预应力锚索加固岩体的机理分析和数值计算
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摘要
预应力锚索技术是一种广泛应用于水利水电、铁路、公路、工业与民用建筑中的加固支护技术。它对充分发挥岩体的自承潜力,调节和提高岩土的自身强度和自稳能力,减轻支护结构的自重有着重要的作用。预应力锚索还能节约工程材料,保证施工的安全与稳定,因而具有显著的经济和社会效益。但由于实际工程的复杂性,对预应力锚索作用效果造成影响的因素很多,导致锚索作用机理的研究仍然存在不少问题。因而,探求预应力锚索作用效果的具有普遍意义的结果是值得关注的课题。理论研究方面,本文推导了预应力锚索锚头周边岩体的附加应力场和位移场的理论公式,并对群锚效应进行了理论分析;建立了拉力型锚索和压力型锚索锚固段附近岩体的附加应力场和位移场的理论公式,以及锚固段注浆体与岩体接触面上的摩擦应力的理论公式。数值计算方面,确定了三维八结点和四结点点辐射映射无限元的位移函数和坐标映射函数,并与等参元耦合,对预应力锚索锚头和锚固段的受力进行了数值模拟计算。本文完成的主要工作有:
(1)根据半空间无限体理论的Boussinesq解,推导了预应力锚索锚头附近岩体附加应力场和位移场的理论公式,得出了预应力在锚头周边岩体中产生的附加应力和位移的形态及影响范围,并讨论了各自的受力特征、分布规律、影响因素等。将理论分析结果与用FLAC3D软件进行的数值计算结果进行了对比。两者结果一致,表明本文的理论推导是正确的。
(2)由空间无限体理论的Kelvin解,提出了拉力型锚索锚固段周边岩体的附加应力和变形的理论公式,得出了预应力在锚固段周边岩体中产生的附加应力和位移的形态及影响范围。在此基础上,推导了拉力分散型锚索锚固段附近岩体的应力和位移的理论公式,以及锚固段注浆体与岩体接触面上的摩擦应力的理论公式,得出了摩擦应力的空间形态。
(3)由空间无限体理论的Kelvin解,推导了压力型锚索锚固段附近岩体的附加应力场和位移场的理论公式。在此基础上,推导了压力分散型锚索锚固段的附加应力和位移以及锚固段注浆体与岩体接触面上的剪应力的理论公式。讨论了预应力在锚固段周边岩体中产生的附加应力和位移的形态及影响范围,以及锚固段注浆体与岩体接触面上剪应力的分布规律。
(4)由锚索锚头周边岩体附加应力场和位移场的理论公式推导了群锚的理论公式,并对群锚效应在岩体表层产生的岩石表层效应做出分析,指出这种效应相当于在岩体表层形成了一堵岩石锚固墙。将理论结果与用FLAC3D分析的数值结果进行了对比,两者的结论是一致的。
(5)将一维点辐射无限元理论推广到三维,推导了三维四结点和三维八结点点辐射无限元的形函数和坐标变换函数,并将其分别与八结点和二十结点等参元耦合,模拟计算了施加预应力后预应力锚索锚头和锚固段的位移,并与理论推导结果进行了对比分析。实践表明,无限元法是模拟无限域问题比较好的一种数值方法。
As a reinforcing and supporting technology, pre-stress anchor has been widely used in the reinforcement of water conservancy engineering, water and electricity engineering, railway, highway, industry and civil constructions. It takes a key role to inspire the self-bearing capacity of rock mass, to adjust and improve the stregth and self-stabilization of rock and soil, and to decrease the deadweight of the supporting structure. It also can be used to save engineering materials and assure the safty and stability of the construction, bring to a great economy and social benefit. Because of the complexity of practical engineering, there have many influence factors on the effection of pre-stress anchor and difficult problems in the research of anchor mechanism. Therefore, it is need to take more attention to study the action effection of pre-stress anchor. In this paper, the formulas are derived to describe the stress and displacement fields in the rock mass around the pre-stress anchor head. The multi-anchor effection is studied. The formulas of the stress and the displacement fields in the rock mass around the pull-type and compression-type pre-stress anchorage segments are given. The formulas of the friction stress on the interface of anchorage segment plasm and rock mass are obtained furtherly. In numerical study, the displacement functions and coordinate radiation functions of the 3D 4-node and 8-node dot radiation infinite elements are derived. They are coupled with the isoparameter elements to simulate the action of the pre-stress anchor head and segment. The thesis includes the following contents:
(1)Based on Boussinesq equation of the semi-space infinite solution, the theoretical formulas of the extral stress and displacement fields in the rock mass around the pre-stress anchor head are proposed. The distribution shape of the stress, displacement and the influence range of the pre-stress around the anchor head are obtained. The stress characters, distributing rule and influence factors are discussed. The theoretical results are compared with the numerical simulation results by FLAC3D, and agree with each other.
