深基坑支护细部结构优化及应用研究
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摘要
深基坑工程是一个十分庞杂的系统工程，在其设计过程中既要保证支护结构安全可靠又要造价经济，为了协调两者的关系，深基坑支护工程的优化设计就应运而生。由于深基坑支护工程的优化存在诸多难点，例如，1.设计变量中的连续变量和离散变量共存，变量数目众多，变量组合庞大；2.优化目标和设计变量的关系复杂，各个设计变量对优化目标的敏感性不一致，建立合理的显性表达式比较困难，所以传统的优化算法面对复杂的深基坑优化的问题往往无能为力，因此，寻找一种合理的、可行的优化算法成为关键。为了实现深基坑的优化设计，首先要解决以下四个方面的问题：一是建立一个以造价为目标的深基坑支护细部结构优化设计模型；二是分析不同支护型式的土压力计算方法；三是建立深基坑支护设计力学模型；四是寻求能求出的优化设计模型最优解的优化算法。为此，本文以国家“十一五”科技支撑计划课题《基坑支护优化设计集成系统研究及深大基坑工程示范》为依托，选择了上述四个问题作为论文的研究课题。
①对深基坑工程细部结构优化设计问题的进行了数学描述，给出了设计变量的选取、约束条件的确定、目标函数的建立三方面的内容。分别对不同的支护结构的设计变量进行了敏感性分析，筛选出对优化结果影响较大的设计变量，归纳总结了深基坑支护细部结构的主要约束条件，构造出以综合造价为优化目标的最终优化目标函数，进而建立了深基坑支护细部结构优化设计数学模型；
②为了求解优化设计模型中的约束条件，研究了深基坑不同支护型式的土压力和支护结构计算分析方法。首先从土压力的理论发展出发，研究了考虑墙背与土之间相互摩擦引起的剪切作用及放坡角度的土钉墙侧向土压力；然后分析了排桩和地下连续墙这两种支护结构在土拱效应下的土压力原理，分别对圆弧和悬链线两种拱形的土拱效应进行了分析，并两种拱形的计算结果进行了比较。根据两种土拱形状计算其平均竖直应力，由此得到了对应于不同内摩擦角和外摩擦角的侧土压力系数；将其用于水平微分单元法求解支护结构主动土压力，得到了其主动土压力强度、土压力合力和合力作用点的解析公式；
③针对三种不同的深基坑支护结构，分别提出了各自稳定性约束的计算方法。首先，运用简单条分法对层状非均质土中土钉支护结构进行了稳定性分析，得出了最危险滑动面的搜索模型和最小安全系数的计算公式。然后，采用半无限大弹性空间内部水平矩形荷载作用下的Mindlin解来模拟弹簧刚度K，运用到排桩支护结构的弹性地基梁模型的弹簧刚度求解中，得到其内力和变形的理论计算式；最后，对半无限大弹性空间内部水平线性荷载作用下的Melan公式进行推导，得到条形荷载作用下的位移解答，并将解答运用在矩阵位移法中得到了地下连续墙的受力情况；同时，为了考虑逐步开挖和加撑的支护结构的变形和内力，采用增量法对施加在支护结构上的荷载进行修正，得出的支护结构的位移和内力更加符合实际情况；
④采用动态自适应技术改进交叉算子p_c和变异算子p_m，提出了新的优化算法DAGA。这种算法克服了传统的遗传算法在迭代过程中出现的适应度值标定方式复杂、过早的收敛到局部最优解和在最优值附近收敛速度慢等缺点，从而大大提高了优化算法的收敛速度和计算精度；在此基础上，建立了土钉墙、排桩和地下连续墙的优化系统，开发了“深基坑优化设计软件”。该软件在开发过程中，运用了VC进行了数据的控制与界面的开发，而对于改进遗传算法的实现则采用了Matlab，再通过COM组件的方法将二者相结合。在软件实现过程中成功地解决了程序的结构设计和COM组件部分这两类的技术难点，并完成了这两部分的封装，最终实现了软件的完整功能。
⑤应用深基坑优化设计软件对北京王府井海港城项目深基坑支护工程进行优化分析。在优化设计中，保持深基坑支护结构原设计中预应力锚杆参数不变，对设计变量支撑位置、桩径、桩间距、嵌固深度和混凝土强度等级进行了优化。通过对原设计和优化结果的比较，验证了该软件完全适用于深基坑支护细部结构的优化设计领域。
Deep excavation engineering is a huge systematic project. It is designed both toensure the safety of retaining structure and to reduce engineering cost. In order toharmonize the relationship between the cost and reliability of engineering, theoptimization design of retaining structure for deep excavation was born. Many problemsexist in the optimization design, for example,1. The optimization design of retainingstructure usually comes down to a great lot kind of design variables and combinationvariables, including continuously variable and discrete variables.2. The relationbetween optimization target and design variables is relatively complex. Since thesensitivity of design variables towards optimization target are abhorrent, it is difficult toestablish the dominant relationships between them. As a result, to search for aoptimization algorithm is key. For the sake of the optimization design of retainingstructure, its contents involve primarily the following aspects:①It is necessary toestablish the optimization design model for retaining structure of deep excavation.②The calculation method of earth pressure for different retaining type are described.③The mechanical model for retaining structure of deep excavation was set up.④A newoptimization method based on genetic algorithm for solving this model is presented.Thus, With the support of the country “11th Five-Year Plan” to support science andtechnology project-Study on the Optimization Design System and EngineeringDemonstration of Retaining Structure for Deep Excavation, the above-mentionedproblems were chosen as research project, which has important academic significanceand application value.
①The optimization design of retaining structure was mathematically described.The content was proposed which including selection of design variables, determinationof rectrained conditions and construction of objective functions. According to analysethe relationship among design variables, the range of preliminary values of designvariables are given for constraint conditions. Finally, the optimization model wasestablished.
