断续节理岩体锚固效应数值模拟方法研究
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摘要
随着国民经济的持续稳定增长,对地下洞室开发利用的需求日益增加,如城市地下铁道与海底隧道、地下商城与地下车库工程、大型人民防空建筑物、市政地下工程、大型水电地下厂房与超长水工隧洞、多线铁路与公路隧道、冶金和煤炭矿山井巷工程、重大军用国防工程、能源地下储存库及核废料地下处置库等等。岩土锚固技术,无疑是保证地下洞室开挖顺利进行和正常使用,有效的控制围岩变形的有效措施,目前已经成为一种无可替代的岩土工程安全加固措施。
结构面是岩体作为工程材料的一个显著特征,它遍布于天然岩体中将岩石料切割成断续介质,其中又尤以断续节理最为普遍。结构面的数量、分布、形态和性质直接决定着岩体的整体力学效应和破坏形式。岩体的失效破坏往往是由于赋存于其中节理在荷载作用下萌生、发育、扩展、贯通造成的。锚杆作为广泛应用于岩体工程中的一种加固构件,其锚固效果是显著的,但其加固机理尚不十分明确。本文以加锚断续节理岩体为研究对象,通过损伤理论和数值分析手段,致力于得到一种简单、有效、易于推广,可以适用于工程实践的能够计算出断续节理岩体加锚加固效应的数值方法。
对断续节理岩体儿何损伤张量进行了定义和推导,引入狄拉克奇异函数来描述裂纹密度的方向分布特征,积分即得到损伤张量D。不同的损伤张量D阶数,对裂纹描述的精确性不一样,低阶张量可以完全由高阶张量经过简化得到,高阶张量包含有所有低阶张量的信息。在多族裂纹情况下,二阶张量对多族裂纹的描述能力有所欠缺。
基于对固有损伤定义的模仿,将损伤的定义进行扩展,将因增强材料的介入(锚杆、注浆、加筋土、土工织物)而引起的受力面积或刚度的变化量定义为负损伤(Anti-Damage)或增强(Reinforcement)。负损伤概念的提出实际上是对现有损伤概念的扩展,其量值的定义、空间方向分布的确定、推导和运算均可遵循损伤变量的法则。
建立了能够计算翼裂纹尖端应力强度因子并同时考虑裂纹面接触效应的有限元模型。为克服目前应用最广泛的虚拟弹簧法无法提供抗弯的缺点,本文模型将锚杆建为实体,并充分考虑了锚杆与岩体之间的接触。利用此模型可以计算出加锚前后岩体内翼裂纹裂尖应力强度因子的变化。
运用准唯象损伤力学方法,利用本文建立的实体锚杆有限元模型,以裂纹尖端应力强度因子的减小程度作为评价锚固效应的依据,发现应力强度因子的衰减符合高斯分布规律,即锚杆对岩体的加固具有非局部效应,且在不同锚杆几何尺寸与锚杆刚度下,强度因子的衰减的趋势也有不同。用高斯分布函数拟合这些趋势,得到了不同锚杆工况对应的高斯函数具体表达式。
用Fortran程序实现了上述设想。从程序的运行结果看,本文所编制的程序能体现出裂隙存在对岩体的削弱现象,以及这种削弱效应的各向异性；在加锚后,也能够体现出锚杆对岩体的增强效果,和增强效果的各向异性。程序能够实现本文所提出的模拟锚固效应的设想,并且结果符合实际情况。
The demand of underground cavern development increases rapidly with the sustained stable growth of the national economy. These underground caverns include urban subway, submarine tunnel, underground shopping mall and garage, large-scale air-raid shelter structure, municipal underground engineering, underground workshop of hydropower station, super-long hydraulic tunnel, multiple line tunnel of highway and railway, mineral engineering, momentous national defense projects and military engineering, underground storage of fuel and nuclear waste. Geotechnical anchoring technology which can ensure the project smooth progress and normal operation also can control the deformation of surrounding rockmass has become an irreplaceable reinforcement measures in geotechnical engineering safety.
