圆形巷道围岩偏应力场及塑性区分布规律研究

以弹塑性力学中的圆孔应力解和塑性力学的偏应力理论为基础,利用莫尔-库仑强度准则,研究了围岩偏应力场和塑性区分布规律,得到了非均匀应力场下圆形巷道围岩偏应力的计算式和塑性区半径计算方法.结果表明:巷道埋深、极坐标r、极坐标θ和侧压系数与最大和最小主偏应力的大小曲线分别呈线性分布、"八"字型分布、"笔尖"型和"X"型分布;侧压系数小于、等于和大于1.0时,会出现不同形态的蝶形塑性区;随着侧压系数的增大,塑性区边界各位置的最大主偏应力会逐渐增大,而最小主偏应力却逐渐减小,两者之间的差值越来越大;内摩擦角、内聚力和圆形巷道半径的增加,都会导致塑性区半径的减小.     

考虑中间主应力的深埋圆形巷道弹塑性位移解

平面应变条件下的深埋圆形巷道一般忽略中间主应力的影响,但塑性区围岩的变形与实际情况会产生较大差异．为了充分考虑中间主应力对深埋圆形巷道的影响,基于平面应变假设与关联流动法则将Mohr-Coulomb准则精确匹配为Drucker-Prager准则,在此基础上推导了理想弹塑性材料在塑性阶段的中间主应力表达式;根据所得的中间主应力表达式结合关联流动法则．不引入任何假设,得出塑性区体积扩容的关系式;进一步推导了考虑中间主应力影响的深埋圆形巷道塑性区应力位移解析式,其中径向应力、切向应力及塑性区半径的表达式与卡斯特奈（Kastner）解完全一致,但卡斯特奈（Kastner）解无法得出中间主应力,而新的位移解析式则与以往的文献完全不同;经与以往文献的位移理论解比较分析知,新的位移解答更加合理．因此,考虑中间主应力的解答为深埋圆形巷道的计算与设计提供更为科学的理论基础．     

运用Drucker-Prager准则的深埋圆形硐室弹塑性分析

基于Drucker-Prager准则,考虑了中间主应力对煤岩塑性屈服的影响,得出了深埋圆形硐室围岩的弹塑性解.与修正的Fenner方程作比较,分析得出了在考虑了中间主应力的情况下,圆形硐室的塑性圈半径变大,而且内摩擦角在20°~45°以及粘结力较大时,两者的塑性圈半径相差并不大,但粘结力较小时两者相差较大,且相差趋势越来越明显.推导结果对现场巷道的支护设计具有参考作用.     

运用Drucker—Prager准则的深埋圆形硐室弹塑性分析

基于Drucker—Prager准则,考虑了中间主应力对煤岩塑性屈服的影响,得出了深埋圆形硐室围岩的弹塑性解．与修正的Fenner方程作比较,分析得出了在考虑了中间主应力的情况下,圆形硐室的塑性圈半径变大,而且内摩擦角在20°～45°以及粘结力较大时,两者的塑性圈半径相差并不大,但粘结力较小时两者相差较大,且相差趋势越来越明显．推导结果对现场巷道的支护设计具有参考作用．     

双模量-强度跌落耦合特征下深部围岩应力场演化

深部地下空间开发在深地能源贮存与开采、生态圈与地下生态城市等领域都有着巨大的潜在价值.针对深部均匀应力场作用下圆形硐室开挖,采用拉压双模量理论和弹性-脆性-理想塑性本构模型,推演了不同远场应力和内压力下围岩的应力解析解及塑性区边界方程,详细分析了围岩弹塑性应力场和塑性区随弹性常数比及残余强度系数的变化规律.结果表明:内...     

应变非线性软化的预应力衬砌隧洞弹塑性应力解

基于岩体单轴应变非线性软化本构模型,采用全量理论将其推广,获得考虑中间主应力影响的复杂应力状态下的岩体等效应力和等效应变关系,由此对灌浆式预应力衬砌隧洞进行弹塑性分析.指出预应力作用下围岩可能处于弹性或弹塑性两种状态,给出了两种情况下围岩压力、塑性区半径及衬砌应力的解析计算式,得到了围岩产生塑性变形的临界灌浆压力,并结合某工程进行了具体分析.     