②In order to solve the optimization design model with constraint condition, thecalculation methods of earth pressure and security for different retaining type aredescribed. First, based on the limit equilibrium theory and the hypothesis of planarsliding surface, a formula was proposed to compute the lateral earth pressure of soilnailing wall. Then, the earth pressure principle of row piles and diaphragm wall considering the effect of the soil arching is researched, and the two shapes of minorprincipal stress arch are theoretically analyzed. According to the shapes of minorprincipal stress arch, the coefficients of earth pressure corresponding to different angleof internal friction and that of wall friction are gained. Using the method of horizontaldifferential elemeng the theoretical formula for active earth pressure on retainingstructure, the resultant earth pressure and its acting point are obtained and comparedwith the Coulomb’S formula, the previous methods and some experimental observations.This overcomes the shortcoming involved with existed active earth pressure theory thatconsider soil arching effect but takes no consideration of the influence of the internalfriction angle on the inclination of sliding plane of soils behind retaining structure.
③Different calculating methods are put forward based on the stability analysis ofthree different kinds of support structure in deep foundation pit. Firstly, the formula ofminimum safety factor and search model of the most dangerous sliding surface areobtained by means of Simple-Swedish Slices Method for the stability analysis ofsoil-nail support structure in layered uneven soil; then, stiffness of the elastic foundationbeam model in row-pile support structure is figured out by the Mindlin formula used forthe horizontal and rectangular load in the elastic half-space, theoretical formula ofinternal forces and deformation can be obtained. Lastly, forcing cases of undergroundcontinuous wall can also be indicated by the displacement solution of strip load in thematrix displacement method based on the deduced Melan formula used for thehorizontal and linear load in the elastic half-space, meanwhile, taking the excavationand lateral brace into consideration step by step, the loads on the support structure arecorrected by the increment method, which can obtain the more actual displacement anddeformation.
④Based on the crossover operator and mutation operator improved by thedynamic adaptive technology, the new optimized algorithm DAGA is put forward,which can improve the convergence rate&calculating accuracy and can overcome suchdefects as complicated ways in determining the value of adaptability during the processof traditional genetic iteration, early convergence to the local optimized solution and theslow convergence rate nearby the optimized value. On the basis of the new optimizedalgorithm DAGA, the optimized system of soil-nail wall, row-pile and undergroundcontinuous wall is established and the software of optimized design in deep foundationpit is also developed. During the developing process of the software, VC is used tocontrol the data and develop the interface, and Matlab is also used to fulfill theimproved genetic algorithm, combined with the method of COM component. Fulfilled process of such software can successfully solve the technical difficulties inencapsulating the structural design and COM component, which leads to the fulfillmentof the entire functions.
