119-126.
[98]邓学钧,黄晓明,沈伟新.弹性层状体系的动力响应分析[J].土木工程学报.1995(3)：9-16.
[99]俞建荣,陈荣生,金志强.半刚性基层与刚性面层联结状态对刚性路面荷载应力的影响析[J].岩土工程学报.1996(4)：37-42.
[100]陶向华,黄晓明.人-车-路相互作用三质量车辆模型分析[J].交通运输工程学报.2004(3)：11-15.
[101]周华飞,蒋建群.刚性路面在运动车辆作用下的动力响应[J].土木工程学报.2006(8)：117-125.
[102]刘俊卿,刘超,赵洪金.横观各向同性刚性路面体系静动力分析[J].长安大学学报(自然科学版).2010(2)：48-52.
[103]张军辉,王鹏,黄晓明.软土地基上高速公路加宽工程的数值分析[J].公路交通科技.2006(6)：32-35.
[104]颜可珍,夏唐代,黄立葵.双参数粘弹性地基无限长板的瞬态动力响应分析[J].岩石力学与工程学报.2005(24)：4576-4580.
[105]颜可珍,吴罗成,朱向平.移动荷载作用下弹性半空间土体的动力响应[J].建筑科学与工程学报.2011(4)：30-34.
[106]周华飞,蒋建群,张土乔.移动荷载下Kelvin地基上无限长梁的稳态响应[J].浙江大学学报(工学版).2004(10)：91-96.
[107]蒋建群,周华飞,张土乔.移动荷载下Kelvin地基上无限大板的稳态响应[J].浙江大学学报(工学版).2005(1)：28-33.
[108]蒋建群,周华飞,张土乔.移动荷载下粘弹性地基上无限大板的稳态响应[J].中国公路学报.2006(1)：6-11.
[109]曹志刚,蔡袁强,徐长节.移动车辆荷载作用下路面的动力响应[J].浙江 大学学报(工学版).2009(4)：777-781.
[110]张洪亮,胡长顺,许伟清.移动荷载作用下柔性路面的动力响应[J].长安大学学报(自然科学版).2005(5)：6-10.
[111]赖国麟.桥头跳车防治措施的研究报告之附件二—关于桥头搭板沉降坡差容许值的建议.东南大学运输工程研究所.
[112]张洪亮.路桥过渡段车路动力学分析及容许差异沉降研究[D].长安大学博士论文,2005.
[113]Biot M A. General Theory of Three-Dimensional ConsolidationJ]. J. Appl.Phys.,1941,12:155-164
[114]Biot M A.Theory of Elastic Wave in a Fluid-Saturated Porous Solid, I.Low-Frequency Range [J].J. Acoust. Soc. Am.,1956a,28:168-178
[115]Biot M A. Theory of Elastic Wave in a Fluid-Saturated Porous Solid, II.Low-Frequency Range [J].J. Acoust. Soc. Am.,1956b,28:179-191
[116]Biot M A. Mechanics of Deformation and Acoustic Propagation in Porous Media [J].J. Appl. Phys.,1962,33(4):1482-1498
[117]Boer D. Theory of Porous media:highlights in the historical development and current state [M].Berlin:Spring-Verlag,2000.