用塑性应力摩尔圆求证沿滑移线上正应力的变化规律

滑移线上平均正应力的变化规律通常都是用平面应变条件下微分方程与塑性条件联立求解而得到的所谓Hencky 方程来表达〔1〕〔2〕〔3〕〔6〕〔9〕。本文借助于塑性状态下应力摩尔圆的若干特性略加推证。即能简明的得到该规律,为求证滑移线上平均应力的变化规律提供一个新的方法。     

基于Mogi-Coulomb强度准则的隧道围岩理想弹塑性解答

合理选择岩石强度准则对隧道应力及位移预测和支护设计都具有重要意义,基于Mogi‐Coulomb强度准则和理想弹塑性模型,通过中间主应力系数反映中间主应力的影响,推导了圆形隧道围岩应力和位移的解析解,并对所得结果进行比较与验证,得到了中间主应力和围岩抗剪强度参数的影响特性。研究表明：具有广泛的适用性和较好的可比性,Mohr‐Coulomb强度准则解答和Matsuoka‐Nakai准则解答均为其特例;结果关于中间主应力系数 b＝0.5对称,较好地反映了岩石强度的中间主应力效应及其区间性;粘聚力及内摩擦角对围岩塑性区半径和隧道洞壁位移的影响显著,应充分考虑中间主应力影响及围岩抗剪强度参数变化对隧道设计与施工的影响。     

考虑巷道轴向影响的地下围岩应力场简化模型

由于多种因素影响的缘故，地下巷道轴向往往与最大主应力方向并不一致，这使巷道问题视为平面应变问题失去了应有的基础。从空间三维应力场简化模式出发，推导出圆形巷道围岩应力场与巷道轴向的对应关系，并提出了将广义平面应变问题转化为狭义平面应变问题的应力修正公式，这为巷道问题的理论分析与数值计算提供了必要的理论依据。     

双层隧道内力分析

根据弹塑性理论，采用四节点、四边形等参数单元和理想弹塑性德鲁克－普拉格弹塑性材料模型，对双层隧道进行了平面应变有限元分析，自编了考虑初应力分阶段释放、模拟具体施工过程的计算处理软件，运用该软件，计算得到了衬砌与围岩共同工作时的变形情况，应力分布和塑性区分布的状况，并最终给出了衬砌的各个横截的设计内力值。     

出砂水平井近井塑性区出砂半径预测研究

基于地层岩石弹塑性变形理论,建立出砂水平井近井塑性区应力分布模型.根据弹性区与塑性区边界应力连续的原理,提出水平井弹塑性区边界即塑性出砂半径的预测模型与方法,分析了出砂水平井近井塑性区应力分布规律及出砂半径的敏感性因素.结果表明:水平井塑性应力分布及出砂半径与原始主应力关系、井周角、井斜方位角、流压等参数有直接关系;塑性出砂半径随井周角的变化规律与原始垂向主应力和最大水平主应力的大小关系有关,当最大水平主应力较大时,井周铅垂方向的出砂半径大于水平方向的出砂半径,即铅垂方向更容易出砂,当垂向主应力较大时则相反;随着井斜方位角变化出砂半径呈周期性变化,在原始水平最大主应力σH大于垂向主应力σv的情况下,井斜方位角为0°和180°时,水平方向出砂半径较大,更容易出砂;井斜方位角为90°和270°时,铅垂方向更容易出砂;由于岩石力学参数及地应力的非均质性分布,水平井出砂半径沿着井身轨迹方向也表现出明显的非均质性.     

Confining stress effect on the elastoplastic ground reaction considering the Lode angle dependence

The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC~(3D). It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.     

