Determination of safe mud window considering time-dependent variations of temperature and pore pressure:Analytical and numerical approaches

Wellbore stability is a key to have a successful drilling operation.Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations.These stresses are significantly impacted by pore pressure variation and thermal stresses in the field.In order to address wellbore instability problems,it is important to investigate the mechanisms of rockefluid interaction with respect to thermal and mechanical aspects.In order to understand the induced stresses,different mathematical models have been developed.In this study,the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically in Laplace domain.The results are transferred to time domain using Fourier inverse method.Finite difference method is also utilized to validate the results.Pore pressure and temperature distributions around the wellbore have been focused and simulated.Next,induced radial and tangential stresses for different cases of cooling and heating of formation are compared.In addition,the differences between thermo-poroelastic and poroelastic models in situation of permeable and impermeable wellbores are described.It is observed that cooling and pore pressure distribution reinforce the induced radial stress.Whereas cooling can be a tool to control and reduce tangential stress induced due to invasion of drilling fluid.In the next step,safe mud window is obtained using Mohr-Coulomb,Mogi-Coulomb,and modified Lade failure criteria for different inclinations.Temperature and pore pressure distributions do not change the minimum allowable wellbore pressure significantly.However,upper limit of mud window is sensitive to induced stresses and it seems vital to consider changes in temperature and pore pressure to avoid any failures.The widest and narrowest mud windows are proposed by modified Lade and Mohr-Coulomb failure criteria,respectively.     

深部煤层力学参数反演和气体钻井井壁稳定性

如何确定深部煤层的地质力学参数是气体钻井井壁稳定评价的关键。基于量化的地质强度指标GSI和Hoek-Brown强度准则分析了反演深部煤层地质力学参数的方法,结合DB1井氮气钻井,以弹塑性方法分析了侏罗系炭质泥岩和煤层的井壁稳定性。研究表明,塔里木盆地依奇克里克区块侏罗系煤GSI介于45~55,变形模量约在1 560~2 850 MPa之间。井眼钻开后炭质泥岩和煤层井周存在塑性区,炭质泥岩层井周塑性区约为1.37倍井眼半径,煤层井周塑性区约为2.07~2.59倍井眼半径。塑性区应力松弛造成围压减小,导致节理岩体抵抗工程扰动的能力减弱。以工程允许塑性半径等于1.5倍井眼半径为临界稳定条件,井眼钻开后煤层会出现大面积坍塌失稳,不宜采用气体钻井;工程扰动造成炭质泥岩井眼扩径,扩径后井眼仍能保持稳定。     

深埋水工圆形隧洞塑性位移三剪统一解

基于三剪统一强度准则和弹脆塑性模型,考虑中间主应力、渗流、剪胀、软化和塑性区弹性模量等因素的影响,推导了含有5种因素综合影响的水工圆形隧洞塑性区位移解析解;通过算例分析,得出了各参数对隧洞塑性区位移的影响规律。结果表明:各参数取不同值时,位移解可退化为一系列解,参数值可根据具体工程进行合理选择,具有广泛的适用性;围岩剪胀特性对隧洞塑性区位移的影响显著,若不考虑其影响,将明显低估隧洞的变形以致工程设计偏于危险;考虑中间主应力的影响能发挥围岩的强度潜能,减少支护,节约工程造价;考虑渗流和软化特性对隧洞塑性区半径的影响可使塑性区范围更接近围岩真实的变形范围;塑性区弹性模量采用含有半径幂函数的表达式可充分考虑围岩受扰劣化后的应力重分布及爆破损伤等影响,更符合隧洞真实变形情况;该位移解为隧洞塑性区位移计算提供了理论依据,对工程设计有一定的参考价值。     

基于Hoke-Brown准则的深埋圆形透水隧洞弹塑性分析

针对深埋圆形隧洞轴对称问题,将Hoke-Brown准则方程代入考虑渗透体积力影响的平衡微分方程进行求解,得到关于塑性区洞周应力的隐式方程,通过求解超越方程得到塑性区洞周应力数值解;再考虑应力重分布影响,利用塑性区半径处应力连续条件得到弹性区岩体应力数值解。将该解答与基于Mohr-Coulomb准则的解答进行了比较。结果表明,两种准则条件下岩体应力分布规律相似。采用Hoke-Brown准则计算时,塑性区较小,径向应力绝对值较大,塑性区环向应力也较大;采用Mohr-Coulomb准则准则计算时,塑性区较大,径向应力绝对值较小,塑性区环向应力也较小。在内外水头比值较小时,按Mohr-Coulomb准则求得的峰值应力较按Hoke-Brown准则求得值大,当水头比较大时则相反。     

