边坡框架锚杆锚固系统力学行为及特性研究
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摘要
历次地震震害调查表明,边坡框架锚杆支护技术具有良好的抗震性能,然而,目前边坡框架锚杆锚固系统力学行为及特性研究,尤其是其动力领域极不成熟,严重滞后于工程应用,开展此项研究,对边坡锚固工程科学设计与安全评价均具有重要理论和工程实践意义。
鉴于此,本文采用理论分析、数值模拟与工程资料对比验证等技术手段,在弄清边坡锚固系统锚杆静载拉拔受力机制的基础上,着重研究边坡锚固系统锚杆自由振动、锚杆共振效应、锚杆受迫振动、锚杆动力固坡效应以及坡面框架格梁受迫振动特性等。通过系统分析,得到以下几点认识：
根据界面二阶段黏滑本构模型假定,推导了锚杆拉拔临界松动荷载理论公式、锚杆拉拔荷载与松动长度内在关系表达式；依据界面抗剪强度与残余强度之间大小关系,将锚杆拉拔松动破坏类型划分为渐进式和突发式两种类型,并给出了破坏类型定量判别标准及其所对应的锚杆拉拔极限荷载理论解；同时,以此为基础,给出了层状地层锚杆、缺陷锚杆锚固迭代计算方法与求解步骤,并开展此两种复杂情形下锚杆拉拔力学行为及特性分析。
基于一定假定,建立了边坡锚固系统锚杆自由振动力学模型,给出了锚固系统自由振动控制方程及其边界条件；分别推导了无阻尼和有阻尼情形下有关系统固有频率或特征参数、振型理论计算公式；结合锚固工程抗震设防要求,给出了确定场地锚固工程危险区域与共振锚杆设计图谱的计算方法；同时,通过参数灵敏度分析,进一步揭示了影响锚固系统无阻尼固有频率和有阻尼特征参数的主要因素及其内在规律。
基于锚杆微段动力受力分析,给出了锚固系统锚杆受迫振动动力平衡方程；分别推导了无阻尼和有阻尼情形锚杆简谐受迫振动力学响应理论解,同时还建立了锚杆受迫振动响应具体的有限差分格式,并结合MATLAB编程技术使其程序化,通过算例,相互验证方法的可行性与正确性,并指出了各方法的优劣及锚固系统锚杆受迫振动力学响应分析计算方法的选取原则；通过算例分析,揭示了在水平地震荷载作用下锚杆动力响应规律。
通过FLAC数值模拟,在重新审视地震边坡岩土体变形破坏机制的基础上,通过不同工况下地震边坡位移场、应力场及典型单元应力状态的对比分析,进行了地震边坡加锚效应分析；同时,通过锚杆动力固坡效应参数影响分析,提出了一些指导边坡锚固工程抗震设计的参考建议。
基于一定假定,建立了坡面框架格梁支护结构动力力学模型,推导了框架竖梁受迫振动动力平衡控制方程；获得了锚固系统无阻尼和有阻尼情形竖梁简谐受迫振动动力力学响应理论解析解；同时,根据有限差分原理,建立了框架竖梁受迫振动响应具体的有限差分格式及其计算流程,并采用MATLAB编程技术使其程序化；通过算例相互验证方法的可行性与正确性,并指出了各方法的计算特点；通过算例分析,揭示了在水平地震荷载作用下竖梁动力响应规律。
All previous earthquake disasters have demonstrated that slope supporting techniques which using anchor has good seismic performance. However, the mechanical behaviors and characteristics to anchorage system of slope supporting structure has not been understood well so far, among them the research of dynamic properties is especially immature and strongly hinders the engineering application. Therefore the research to these fields is of great theoretical and engineering practical significant to the seismic design and safety evaluation of slope supporting structures.
In this paper, the techniques such as theoretical analysis, numerical simulation and verification of engineering data etc. have been used. The pull-out mechanism of anchor under static loading is fundamentally investigated; the free vibration, resonance effect, forced vibration and dynamic response of anchor are also researched; and the forced vibration effect of slope frame structure is studied as well. Through systematically analyses, it is found that:
According to the assumption of viscous-slip model, the equation which used to calculate the critical loading of pull-out can be derived, the relation between critical loading and loose length can be obtained as well. The failure type of pull-out can be divided as gradual change or mutation in terms of the ratio between shear strength and residual strength at interface. The qualitative discrimination standard of different failure modes and corresponding solution to ultimate loading are given. Based on this, the iterative calculation method and its calculating process to the defective anchors and the anchors in strata ground are given, and the mechanical behaviors and characteristics of these two kinds of anchors which under complicated conditions are analyzed as well.