Hoek-Brown破坏准则求解圆形硐室塑性区半径与修正的芬纳公式比较

目的 为定量确定围岩塑性区半径和给支护锚杆的深度设计提供科学依据.方法 以Hoek-Brown破坏准则为极限平衡条件,推求侧压力系数为1.0时圆形硐室理想弹塑性围岩的弹塑性应力和塑性区半径,运用Mohr-Coulomb准则直线拟合Hoek-Brown准则曲线和面积差补方法 ,求取等效的岩体Mohr-Coulomb强度参数后,建立相对塑性区半径随支护力和地质强度指标变化的二元非线性回归数学模型,并与源自于Mohr-Coulomb强度准则为屈服条件的修正的芬纳公式进行比较研究.结果 支护力每增加1.0 MPa,就可确保地质强度指标降低10～20的岩体中不会出现塑性区.在支护力较小和岩体质量较差情况下,采用Hoek-Brown破坏准则推导得出的塑性区半径和修正的芬纳公式计算得出的塑性区半径差别稍大.相对塑性区半径与地质强度指标都呈负乘幂函数关系,随着支护力的增大,塑性区半径随着岩体质量等级的升高而下降的趋势逐渐变缓.建立的相对塑性区半径随地质强度指标和支护力变化的二元非线性回归数学模型简明,使支护力连续变化,提高了工程实用性.结论 在岩体质量较差情况下,锚杆深度取1.8～3.0倍硐半径为宜.     

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is illustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and displacement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisymmetrical stress conditions, the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses （GSI〈25）, measures （such as grouting, setting rock bolts, etc.） that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the stability of the tunnels by providing a small support resistance p through shotcrete, except for very poor quality jointed rock masses. Without reference to the quality of the rock mass, the disturbance factor D should not less than 0.5. Measures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.     

变双曲圆弧齿线圆柱齿轮齿面曲率特性研究

齿轮副共轭齿面间的曲率关系是表征齿轮传动质量好坏的重要参数,对齿面诱导法曲率、接触区形状、接触特性、润滑特性、磨损和齿面压应力都有直接的影响。作者基于变双曲圆弧齿线圆柱齿轮的齿面方程对其曲率表达式进行推导并研究了其变化规律。首先根据大刀盘加工原理,利用坐标变换得到了变双曲圆弧齿线圆柱齿轮的齿面方程。基于得到的齿面方程,利用微分几何和空间啮合原理对变双曲圆弧齿线圆柱齿轮的主曲率、高斯曲率、平均曲率和诱导法曲率的数学表达式进行了推导。根据所推导的数学方程利用计算机软件得到变双曲圆弧齿线圆柱齿轮副的齿面数据点,并对该齿轮副的主曲率、高斯曲率、平均曲率和诱导法曲率进行了仿真分析,得到了在啮合过程中齿轮曲率的变化规律。通过仿真结果可知齿轮副的凹、凸齿面在齿线方向的主曲率变化趋势是一致的,但略有差异;在齿廓方向主曲率都在逐渐增大,但增加幅度恰好相反,并且主曲率的变化趋势与齿形的凹凸性是一致的。齿轮副的高斯曲率和平均曲率都很小,在啮合过程中变化幅度很小,没有发生突变,这就证明了该齿轮副的光滑程度很高,齿面连续。诱导法曲率在齿线方向的主值很小,基本接近于0,在齿廓方向的主值为负值,从而证明了该齿轮副在啮合过程中没有干涉现象发生。通过曲率研究证明了该齿轮传动性能很好、传动平稳,同时也为该齿轮后续的研究、开发和设计提供了一定的研究基础。     

采用总荷载不变法的非静水压隧道摄动拓展解

为描述实际地应力场下隧道塑性区演化规律和支护设计原则,基于Mohr-Coulomb准则和弹-脆-塑性模型,采用总荷载不变法并引入弹性区应力摄动解,建立了非静水压力下圆形隧道水平轴和竖向轴处的塑性区半径方程,继而利用几何相似原理拓展至其他方位角处,并与文献总荷载不变法(以应力基尔希公式为基础)、Kastner法、复变函数法和实测数据进行对比,结合非关联流动法则推导塑性区位移解析解,探讨侧压力系数与脆性软化对隧道塑性区边界线、塑性区位移分布和围岩特征曲线的影响特性。结果表明：相比文献总荷载不变法和Kastner法,2阶摄动解作为非静水压圆形隧道的弹性区应力表达式更合理,且得到复变函数法的正确性验证;侧压力系数对隧道塑性区边界线的形状和范围均有明显影响,需针对具体方位角选择支护类型和尺寸以调控收敛约束交点处的支护压力与围岩稳定变形;隧道塑性区半径和洞壁位移随围岩峰后强度的降低而显著增加,宜使用弹-脆-塑性模型构建围岩特征曲线。     