考虑渗流场影响深埋圆形隧洞的弹塑性解

将深埋圆形隧洞各影响因素简化为轴对称。首先，求解得到渗流场；然后，以渗透体积力方式作用在应力场，求解得到弹性位移和应力解析表达式，再应用Mohr-Coulomb屈服准则，求解得到塑性应力和塑性半径的解析表达式。通过考虑和不考虑渗流场影响两种方法的实例分析表明，随着洞内外水头差的逐渐增大，渗流场对应力场的影响作用将显著增大，但对切向应力的影响程度要比径向应力的大，且径向应力和切向应力不再符合无渗流时的分布规律，出现大小值交换：同时，随着内水水头的增大，涮周压应力和塑性半径逐渐减小，直到出现无塑性区；另外，考虑渗流场影响计算得到的塑性半径要比不考虑时大。     

围岩中原始垂直地应力对圆形隧洞全长注浆 岩石锚杆应力分布模式的影响分析

 通过分析原始垂直地应力对圆形地下洞室塑性区半径、围岩体塑性区和弹性区内岩体的位移变化以及对锚杆应力分布的影响,揭示原始垂直地应力对锚杆锚固效果的影响。研究结果表明,弹性区内任一点的应力大小与垂直地应力有关,而塑性区内任一点的应力与原始垂直地应力无关;随着垂直地应力的增大,巷道塑性区半径也在不断增大,二者之间呈明显的非线性关系;塑性区的径向位移及隧洞壁的最大位移也随之增大。同时,根据围岩与锚杆的相互作用,建立全长注浆岩石锚杆在圆形隧洞围岩中的应力分布解析本构方程。在此解析模型的基础上,对不同垂直地应力作用下锚杆的应力分布模式进行较详细分析,得出随着垂直地应力增大,锚杆的摩阻力和轴向载荷也随之增大,并且锚杆端部的应力集中现象更加明显,当锚杆端部的摩阻力超过围岩的容许抗剪强度时,则锚杆与围岩发生开裂破坏,故在设计与施工中应予以考虑。最后,提出提高和改善由于锚头开裂导致锚固效果降低的方法,对全长注浆岩石锚杆施加垫板,能有效改善锚杆的锚固效果。     

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MogiCoulomb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。     

拉压模量不同的剪胀土体中的球孔扩张问题

土体具有不同的拉压模量和剪胀特性。为使球形孔扩张问题的解答更符合实际情况,根据不同模量弹性理论和非关联Mohr-Coulomb流动法则研究了球形孔扩张时弹性区和塑性区的应力和位移,得到了弹性区和塑性区的径向应力和环向应力的解析解以及最大塑性区半径与扩张压力的计算表达式。探讨了不同拉压模量之比、拉压泊松比和剪胀角对球形孔扩张的扩张压力及塑性区半径的影响。结果表明:拉压模量比、拉压泊松比和剪胀角对球孔扩张时塑性区的开展和扩张后土体的应力有重要影响,计算中忽略这些参数将带来较大的误差。     

结构性黄土深埋盾构隧道围岩力学特性研究

盾构施工会破坏黄土结构性,为探求黄土结构性变化对盾构隧道围岩力学特性的影响,引入应力比结构性参数对摩尔-库伦强度准则和芬纳公式进行修正,通过建立黄土围岩和管片之间力和位移的连续条件,对围岩塑性区半径进行了求解,并对解析解进行了对比验证,最后分析了关键参数对围岩力学性态的影响。结果表明:(1)太沙基土压力公式计算结果介于解析解上限值与下限值之间;(2)随着应力比结构性参数的增大,对应的塑性区半径和围岩压力值在不断减小;(3)随着覆跨比的增加,塑性区半径不断减小,围岩压力值不断增大,当黄土结构性比较强时,隧道覆土厚度达到一定值之后围岩压力解析公式才适用;(4)围岩压力和塑性区半径与开挖半径近似呈线性正相关关系。     

不同应力路径大理岩物理力学参数变化规律

基于大理岩常规三轴加荷与卸荷试验结果,分析加卸荷应力路径下大理岩各阶段特征应力、黏聚力c、内摩擦角φ在变形破坏中的变化规律。试验结果表明,相同卸荷速率条件下,压密应力对应的环向应变、体积应变随围压的增大而减小,起裂应力及扩容应力随围压增大而增大,加卸荷应力路径下扩容应力对应的环向应变均稳定在(-0.000 4±0.000 1)范围内。大理岩卸荷破坏的初始屈服面和后继屈服面均符合Mogi-Coulomb函数形式,峰值强度前黏聚力c随塑性参数ε^ps的增大而减小,内摩擦角φ随塑性参数ε^ps的增大而增大。     