(2)Based on Kelvin equation of the infinite space theory, the theoretical formulas of the extral stress and displacement in the rock mass around the pull-type anchor segment are derived. The distribution shape and influence range of the extral stress and displacement in the rock around the pull-type anchor segment are obtained. Furthermore, the theoretical formulas of the stresses and the displacements in the rock mass around the dispersing-pull-type anchor segment are deduced. The theoretical formulas of the friction stresses on the interface of the anchor segment plasm and the rock mass are derived, and the distribution shape are also obtained.
(3)Based on Kelvin equation of the infinite space theory, the theoretical formulas of the extral stress and displacement in rock mass around the compression-type anchor segment and the dispersing-compression-type anchor segment are derived. The theoretical formulas of the friction stress on the interface of the anchor segment plasm and the rock mass are derived. The distribution shape and the influence range of the extral stress and displacement in the rock around the compression-type anchor segment are obtained. The distribution rule of the friction stress is summarized.
(4)Based on the theoretical formulas of the extral stress and the displacement in the rock mass around the singal anchor head, the formulas of the multi-anchor are derived. The surfacial effection on the rock mass caused by the multi-anchor effection is studied. The results indicate that the effection is a homologous rock-anchor wall on the rock mass surface. The theoretical results are compared with the numerical simulation results of FLAC3D, and agree with each other.
(5)The theory of 1D dot radiation infinite element is extended to 3D case. The displacement functions and coordinate radiation functions of the 3D 4-node and 8-node dot radiation infinite elements are derived. They are coupled with 8-node and 20-node isoparameter elements to simulate the displacements of the pre-stress anchor head and segment respectively. The numerial results are compared with the theoretical results, showing that the infinite element method is an effective numerical method to simulate the infinite field problem.
(1)根据半空间无限体理论的Boussinesq解,推导了预应力锚索锚头附近岩体附加应力场和位移场的理论公式,得出了预应力在锚头周边岩体中产生的附加应力和位移的形态及影响范围,并讨论了各自的受力特征、分布规律、影响因素等。将理论分析结果与用FLAC3D软件进行的数值计算结果进行了对比。两者结果一致,表明本文的理论推导是正确的。
(2)由空间无限体理论的Kelvin解,提出了拉力型锚索锚固段周边岩体的附加应力和变形的理论公式,得出了预应力在锚固段周边岩体中产生的附加应力和位移的形态及影响范围。在此基础上,推导了拉力分散型锚索锚固段附近岩体的应力和位移的理论公式,以及锚固段注浆体与岩体接触面上的摩擦应力的理论公式,得出了摩擦应力的空间形态。
(3)由空间无限体理论的Kelvin解,推导了压力型锚索锚固段附近岩体的附加应力场和位移场的理论公式。在此基础上,推导了压力分散型锚索锚固段的附加应力和位移以及锚固段注浆体与岩体接触面上的剪应力的理论公式。讨论了预应力在锚固段周边岩体中产生的附加应力和位移的形态及影响范围,以及锚固段注浆体与岩体接触面上剪应力的分布规律。
(4)由锚索锚头周边岩体附加应力场和位移场的理论公式推导了群锚的理论公式,并对群锚效应在岩体表层产生的岩石表层效应做出分析,指出这种效应相当于在岩体表层形成了一堵岩石锚固墙。将理论结果与用FLAC3D分析的数值结果进行了对比,两者的结论是一致的。
(5)将一维点辐射无限元理论推广到三维,推导了三维四结点和三维八结点点辐射无限元的形函数和坐标变换函数,并将其分别与八结点和二十结点等参元耦合,模拟计算了施加预应力后预应力锚索锚头和锚固段的位移,并与理论推导结果进行了对比分析。实践表明,无限元法是模拟无限域问题比较好的一种数值方法。
As a reinforcing and supporting technology, pre-stress anchor has been widely used in the reinforcement of water conservancy engineering, water and electricity engineering, railway, highway, industry and civil constructions. It takes a key role to inspire the self-bearing capacity of rock mass, to adjust and improve the stregth and self-stabilization of rock and soil, and to decrease the deadweight of the supporting structure. It also can be used to save engineering materials and assure the safty and stability of the construction, bring to a great economy and social benefit. Because of the complexity of practical engineering, there have many influence factors on the effection of pre-stress anchor and difficult problems