[118]Truesdell C, Toupin R A. The classical Field Theories [J].In Handbuch der physic, Spring, Berlin3(1)
[119]Green A E, Naghdi P M. A Dynamic Theory of interacting Continua[J].Int J. Engng. Sci.,1965,3:231-241
[120]Bowen R.M.混合物理论[M].江苏科技出版社,1983
[121]Bo wen R M, Reinicke K M. Plane Progressive Waves in a Binary Mixture of Linear Elastic Materials [M].J. Appl.Mech.,1978,45:493-499
[122]Atkin R J, Craine R E. Continuum Theories of Mixtures:Basic Theory and Historical Development[J].Q. J. Appl. Math.,1978,45:209-244
[123]Atkin R J, Craine R E. Continuum Theory of Mixture:Application[J].J. Inst. Maths. Appls,1976,17:153-207
[124]Plona T J. Observation of a second bulk compressional wave in porous mediumat ultrasonic frequencies[J].Appl. Phys. Lett,1980,36:259-261
[125]Berryman J G. Confirmation of Biot's Theory [J].Appl. Phys. Lett,1980, 37:382-384
[126]丁伯阳.含裂隙介质受压破裂前的地震波特性的综合实验研究与理论分析[J].西北地震学报,1983,5(5)：21-33
[127]Stoll R D. Sediment Acoustics[J].Berlin:Spring-Verlag,1989
[128]Burridge P. Vargas C A. The fundamental solution in dynamic poroelasticity[J].Geophys. R. astr. Soc,1979,58:61-82
[129]Auriault J L. Bome L. Dynamics of porous saturated media. Checking of the generalized law of darcey[J]. Acoust. soc. Am,1985,77:2012-2023
[130]Kazi-Aoual M N. Bonnet G. Green's functions in an infinite transversely isotropic saturated poroelastic medium[J].Acoust. Soc. Am.,1988,84:1883-1889
[131]Paul S. On the Disturbance Produced in a Semi-Infinite Poroelastie Medium by a Surface Load[J]. Pure. Appl. Geophys.,1976,114:615-627
[132]Philippacopoulos A J. Lamb's problem for fluid-saturated porous media [J]. Bull Seism, Soc. Am,1988,78(2):908-923
[133]Norris A N. Radiation from a point source and scattering theory in afluid-saturated porous solid [J]. J. Acoust. Soc. Am.,1985,77:2012-2023
[134]Kayrfia A M. Banerjee, P. K. Fundamental solutions of biot's equations ofdynamic poroelasticity [J]. Int. J. Engng. Sci.,1993,31(5):817-830
[135]Chen J. Time domain function solution to Boit's complete equations of dynamic poroelasticity. Part Ⅰ:Two-Dimensional Solution[J]. Int. J. Solid Struct, 1994b,3 (10):1447-1490
[136]Chen J. Time domain function solution to Boit's complete equations of dynamic poroelasticity part Ⅱ:Three-Dimensional Solution [J].Int. J. Solid. Struct, 1994,3(2):169-202
[137]丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用[J].地球物理学报,1999,42(6)：800-808
[138]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2)：234-241
[139]丁伯阳,孟凡丽,胡敏云.两相饱和介质的弹性位错震源矢量与静态位移场[J].地震学报,2002,14(3)：251--258
[140]丁伯阳,樊良本,孟凡丽.两相饱和介质半无限空间位错位移场[J].地球物理学报,2003,46(3)：408-414
[141]Garg S K. Wave propagation effects in a fluid-saturated porous solid [J]Journal of Geophysical Research,197.1,76:7947-7962
[142]Garg S K. Good A. J. Compressional waves in fluid-saturated elastic prous media[J]. Journal of Applied Physics,1974,45:1968-1974
[143]Garg S K. Dynamics of gas-fluidized beds [J]. Journal of Applied Physics, 1975,46:4493-4500
[144]Chen B F. Hung T K. Hydrodynamic pressure of water and sediment onrigid dam [J]. J. Eng. Mech. ASCE,1993,7(119):1411-1433
[145]Ghaboussi J. Variational formulation of dynamics of fluid saturated porous elastic solids.1972,98:947-963
[146]Ghaboussi J. Wilson E L. Finite element for rock joints and interfaces[J]. J. Soil Mech. Div,ASCE,1973,99(10):833-848
[147]Zienkiewicz O C. Shiomi T. Dynamic behaviour of saturated porous media-the generalized Biot formulation and its numerical solution [J]. Int. J. Num. Anal. Mech. Geomech,1984,8:71-96
[148]Johnson L R. Green's function for lamb's problem [J]. Geophys. J. R. Astron. Soc.,1974,37:99-131
[149]Kobayashi S. Nishimmra N. Green's tensors for elastichalf-spaces-application of boundary integral equation method [J]. Memoirs fac. Eng. Kyoto. Univ, 1980,42:228-241
[150]Manolis G D. Dynamic response of lined tunnels by anisoparametric boundary element method [J]. Comp. Meth. Appl. Mech. Eng.,1983,36:291-307
[151]李德寅,王邦楣,林亚超.结构模型试验[M].北京：科学出版社,1996.3
[152]王涛.桩—土相互作用影响的模型试验研究[J].岩土力学,2008,29(6)：1589-1593
[153]王戍平.破碎围岩隧道的模拟试验研究[D].杭州：浙江大学,2004
[154]裘伯永,盛兴旺,乔建东等.桥梁工程[M].北京：中国铁道出版社,2000,12
[155]董昌周,杨建辉,胡挺.公路隧道模型试验相似材料试验研究[J].现代隧道技术.2010(1)：11-16.