基于改进双剪统一强度理论的围岩松动圈分析

为了研究岩石应变软化、剪胀性质、中间主应力和拉压不等特性对围岩松动圈的影响,基于改进双剪统一强度理论,得到了隧道围岩松动圈半径、围岩应力及洞壁位移的解析表达式。通过与已有方法计算结果的对比,验证了该方法的可行性,并进一步分析了中间主应力大小以及软化程度对结果的影响。研究结果表明:(1)随着软化模量的降低,隧道围岩塑性区、松动区(圈)半径以及洞壁位移均逐渐减小;(2)中间主应力大小对隧道围岩弹塑性行为具有一定的影响,随着中间主应力系数b的增大,围岩的切向应力在塑性软化区、破碎区内变大,而在弹性区内减小,围岩的径向应力在3个区域内均增大;(3)隧道洞壁位移随着中间主应力系数b的增大而减小;(4)考虑中间主应力的影响以及围岩软化的程度,能够充分发挥围岩的强度潜能,合理指导隧道布置、支护设计与施工。该结果为隧道围岩松动破裂分析提供了理论依据,具有一定的工程参考价值。     

硬质岩石卸荷破坏特性试验研究

 对硬质灰岩进行加轴压、卸围压试验,研究卸荷应力路径对其力学性质的影响,结合试验数据分析5种强度准则描述岩石卸荷破坏的适用性。Mohr-Coulomb强度准则和Hoek-Brown强度准则回归效果较差,考虑中间主应力影响的Drucker-Prager强度准则和Mogi-Coulomb强度准则回归效果较好,并且Mogi-Coulomb强度准则回归效果优于Drucker-Prager强度准则,抛物线型强度准则对高围压下的试验结果回归较好。岩石卸荷破坏发生强烈的体积扩容,从描述体积应变变化的角度对岩石卸荷破坏本构模型进行修正,理论模型结果与试验结果吻合较好。     

岩样单轴压缩塑性变形及断裂能研究

首先研究了应变软化阶段岩石试件轴向塑性变形。假设局部化开始于峰值强度而轴向塑性位移根源于局部化的剪切位移。剪切带的相对塑性剪切位移与应力水平及剪切带宽度有关，剪切带宽度由梯度塑性理论确定。剪切带的相对塑性剪切位移在轴向的分量为轴向塑性压缩位移。研究结果表明：剪切带倾角对相对应力-塑性变形曲线斜率有一定的影响；若剪切带倾角存在尺寸效应，不同高宽比试件的相对应力-塑性变形曲线不是一条严格直线，而是一个狭窄的区域，类似“马尾”。但是，剪切带倾角对相对应力-塑性变形曲线斜率的影响是有限的，峰后应力-塑性变形曲线的斜率基本上是常量，这与前人的一些试验现象相符。然后，研究了单轴压缩条件下岩石试件全部断裂能的尺度律。全部断裂能由峰前断裂能及峰后断裂能两部分构成。在峰值强度前，采用Scott模型描述了材料的非线性弹性特征，得到了峰前断裂能的解析解。结果表明：峰前断裂能与试件的高度有关。在峰值强度后，材料的剪切应力-塑性剪切应变的本构关系为线性应变软化，采用梯度塑性理论计算了由于剪切带塑性剪切变形而消耗的断裂能。目前提出的关于全部断裂能尺寸效应的解析解的正确性被前人的试验结果的线性回归结果验证。增加试件高度，全部断裂能增加。增加弹性模量，全部断裂能降低。若不考虑剪切带倾角及抗压强度的尺寸效应，全部断裂能存在尺寸效应的原因是：峰前的均匀塑性变形。     

A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium

A theoretically consistent closed-form solution for a spherical cavity in a brittle-plastic infinite medium subject to a hydrostatic stress field was derived. Both linear Mohr-Coulomb (M-C) and nonlinear Hoek-Brown (H-B) yield criteria are considered, and a non-associated flow rule is employed in the solution. Plastic radius, stresses and displacements are explicitly expressed as the functions of radial coordinates, internal pressure and strength parameters. In elastic-perfectly plastic analysis, results for displacements and stresses are in good agreement with those published. Comparison of brittle-plastic solutions with the elasto-plastic ones indicates that brittle-plastic behavior of rock mass increase the extent of plastic zone and the displacements around the cavity significantly. Ground response curves (GRC) are constructed for both M-C and H-B criteria and the potential applications are discussed.     