⑤The optimization design software for deep excavation has been used in theoptimization design of the project,"the retaining structure for deep excavation of theharbor city of Beijing". In the process of the optimization design, keeping the parame ofprestressed anchor unchanged, the design variables of bracing location, pile diameter,pile spacing, embedded depth and concrete strength grade are optimized.It proves thatthe software has good performance in the optimization design.
①对深基坑工程细部结构优化设计问题的进行了数学描述，给出了设计变量的选取、约束条件的确定、目标函数的建立三方面的内容。分别对不同的支护结构的设计变量进行了敏感性分析，筛选出对优化结果影响较大的设计变量，归纳总结了深基坑支护细部结构的主要约束条件，构造出以综合造价为优化目标的最终优化目标函数，进而建立了深基坑支护细部结构优化设计数学模型；
②为了求解优化设计模型中的约束条件，研究了深基坑不同支护型式的土压力和支护结构计算分析方法。首先从土压力的理论发展出发，研究了考虑墙背与土之间相互摩擦引起的剪切作用及放坡角度的土钉墙侧向土压力；然后分析了排桩和地下连续墙这两种支护结构在土拱效应下的土压力原理，分别对圆弧和悬链线两种拱形的土拱效应进行了分析，并两种拱形的计算结果进行了比较。根据两种土拱形状计算其平均竖直应力，由此得到了对应于不同内摩擦角和外摩擦角的侧土压力系数；将其用于水平微分单元法求解支护结构主动土压力，得到了其主动土压力强度、土压力合力和合力作用点的解析公式；
③针对三种不同的深基坑支护结构，分别提出了各自稳定性约束的计算方法。首先，运用简单条分法对层状非均质土中土钉支护结构进行了稳定性分析，得出了最危险滑动面的搜索模型和最小安全系数的计算公式。然后，采用半无限大弹性空间内部水平矩形荷载作用下的Mindlin解来模拟弹簧刚度K，运用到排桩支护结构的弹性地基梁模型的弹簧刚度求解中，得到其内力和变形的理论计算式；最后，对半无限大弹性空间内部水平线性荷载作用下的Melan公式进行推导，得到条形荷载作用下的位移解答，并将解答运用在矩阵位移法中得到了地下连续墙的受力情况；同时，为了考虑逐步开挖和加撑的支护结构的变形和内力，采用增量法对施加在支护结构上的荷载进行修正，得出的支护结构的位移和内力更加符合实际情况；
④采用动态自适应技术改进交叉算子p_c和变异算子p_m，提出了新的优化算法DAGA。这种算法克服了传统的遗传算法在迭代过程中出现的适应度值标定方式复杂、过早的收敛到局部最优解和在最优值附近收敛速度慢等缺点，从而大大提高了优化算法的收敛速度和计算精度；在此基础上，建立了土钉墙、排桩和地下连续墙的优化系统，开发了“深基坑优化设计软件”。该软件在开发过程中，运用了VC进行了数据的控制与界面的开发，而对于改进遗传算法的实现则采用了Matlab，再通过COM组件的方法将二者相结合。在软件实现过程中成功地解决了程序的结构设计和COM组件部分这两类的技术难点，并完成了这两部分的封装，最终实现了软件的完整功能。
⑤应用深基坑优化设计软件对北京王府井海港城项目深基坑支护工程进行优化分析。在优化设计中，保持深基坑支护结构原设计中预应力锚杆参数不变，对设计变量支撑位置、桩径、桩间距、嵌固深度和混凝土强度等级进行了优化。通过对原设计和优化结果的比较，验证了该软件完全适用于深基坑支护细部结构的优化设计领域。
Deep excavation engineering is a huge systematic project. It is designed both toensure the safety of retaining structure and to reduce engineering cost. In order toharmonize the relationship between the cost and reliability of engineering, theoptimization design of retaining structure for deep excavation was born. Many problemsexist in the optimization design, for example,1. The optimization design of retainingstructure usually comes down to a great lot kind of design variables and combinationvariables, including continuously variable and discrete variables.2. The relationbetween optimization target and design variables is relatively complex. Since thesensitivity of design variables towards optimization target are abhorrent, it is difficult toestablish the dominant relationships between them. As a result, to search for aoptimization algorithm is key. For the sake of the optimization design of retainingstructure, its contents involve primarily the following aspects:①It is necessary toestablish the optimization design model for retaining structure of deep excavation.②The calculation method of earth pressure for different retaining type are described.③The mechanical model for retaining structure of deep excavation was set up.④A newoptimization method based on genetic algorithm for solving this model is presented.Thus, With the support of the country “11th Five-Year Plan” to support science andtechnology project-Study on the Optimization Design System and EngineeringDemonstration of Retaining Structure for Deep Excavation, the above-mentionedproblems were chosen as research project, which has important academic significanceand application value.