Joint which is the most significant property of rock as a kind of engineering material distribute universally in natural rockmass. In all kinds of joints, intermittent joints are most universal. The mechanics characteristics and failure style if the entire rockmass are determined directly by the quantity, distribution, feature and properties of the joints. The failure of the rockmass is usually caused by initiation, development, expand, transfixion of the cracks under the external load. As the most widely used reinforcement structure, anchoring effect of the bolts is significant. The mechanism of anchoring effect is not explicit yet. Taking bolted intermittent jointed rockmass as the research object, through the damage theory and numerical simulation, this dissertation is dedicated to obtained a simple, efficient, propagable, engineering-usable technology which is capable of simulating the anchorage effect of bolt to intermittent jointed rockmass.
A FEM model is established to compute stress intensity factor (SIF) of winged-crack in bolted rockmass, contact effect of crack surfaces is also considered in this model. A comparison is conducted between method in this paper and virtual spring method. From the result of this model, the anchoring effect of bolt is embodied by bending resistance. The most fatal defect of virtual spring method which is very popular is that bending can not be expressed from virtual spring.
Geometrical damage tensor of intermittent jointed rockmass is defined and derived. A singular Dirac function is introduced to describe the orientation distribution of crack density and Damage tensor is obtained by integrating the Dirac function. The accuracy of the Damage tensor in crack density description is determined by the order of the tensor. Low order tensor can be adequately derived from high order tensor. Orientation distribution of crack density can not be wholly described by second order tensor while two or more family of crack exist.
Based on the imitation to existing definition of Damage, the increase of bearing area or stiffness caused by reinforcement (bolt, grout, geotechnical grille) is defined as Anti-Damage. In fact this is an extension to existing definition of damage. The definition, special distribution, operational rule of Anti-Damage is just same as Damage tensor.
On the base of quasi-phenomenology damage mechanics and non-location theory, from the calculation result of FEM model, it is found that the attenuation of SIF accord with Gaussian distribution. The parameters of Gaussian distribution vary with the scale and stiffness of bolt. So Gaussian distribution is chosen to fit the attenuation of SIF.
The statement expounded above is programmed via FORTRAN programming language whose version is 6.5.The calculation result of program is capable of expressing the anisotropic weaken effect caused by existence of joints and anisotropic and non-local anchoring effect caused by existence of bolts.
结构面是岩体作为工程材料的一个显著特征,它遍布于天然岩体中将岩石料切割成断续介质,其中又尤以断续节理最为普遍。结构面的数量、分布、形态和性质直接决定着岩体的整体力学效应和破坏形式。岩体的失效破坏往往是由于赋存于其中节理在荷载作用下萌生、发育、扩展、贯通造成的。锚杆作为广泛应用于岩体工程中的一种加固构件,其锚固效果是显著的,但其加固机理尚不十分明确。本文以加锚断续节理岩体为研究对象,通过损伤理论和数值分析手段,致力于得到一种简单、有效、易于推广,可以适用于工程实践的能够计算出断续节理岩体加锚加固效应的数值方法。
对断续节理岩体儿何损伤张量进行了定义和推导,引入狄拉克奇异函数来描述裂纹密度的方向分布特征,积分即得到损伤张量D。不同的损伤张量D阶数,对裂纹描述的精确性不一样,低阶张量可以完全由高阶张量经过简化得到,高阶张量包含有所有低阶张量的信息。在多族裂纹情况下,二阶张量对多族裂纹的描述能力有所欠缺。
基于对固有损伤定义的模仿,将损伤的定义进行扩展,将因增强材料的介入(锚杆、注浆、加筋土、土工织物)而引起的受力面积或刚度的变化量定义为负损伤(Anti-Damage)或增强(Reinforcement)。负损伤概念的提出实际上是对现有损伤概念的扩展,其量值的定义、空间方向分布的确定、推导和运算均可遵循损伤变量的法则。
建立了能够计算翼裂纹尖端应力强度因子并同时考虑裂纹面接触效应的有限元模型。为克服目前应用最广泛的虚拟弹簧法无法提供抗弯的缺点,本文模型将锚杆建为实体,并充分考虑了锚杆与岩体之间的接触。利用此模型可以计算出加锚前后岩体内翼裂纹裂尖应力强度因子的变化。
运用准唯象损伤力学方法,利用本文建立的实体锚杆有限元模型,以裂纹尖端应力强度因子的减小程度作为评价锚固效应的依据,发现应力强度因子的衰减符合高斯分布规律,即锚杆对岩体的加固具有非局部效应,且在不同锚杆几何尺寸与锚杆刚度下,强度因子的衰减的趋势也有不同。用高斯分布函数拟合这些趋势,得到了不同锚杆工况对应的高斯函数具体表达式。