[156]丁浩,蒋树屏,陈林杰.公路隧道外水压力的相似模型试验研究[J].公路交通科技.2008(10)：99-104.
[157]曾开华,许家雄,张国锋.深部巷道破坏过程相似模拟实验研究[J].金属矿山.2011(9)：44-48.
[158]董昌周,曲晨.隧道围岩体相似材料试验研究[J].浙江科技学院学报.2011(6)：499-502.
[159]张强勇,李术才,郭小红,等.铁晶砂胶结新型岩土相似材料的研制及其应用[J].岩土力学.2008(8)：2126-2130.
[160]凌建明,王伟,邬洪波.行车荷载作用下湿软路基残余变形的研究[J].同济大学学报(自然科学版).2002(11)：1315-1320.
[161]张曦,唐益群,周念清,等.地铁振动荷载作用下隧道周围饱和软黏土动力响应研究[J].土木工程学报.2007(2)：85-88.
[162]崔正翔,嵇正毓.地铁隧道振动对地面环境影响预测的探讨[J].噪声与振动控制.1996(1)：9-14.
[163]刘维宁,夏禾,郭文军.地铁列车振动的环境响应[J].岩石力学与工程学报.1996：586-593.
[164]王逢朝,夏禾,张鸿儒.地铁列车振动对邻近建筑物的影响[J].北方交通大学学报.1999(5)：45-48.
[165]由广明,刘维宁.交叠车站与区间隧道列车振动对环境的影响[J].北京交通大学学报.2005(4)：40-44.
[166]雷震宇,周顺华,许恺.列车动荷载对下立交结构的影响分析[J].岩石力学与工程学报.2004(20)：3536-3540.
[167]翟辉,刘维宁.地铁列车引起的低频地表响应及减振措施研究[J].都市快轨交通.2005(4)：116-120.
[168]张玉娥.地铁区间隧道列车振动响应测试与数值分析[D].兰州铁道学院学位论文.
[169]王祥秋,杨林德,周治国.列车振动荷载作用下隧道衬砌结构动力响应特性分析[J].岩石力学与工程学报,2006,25(7)：246-249.
[170]李德武,高峰,韩文峰.列车振动下隧道基底合理结构形式的研究[J].岩石力学与工程学报,2004,23(13)：2292-2297.
[171]李德武,高峰.隧道仰拱对列车振动影响的研究[J].铁道学报,1999,21(4).
[172]Burk M, Kingsbury H B. Response of Poro elastic Layers to Moving Loads[J]. Int. J. Solid Struct,1984,20:499-511.
[173]Siddharthan R, Zafir Z, Norris, GM. Moving Load Response of Layered Soil. I. Formulation [J]. J. Eng. Mech,1993,119:2052-2071.
[174]Biot M A. Mechanics of deformation and acoustic propagation in porous media [J]. J. App 1. phys,1962,33:1482-1498.
[175]Biot M A. Theory of propagation of elastic wave in a fluid satue rated soil[J]. Acoust. Soc. Amer.,1956,28:168-178.
[176]丁伯阳,党改红,袁金华. Green函数对饱和土隧道内集中荷载作用振动位移反应的计算[J].振动与冲击,2009,11：101-112.
[177]Ding B Y, Meng F L, Hu M Y. The source vector and static displacement field by elastic dislocation on the two-phase saturated medium [J]. Acta Seismologica Sinica,2001,14(3):251-258.
[178]Miao T D, Zhu J J, Ding B Y. Essay on constitutive relation of wave propagation in saturated porous media [J]. Acta Mechanica Sinica,1995,27 (5):536-543.