Based on certain assumptions, the mechanical model of free vibration of anchorage system is established, the governing equations and boundary conditions are given, and the equations which used to calculate natural frequency and vibration mode of anchorage system are hence derived with damping effect neglected or considered. Take the precaution requirement of seismic design into consideration, the calculating methods of hazardous areas and resonance map can be given. What is more, through the sensitive analyses of parameters, the inherent law and main factors which influence the natural frequency of anchorage system with damping effect neglected or considered can be revealed.
Based on the dynamic response analyses of the micro-segment of anchor, the equilibrium equation of the anchor under forced vibration can be obtained, the theoretical solution to the anchor in harmonic forced vibration can be got with damping neglected or considered respectively. What is more, the mechanical response of anchor under forced vibration can be expressed as differential format, and hence can be programmed by MATLAB Language. Through a numerical case study, the validity of different methods can be revealed. Specifically, the advantage and disadvantage of different methods can be clearly shown, as a result will give some guidance on how to choose calculating method in the mechanical response analyses. By the case study, the dynamic response law of anchor under horizontal seismic loading can also be demonstrated.
Through the numerical simulation of FLAC, in a view of re-examining the dynamic failure mechanism of rock-soil mass, the displacement, stress and stress state of typical points have been comparatively analyzed for different engineering cases. The effect of anchorage support to slope under earthquake is analyzed as well. What is more, the role of each parameter plays is investigated, and the result can be referred to seismic design of slope anchorage system.
Based on certain assumptions, the dynamic response model of slope supporting structure is established, the governing equations to the forced vibration is derived. The theoretical solutions to the dynamic response of vertical beam under harmonic forced vibration can be achieved with damping neglected or considered. Meanwhile, according to differential method principle, the differential format and calculating process of the dynamic response analyses under forced vibration are established and programmed by using MATLAB Language. The validity and characteristics of each method can be verified or shown by case study; the dynamic response law of vertical beam under horizontal seismic loading can be demonstrated as well.
鉴于此,本文采用理论分析、数值模拟与工程资料对比验证等技术手段,在弄清边坡锚固系统锚杆静载拉拔受力机制的基础上,着重研究边坡锚固系统锚杆自由振动、锚杆共振效应、锚杆受迫振动、锚杆动力固坡效应以及坡面框架格梁受迫振动特性等。通过系统分析,得到以下几点认识：
根据界面二阶段黏滑本构模型假定,推导了锚杆拉拔临界松动荷载理论公式、锚杆拉拔荷载与松动长度内在关系表达式；依据界面抗剪强度与残余强度之间大小关系,将锚杆拉拔松动破坏类型划分为渐进式和突发式两种类型,并给出了破坏类型定量判别标准及其所对应的锚杆拉拔极限荷载理论解；同时,以此为基础,给出了层状地层锚杆、缺陷锚杆锚固迭代计算方法与求解步骤,并开展此两种复杂情形下锚杆拉拔力学行为及特性分析。
基于一定假定,建立了边坡锚固系统锚杆自由振动力学模型,给出了锚固系统自由振动控制方程及其边界条件；分别推导了无阻尼和有阻尼情形下有关系统固有频率或特征参数、振型理论计算公式；结合锚固工程抗震设防要求,给出了确定场地锚固工程危险区域与共振锚杆设计图谱的计算方法；同时,通过参数灵敏度分析,进一步揭示了影响锚固系统无阻尼固有频率和有阻尼特征参数的主要因素及其内在规律。
基于锚杆微段动力受力分析,给出了锚固系统锚杆受迫振动动力平衡方程；分别推导了无阻尼和有阻尼情形锚杆简谐受迫振动力学响应理论解,同时还建立了锚杆受迫振动响应具体的有限差分格式,并结合MATLAB编程技术使其程序化,通过算例,相互验证方法的可行性与正确性,并指出了各方法的优劣及锚固系统锚杆受迫振动力学响应分析计算方法的选取原则；通过算例分析,揭示了在水平地震荷载作用下锚杆动力响应规律。
通过FLAC数值模拟,在重新审视地震边坡岩土体变形破坏机制的基础上,通过不同工况下地震边坡位移场、应力场及典型单元应力状态的对比分析,进行了地震边坡加锚效应分析；同时,通过锚杆动力固坡效应参数影响分析,提出了一些指导边坡锚固工程抗震设计的参考建议。
基于一定假定,建立了坡面框架格梁支护结构动力力学模型,推导了框架竖梁受迫振动动力平衡控制方程；获得了锚固系统无阻尼和有阻尼情形竖梁简谐受迫振动动力力学响应理论解析解；同时,根据有限差分原理,建立了框架竖梁受迫振动响应具体的有限差分格式及其计算流程,并采用MATLAB编程技术使其程序化；通过算例相互验证方法的可行性与正确性,并指出了各方法的计算特点；通过算例分析,揭示了在水平地震荷载作用下竖梁动力响应规律。
All previous earthquake disasters have demonstrated that slope supporting techniques which using anchor has good seismic performance. However, the mechanical behaviors and characteristics to anchorage system of slope supporting structure has not been understood well so far, among them the research of dynamic properties is especially immature and strongly hinders the engineering application. Therefore the research to these fields is of great theoretical and engineering practical significant to the seismic design and safety evaluation of slope supporting structures.