三维应力状态下圆筒形巷道塑性区次生应力、半径和位移

现有的圆筒形巷道塑性区次生应力、半径和位移的理论解是基于Mohr Coulomb准则推导而得 ,但是Mohr Coulomb准则没有考虑中间主应力的影响。为此本文利用双剪强度理论分析了三维应力状态下圆筒形巷道塑性区次生应力、半径和位移。计算表明圆筒形巷道在三维应力状态下塑性区半径和位移比二维应力状态下更小 ,据此可充分发挥岩体自身的承载能力 ,对岩体工程具有重要意义     

三轴应力下再生粗骨料塑性混凝土的力学性能和破坏准则

通过单轴、侧压相等和侧压不等三轴压缩试验,研究了再生粗骨料塑性混凝土(RPC)的应力-应变-强度特征,与原生粗骨料塑性混凝土(PC)性能进行了对比,并建立了基于空间八面体的强度破坏准则.结果表明:再生粗骨料塑性混凝土强度与围压的关系符合库伦破坏准则,其黏聚力低于原生粗骨料塑性混凝土,内摩擦角相差不大;再生粗骨料塑性混凝土应力-应变曲线由单轴下应变软化转变为三轴下塑化,且侧压越大,理想塑化越明显;在3种试验下,试件均出现了最大体应变,且随着侧压的增加而增大;再生塑性混凝土抗裂性能高于原生粗骨料塑性混凝土,且随侧压增大而增强.     

A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass

A simple numerical procedure for calculating the distribution of stresses and radial displacements around a circular tunnel excavated in a strain-softening Mohr–Coulomb or generalized Hoek–Brown rock mass is proposed. The problem is considered as axisymmetric, i.e. the initial stress state is assumed to be hydrostatic and the rock mass is said to be isotropic. By invoking the finite difference approximation of the equilibrium and compatibility equations, the increments of stresses and strains for each ring, starting from the outmost one for which boundary conditions are known a priori, are calculated in a successive manner. In the proposed approach, the potential plastic zone is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium equation. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain. Several illustrative examples are given to demonstrate the performance of the proposed method. For the brittle–plastic case, the results show a very good agreement with the closed-form solution. For strain-softening cases, the predictions by the proposed method are also in good agreement with the known rigorous numerical solutions. It is shown that the approximate solution converges to the exact solution when the increment of stress for each ring becomes smaller. The influence of the strength parameter ‘a’, appearing in the generalized Hoek–Brown criterion, on the elasto-plastic solutions is examined through the establishment of ground reaction curves and the discussion for the locations of the plastic radii.     

Analytical solutions for the stresses and deformations of deep tunnels in an elastic-brittle-plastic rock mass considering the damaged zone

The excavation impact (e.g. due to blasting, TBM drilling, etc.) induces an excavation damaged or disturbed zone around a tunnel. In this regard, in drill and blast method, the damage to the rock mass is more significant. In this zone, the stiffness and strength parameters of the surrounding rock mass are different. The real effect of a damage zone developed by an excavation impact around a tunnel, and its influence on the overall response of the tunnel is of interest to be quantified. In this paper, a fully analytical solution is proposed, for stresses and displacements around a tunnel, excavated in an elastic–brittle–plastic rock material compatible with linear Mohr–Coulomb criterion or a nonlinear Hoek–Brown failure criterion considering the effect of the damaged zone induced by the excavation impact. The initial stress state is assumed to be hydrostatic, and the damaged zone is assumed to have a cylindrical shape with varied parameters; thus, the problem is considered axial-symmetric. The proposed solution is used to explain the behavior of tunnels under different damage conditions. Illustrative examples are given to demonstrate the performance of the proposed method, and also to examine the effect of the damaged zone induced by the excavation impact. The results obtained by the proposed solution indicate that, the effects of the alteration of rock mass properties in the damaged zone may be considerable.     

An elasto-plastic damage constitutive model with double yield surfaces for saturated soft rock

An elasto-plastic damage constitutive model with double yield surfaces is developed based on irreversible thermodynamics theory and damage mechanics theory. Two kinds of plastic deformation mechanisms, including plastic friction and plastic pore deformation mechanisms, are considered. The plastic friction yield criterion is established by a parabolic open function that incorporates the volumetric deformation effect, and the motion of yield function in stress space is governed by its center position and rotation hardening rule. Meanwhile, a plastic pore yield criterion is established by adopting Gurson's criterion using the proposed friction yield model to determine the matrix deformation of porous materials. A damage variable is defined to describe the development of various microscopic defects. Comparisons between numerical predictions and experimental data of triaxial compression tests are presented with various confining pressure conditions to verify the rationality of the proposed model.     

基于Drucker-Prager分析深埋球形洞室弹塑性

基于岩体力学中关于深埋圆形洞室的假设和Drucker-Prager准则,推导了深埋球形洞室开挖后应力弹性分布、塑性分布和塑性区半径的公式,并用所得到的公式与圆形洞室进行了比较,算例表明,在相同荷载和岩体强度参数的前提下,球形洞室的受力比圆形洞室的受力合理。