in the research of anchor mechanism. Therefore, it is need to take more attention to study the action effection of pre-stress anchor. In this paper, the formulas are derived to describe the stress and displacement fields in the rock mass around the pre-stress anchor head. The multi-anchor effection is studied. The formulas of the stress and the displacement fields in the rock mass around the pull-type and compression-type pre-stress anchorage segments are given. The formulas of the friction stress on the interface of anchorage segment plasm and rock mass are obtained furtherly. In numerical study, the displacement functions and coordinate radiation functions of the 3D 4-node and 8-node dot radiation infinite elements are derived. They are coupled with the isoparameter elements to simulate the action of the pre-stress anchor head and segment. The thesis includes the following contents:
(1)Based on Boussinesq equation of the semi-space infinite solution, the theoretical formulas of the extral stress and displacement fields in the rock mass around the pre-stress anchor head are proposed. The distribution shape of the stress, displacement and the influence range of the pre-stress around the anchor head are obtained. The stress characters, distributing rule and influence factors are discussed. The theoretical results are compared with the numerical simulation results by FLAC3D, and agree with each other.
(2)Based on Kelvin equation of the infinite space theory, the theoretical formulas of the extral stress and displacement in the rock mass around the pull-type anchor segment are derived. The distribution shape and influence range of the extral stress and displacement in the rock around the pull-type anchor segment are obtained. Furthermore, the theoretical formulas of the stresses and the displacements in the rock mass around the dispersing-pull-type anchor segment are deduced. The theoretical formulas of the friction stresses on the interface of the anchor segment plasm and the rock mass are derived, and the distribution shape are also obtained.
(3)Based on Kelvin equation of the infinite space theory, the theoretical formulas of the extral stress and displacement in rock mass around the compression-type anchor segment and the dispersing-compression-type anchor segment are derived. The theoretical formulas of the friction stress on the interface of the anchor segment plasm and the rock mass are derived. The distribution shape and the influence range of the extral stress and displacement in the rock around the compression-type anchor segment are obtained. The distribution rule of the friction stress is summarized.
(4)Based on the theoretical formulas of the extral stress and the displacement in the rock mass around the singal anchor head, the formulas of the multi-anchor are derived. The surfacial effection on the rock mass caused by the multi-anchor effection is studied. The results indicate that the effection is a homologous rock-anchor wall on the rock mass surface. The theoretical results are compared with the numerical simulation results of FLAC3D, and agree with each other.
(5)The theory of 1D dot radiation infinite element is extended to 3D case. The displacement functions and coordinate radiation functions of the 3D 4-node and 8-node dot radiation infinite elements are derived. They are coupled with 8-node and 20-node isoparameter elements to simulate the displacements of the pre-stress anchor head and segment respectively. The numerial results are compared with the theoretical results, showing that the infinite element method is an effective numerical method to simulate the infinite field problem.
引文
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