[179]丁伯阳,宋新初,袁金华.饱和土隧道内集中荷载作用下振动位移反应的Green函数解答[J].工程力学,2009,6：154-155.
[180]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2)：234-241
[181]Fakhimi A, Salehi D, Mojtabai N. Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project[J]. Tunnelling and Underground Space Technology.2004,19(1):57-67.
[182]Yazdani M, Sharifzadeh M, Kamrani K, et al. Displacement-based numerical back analysis for estimation of rock mass parameters in Siah Bisheh powerhouse cavern using continuum and discontinuum approach[J]. Tunnelling and Underground Space Technology.2012,28(0):41-48.
[183]Deng J H, Lee C F. Displacement back analysis for a steep slope at the three gorges project site[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(2):259-268
[184]陈鹏,杨小礼,黄阜.浅埋三孔隧道围岩位移场解析解研究[J].铁道科学与工程学报,2011,32(1)：87～90.
[185]姜功良.浅埋软土隧道稳定性极限分析[J].土木工程学报,1998,31(5)：65～72.
[186]谢骏,刘纯贵,于海勇.双平行圆形隧道稳定的塑性极限分析上限解[J].岩石力学与工程学报,2006,25(9)：1835～1841.
[187]杨小礼,王作伟.非线性破坏准则下浅埋隧道围岩压力的极限分析[J].中南大学学报(自然科学版),2010,41(1)：299～302.
[188]靳晓光,刘伟,郑学贵.小净距偏压公路隧道开挖顺序优化[J].公路交通科技,2005,22(8)：61-64.
[189]刘伟,靳晓光,陈少华.高速公路小净距隧道合理净距的探讨[J].地下空间,2004,24(3)：380-385.
[190]刘艳青,钟世航,卢汝绥.小净距并行隧道力学状态的试验研究[J].岩石力学与工程学报,2000,19(9)：590-594.
[191]庄宁,廖少明等.大跨度小净距群洞隧道施工方案优化研究[J].地下空间与工程学报,2007,3(1)：96-100.
[192]孙元国,李文江,朱永全.客运专线小净距隧道施工效应的数值模拟分析 [J].石家庄铁道学院学报(自然科学版),2007,20(3)：6-14.
[193]舒志乐,刘保县,李月.偏压小净距隧道围岩压力分析[J].地下空间与工程学报,2007,3(3)：430-433.
[194]曹林,胡居义,黎冬林.小净距公路(双洞)隧道围岩破坏模式研究[J].2007,18(3)：65-69.
[195]王作伟.非线性破坏准则下浅埋隧道围岩压力的上限分析[D].中南大学,2010.
[196]李树忱,李术才,徐帮树.隧道围岩稳定分析的最小安全系数法[J].岩土力学,2007,28(3)：549-554.
[197]张黎明,郑颖人,王在泉,等.有限元强度折减法在公路隧道中的应用探讨[J].岩土力学,2007,28(1)：97-101.
[198]喻言,柳群义,冯德山.隧道岩体稳定性的非线性单元安全系数分析[J].中南大学学报(自然科学版),2010,41(3)：1085-1089.
[199]陈鹏,吴责,杨小礼.三孔小净距隧道围岩安全系数分析[J].湖南文理学院学报(自然科学版),2011,11(2)：55-58.
[200]刘小文,张功.强度折减应用于隧道群整体稳定性分析的判据比较[J].南昌大学学报(工科版),2010,18(2)：154-157.
[201]周小波,龙绪健.基于强度折减理论的软弱围岩隧道坍方机理分析[J].中外公路,2011,22(5)：197-200.
[202]张红,郑颖人,杨臻,等.黄土隧洞安全系数初探[J].地下空间与工程学报,2009,19(2)：297-306.
[203]陈建锋.三台阶法在软弱围岩隧道开挖施工中的应用探讨[J].中国西部科技,2010,25(26)：16-17.
[204]陈立保.三台阶法在客运专线山岭隧道软弱围岩中的推广应用[J].铁道工程学报,2008,19(12)：72-74.