In this paper, the techniques such as theoretical analysis, numerical simulation and verification of engineering data etc. have been used. The pull-out mechanism of anchor under static loading is fundamentally investigated; the free vibration, resonance effect, forced vibration and dynamic response of anchor are also researched; and the forced vibration effect of slope frame structure is studied as well. Through systematically analyses, it is found that:
According to the assumption of viscous-slip model, the equation which used to calculate the critical loading of pull-out can be derived, the relation between critical loading and loose length can be obtained as well. The failure type of pull-out can be divided as gradual change or mutation in terms of the ratio between shear strength and residual strength at interface. The qualitative discrimination standard of different failure modes and corresponding solution to ultimate loading are given. Based on this, the iterative calculation method and its calculating process to the defective anchors and the anchors in strata ground are given, and the mechanical behaviors and characteristics of these two kinds of anchors which under complicated conditions are analyzed as well.
Based on certain assumptions, the mechanical model of free vibration of anchorage system is established, the governing equations and boundary conditions are given, and the equations which used to calculate natural frequency and vibration mode of anchorage system are hence derived with damping effect neglected or considered. Take the precaution requirement of seismic design into consideration, the calculating methods of hazardous areas and resonance map can be given. What is more, through the sensitive analyses of parameters, the inherent law and main factors which influence the natural frequency of anchorage system with damping effect neglected or considered can be revealed.
Based on the dynamic response analyses of the micro-segment of anchor, the equilibrium equation of the anchor under forced vibration can be obtained, the theoretical solution to the anchor in harmonic forced vibration can be got with damping neglected or considered respectively. What is more, the mechanical response of anchor under forced vibration can be expressed as differential format, and hence can be programmed by MATLAB Language. Through a numerical case study, the validity of different methods can be revealed. Specifically, the advantage and disadvantage of different methods can be clearly shown, as a result will give some guidance on how to choose calculating method in the mechanical response analyses. By the case study, the dynamic response law of anchor under horizontal seismic loading can also be demonstrated.
Through the numerical simulation of FLAC, in a view of re-examining the dynamic failure mechanism of rock-soil mass, the displacement, stress and stress state of typical points have been comparatively analyzed for different engineering cases. The effect of anchorage support to slope under earthquake is analyzed as well. What is more, the role of each parameter plays is investigated, and the result can be referred to seismic design of slope anchorage system.
Based on certain assumptions, the dynamic response model of slope supporting structure is established, the governing equations to the forced vibration is derived. The theoretical solutions to the dynamic response of vertical beam under harmonic forced vibration can be achieved with damping neglected or considered. Meanwhile, according to differential method principle, the differential format and calculating process of the dynamic response analyses under forced vibration are established and programmed by using MATLAB Language. The validity and characteristics of each method can be verified or shown by case study; the dynamic response law of vertical beam under horizontal seismic loading can be demonstrated as well.
引文
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