Mechanism of zonal disintegration phenomenon in enclosing rock mass around deep tunnels

In order to study the mechanism of the zonal disintegration phenomenon (ZDP), both experimental and theoretical investigations were carried out. Firstly, based on the similarity law, gypsum was chosen as equivalent material to simulate the deep rock mass, the excavation of deep tunnel was modeled by drilling a hole in the gypsum models, two circular cracked zones were measured in the model, and ZDP in the enclosing rock mass around deep tunnel was simulated in 3D gypsum model tests. Secondly, based on the elasto-plastic analysis of the stressed-strained state of the surrounding rock mass with the improved Hoek-Brown strength criterion and the bilinear constitutive model, the maximum stress zone occurred in vicinity of the elastic-plastic interface due to the excavation of the deep tunnel, rock material in maximum stress zone is in the approximate uniaxial loading state owing to the larger tangential force and smaller radial force, the mechanism of ZDP was explained, which lay in the creep instability failure of rock mass due to the development of plastic zone and transfer of the maximum stress zone within the rock mass. Thirdly, the analytical critical depth for the occurrence of ZDP was obtained, which depended on the mechanical indices and stress concentration coefficient of rock mass. Foundation item: Projects(50525825, 90815010) supported by the National Natural Science Foundation of China; Project(2009CB724608) supported by the Major state Basic Research Development Program of China     

应力剪胀对浅埋隧道稳定性系数的影响

考虑剪胀对隧道围岩稳定性的影响,对浅埋圆形盾构隧道、浅埋两车道公路隧道和浅埋双线铁路隧道在围岩发生塑性流动时进行力学特征分析。分析圆形盾构隧道围岩的位移,塑性区分布和最大剪切应变率;计算圆形断面、双线铁路隧道、双车道公路隧道等3种不同断面形状隧道的稳定性系数,分析剪胀角对围岩稳定性系数的影响。研究结果表明：剪胀角对围岩位移的影响存在一个临界值;在围岩发生塑性流动时,塑性区随着剪胀角的增大而逐渐增加;剪胀角对围岩剪切破坏带和围岩稳定性系数都有较大影响;随着剪胀角的变化,隧道临界稳定系数也发生变化。     

An Estimation Method of Stress in Soft Rock Based on In-situ Measured Stress in Hard Rock

The law of variation of deep rock stress in gravitational and tectonic stress fields is analyzed based on the Hoek-Brown strength criterion. In the gravitational stress field, the rocks in the shallow area are in an elastic state and the deep, relatively soft rock may be in a plastic state. However, in the tectonic stress field, the relatively soft rock in the shallow area is in a plastic state and the deep rock in an elastic state. A method is proposed to estimate stress values in coal and soft rock based on in-situ measurements of hard rock. Our estimation method relates to the type of stress field and stress state. The equations of rock stress in various stress states are presented for the elastic, plastic and critical states. The critical state is a special stress state, which indicates the conversion of the elastic to the plastic state in the gravitational stress field and the conversion of the plastic to the elastic state in the tectonic stress field. Two cases studies show that the estimation method is feasible.     

Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels—mechanism and discussion of characteristic parameters

The mechanism of the zonal disintegration phenomenon (ZDP) was realized based on the analysis of the stressedstrained state of the rock mass in the vicinity of the maximum stress zone, which resides in the creep instability failure of rock mass due to the development of a plastic zone and transfer of the maximum stress zone within the rock mass. Some characteristic parameters of the ZDP are discussed theoretically. In first instance, the analytical critical depth condition for the occurrence of ZDP was obtained, which depends on the characteristics and stress concentration coefficient of the rock mass. Secondly, based on creep theory, the expression of the outer radius of the undisturbed zones in the deep rock mass was obtained with the use of an improved Burgers theological model, which indicated that the radius depends on the characteristics of the rock mass and the depth of excavation and increases quasi-linearly with the rise of creep compliance of the rock mass. Finally, the formula for the distance of the most remote fissured zone away from the working periphery was derived, which increases logarithmically with the increase in the ratio of the in-situ stress and ultimate strength of rock mass. The distances between fissured zones are discussed in qualitative terms.