①The optimization design of retaining structure was mathematically described.The content was proposed which including selection of design variables, determinationof rectrained conditions and construction of objective functions. According to analysethe relationship among design variables, the range of preliminary values of designvariables are given for constraint conditions. Finally, the optimization model wasestablished.
②In order to solve the optimization design model with constraint condition, thecalculation methods of earth pressure and security for different retaining type aredescribed. First, based on the limit equilibrium theory and the hypothesis of planarsliding surface, a formula was proposed to compute the lateral earth pressure of soilnailing wall. Then, the earth pressure principle of row piles and diaphragm wall considering the effect of the soil arching is researched, and the two shapes of minorprincipal stress arch are theoretically analyzed. According to the shapes of minorprincipal stress arch, the coefficients of earth pressure corresponding to different angleof internal friction and that of wall friction are gained. Using the method of horizontaldifferential elemeng the theoretical formula for active earth pressure on retainingstructure, the resultant earth pressure and its acting point are obtained and comparedwith the Coulomb’S formula, the previous methods and some experimental observations.This overcomes the shortcoming involved with existed active earth pressure theory thatconsider soil arching effect but takes no consideration of the influence of the internalfriction angle on the inclination of sliding plane of soils behind retaining structure.
③Different calculating methods are put forward based on the stability analysis ofthree different kinds of support structure in deep foundation pit. Firstly, the formula ofminimum safety factor and search model of the most dangerous sliding surface areobtained by means of Simple-Swedish Slices Method for the stability analysis ofsoil-nail support structure in layered uneven soil; then, stiffness of the elastic foundationbeam model in row-pile support structure is figured out by the Mindlin formula used forthe horizontal and rectangular load in the elastic half-space, theoretical formula ofinternal forces and deformation can be obtained. Lastly, forcing cases of undergroundcontinuous wall can also be indicated by the displacement solution of strip load in thematrix displacement method based on the deduced Melan formula used for thehorizontal and linear load in the elastic half-space, meanwhile, taking the excavationand lateral brace into consideration step by step, the loads on the support structure arecorrected by the increment method, which can obtain the more actual displacement anddeformation.
④Based on the crossover operator and mutation operator improved by thedynamic adaptive technology, the new optimized algorithm DAGA is put forward,which can improve the convergence rate&calculating accuracy and can overcome suchdefects as complicated ways in determining the value of adaptability during the processof traditional genetic iteration, early convergence to the local optimized solution and theslow convergence rate nearby the optimized value. On the basis of the new optimizedalgorithm DAGA, the optimized system of soil-nail wall, row-pile and undergroundcontinuous wall is established and the software of optimized design in deep foundationpit is also developed. During the developing process of the software, VC is used tocontrol the data and develop the interface, and Matlab is also used to fulfill theimproved genetic algorithm, combined with the method of COM component. Fulfilled process of such software can successfully solve the technical difficulties inencapsulating the structural design and COM component, which leads to the fulfillmentof the entire functions.
⑤The optimization design software for deep excavation has been used in theoptimization design of the project,"the retaining structure for deep excavation of theharbor city of Beijing". In the process of the optimization design, keeping the parame ofprestressed anchor unchanged, the design variables of bracing location, pile diameter,pile spacing, embedded depth and concrete strength grade are optimized.It proves thatthe software has good performance in the optimization design.
引文
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