用Fortran程序实现了上述设想。从程序的运行结果看,本文所编制的程序能体现出裂隙存在对岩体的削弱现象,以及这种削弱效应的各向异性；在加锚后,也能够体现出锚杆对岩体的增强效果,和增强效果的各向异性。程序能够实现本文所提出的模拟锚固效应的设想,并且结果符合实际情况。
The demand of underground cavern development increases rapidly with the sustained stable growth of the national economy. These underground caverns include urban subway, submarine tunnel, underground shopping mall and garage, large-scale air-raid shelter structure, municipal underground engineering, underground workshop of hydropower station, super-long hydraulic tunnel, multiple line tunnel of highway and railway, mineral engineering, momentous national defense projects and military engineering, underground storage of fuel and nuclear waste. Geotechnical anchoring technology which can ensure the project smooth progress and normal operation also can control the deformation of surrounding rockmass has become an irreplaceable reinforcement measures in geotechnical engineering safety.
Joint which is the most significant property of rock as a kind of engineering material distribute universally in natural rockmass. In all kinds of joints, intermittent joints are most universal. The mechanics characteristics and failure style if the entire rockmass are determined directly by the quantity, distribution, feature and properties of the joints. The failure of the rockmass is usually caused by initiation, development, expand, transfixion of the cracks under the external load. As the most widely used reinforcement structure, anchoring effect of the bolts is significant. The mechanism of anchoring effect is not explicit yet. Taking bolted intermittent jointed rockmass as the research object, through the damage theory and numerical simulation, this dissertation is dedicated to obtained a simple, efficient, propagable, engineering-usable technology which is capable of simulating the anchorage effect of bolt to intermittent jointed rockmass.
A FEM model is established to compute stress intensity factor (SIF) of winged-crack in bolted rockmass, contact effect of crack surfaces is also considered in this model. A comparison is conducted between method in this paper and virtual spring method. From the result of this model, the anchoring effect of bolt is embodied by bending resistance. The most fatal defect of virtual spring method which is very popular is that bending can not be expressed from virtual spring.
Geometrical damage tensor of intermittent jointed rockmass is defined and derived. A singular Dirac function is introduced to describe the orientation distribution of crack density and Damage tensor is obtained by integrating the Dirac function. The accuracy of the Damage tensor in crack density description is determined by the order of the tensor. Low order tensor can be adequately derived from high order tensor. Orientation distribution of crack density can not be wholly described by second order tensor while two or more family of crack exist.
Based on the imitation to existing definition of Damage, the increase of bearing area or stiffness caused by reinforcement (bolt, grout, geotechnical grille) is defined as Anti-Damage. In fact this is an extension to existing definition of damage. The definition, special distribution, operational rule of Anti-Damage is just same as Damage tensor.
On the base of quasi-phenomenology damage mechanics and non-location theory, from the calculation result of FEM model, it is found that the attenuation of SIF accord with Gaussian distribution. The parameters of Gaussian distribution vary with the scale and stiffness of bolt. So Gaussian distribution is chosen to fit the attenuation of SIF.
The statement expounded above is programmed via FORTRAN programming language whose version is 6.5.The calculation result of program is capable of expressing the anisotropic weaken effect caused by existence of joints and anisotropic and non-local anchoring effect caused by existence of bolts.
引文
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