Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

Moment tensor and stress inversion solutions of acoustic emissions during compression and tensile fracturing in crystalline rocks

We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in the specimens introduce a complex stress field,resulting in a spatial and temporal variation of focal mechanisms.Specifically,we consider two experimental setups:(1)where the rock is loaded in compression to generate primarily shear-type fractures and(2)where the material is loaded in indirect tension to generate predominantly tensile-type fractures.In each test,we first decompose AE moment tensors into double-couple(DC)and non-DC terms and then derive unambiguous normal and slip vectors using k-means clustering and an unstructured damped stress inversion algorithm.We explore temporal and spatial distributions of DC and non-DC events at different loading levels.The majority of the DC and the tensile non-DC events cluster around the pre-cut flaws,where macro-cracks later develop.Results of stress inversion are verified against the stress field from finite element(FE)modeling.A good agreement is found between the experimentally derived and numerically simulated stress orientations.To the best of the authors’knowledge,this work presents the first case where stress inversion methodologies are validated by numerical simulations at laboratory scale and under highly heterogeneous stress distributions.

Three-dimensional stress variation characteristics in deep hard rock of CJPL-Ⅱ project based on in-situ monitoring

In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.

Vertical variations of wave-induced radiation stress tensor

The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough level, and between these two levels. The computational expressions of the wave-in- duced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordi- nate transformation, and the asymptotic forms for deep and shallow water are also presented. The verti- cal variations of a 30°incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations. The wave-induced radiation stress tensor below the wave trough level is induced by the water wave parti- cle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress ten- sor are influenced substantially by the velocity component in the direction of wave propagation. The dis- tributions of the wave-induced radiation stress tensor over depth are nonuiniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

Gedanken Experiment for Fluctuation of Mass of a Graviton, Based on the Trace of GR Stress Energy Tensor-Pre Planckian Conditions that Lead to Gaining of Graviton Mass, and Planckian Conditions That Lead to Graviton Mass Shrinking to 10-62 Grams

We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the graviton would be shrinking right after Planck time and presumably it would be going to its equilibrium value of about 10-62 grams, for its present day value. It, graviton mass, would increase up to the Plank time of about 10-44 seconds. Note that the result that graviton mass shrinks to 10-62 grams for its present day value works only for relic gravitons.

STUDY ON THE GENERALIZED PRANDTL-REUSS CONSTITUTIVEEQUATION AND THE COROTATIONALRATES OF STRESS TENSOR

In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

THE STRESS-ENERGY TENSOR AND POHOZAEV'S IDENTITY FOR SYSTEMS

Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60were prepared,and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes.The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz.At each level of confining pressure,the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed.Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude(i.e.critical dynamic deviatoric stress)beyond which the jointed rock specimens yielded.The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress.At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress,minor cumulative residual axial strains were observed,resulting in hysteretic damping.However,for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress,the plastic strains increased promptly,and the resilient moduli degraded rapidly during the initial loading cycles.Cyclic triaxial test results showed that at higher confining pressures,the ultimate residual axial strain attained by the jointed rock specimen decreased,the steadystate dissipated energy density and steady-state damping ratio per load cycle decreased,while steadystate resilient moduli increased.

纤维加筋膨胀土的蠕变规律及模型预测

膨胀土是具有流变性质的灾害性土,其蠕变行为直接影响到工程结构的稳定性和安全性。为探究剑麻纤维加筋膨胀土的蠕变特性及应力-应变数学模型,采用室内固结排水三轴蠕变试验,分别进行了不同含水率、不同围压和不同偏应力条件下素膨胀土和剑麻纤维加筋膨胀土的蠕变特性研究,根据蠕变特征曲线提出了基于Mesri蠕变经验模型的剑麻纤维加筋膨胀土的修正蠕变模型。结果表明:相同条件下,剑麻纤维加筋土的蠕变变形量明显小于素土的蠕变变形量,说明掺入剑麻纤维可有效提高膨胀土的结构性能和抗变形能力;素土和剑麻纤维加筋土的蠕变变形量随含水率增大而增大,而随围压的增大呈减小趋势;素土和剑麻纤维加筋土在受到偏应力时均会产生瞬时应变量和蠕变变形量,其蠕变变形量随偏应力的增大而增大;素土和加筋土的蠕变曲线分4个阶段,分别为弹性变形阶段、稳态蠕变阶段、衰减蠕变阶段和加速蠕变阶段;高偏应力下,基于传统Mesri蠕变经验模型的剑麻纤维加筋土蠕变预测误差高达37.95%,对Mesri蠕变经验模型进行修正后预测误差降至1.5%内,说明修正模型能较好地描述剑麻纤维加筋土的蠕变特性。此研究结果可为膨胀土工程提供理论参考。

2022年四川芦山M_(S)6.1地震前应力状态研究

为研究2022年6月1日四川芦山M_(S)6.1地震的孕育和发生过程,采用CAP方法反演了2013年芦山M_(S)7.0主震及M_(S)≥5.0余震的震源机制解,并基于应力张量方差与b值时空分布特征,探讨了芦山M_(S)6.1地震的力学机制和震源区的应力状态。结果表明:2022年芦山M_(S)6.1地震震源机制表现出与2013年芦山M_(S)7.0主震和5级余震相似的逆冲型破裂特征,压应力轴方位与龙门山断裂带南段区域应力场一致。2013年芦山M_(S)7.0地震后震中及附近的应力张量方差和b值长期处于低值状态,2022年芦山M_(S)6.1地震前震中及附近出现了应力张量方差和b值的低值异常,表明芦山余震区处于较高的应力水平。分析认为:巴颜喀拉块体持续东向运动受到华南块体的阻挡,震中所在区域长期受挤压逆冲作用,从而使芦山余震区长期处于应力积累的状态,芦山M_(S)6.1地震也是在这种动力学背景下发生的。

深部孤岛充填工作面沿空掘巷围岩偏应力演化与控制

目的 为解决深部孤岛充填工作面沿空掘巷围岩控制问题,方法 以邢东矿12216运料巷为背景,采用FLAC3D数值模拟软件,研究孤岛面临侧采空区在不同充填率条件下沿空掘巷围岩偏应力分布规律,模拟分析孤岛工作面充填开采时,工作面超前段围岩受动压影响时的偏应力演化特征。结果 结果表明:(1)孤岛工作面沿空掘巷巷道煤柱帮受临侧采空区充填效应影响较大,临侧采空区充填率增加使煤柱上偏应力峰值区呈椭圆形并逐步向采空区侧转移;(2)孤岛充填工作面沿空掘巷顶底板偏应力场形成一个朝向采空区侧的弧形低值带;(3)孤岛充填动压扰动时期,最大偏应力区位于实体煤一侧,距工作面前方8 m左右,距巷道4.3 m左右,峰值可达34 MPa。结论 结合数值模拟分析结果,提出采用“高强度锚杆+大直径高延伸率锚索”协同支护方式,现场工程实践表明,该支护方式沿空巷道围岩控制效果良好。

漾濞6.4级地震前后震源机制一致性时空演化特征

利用CAP方法反演2021年漾濞6.4级地震震源机制,并基于云南地区2015~2022年M≥3.0地震震源机制解结果,采用叠加应力场反演方法反演漾濞6.4级地震前后不同时段的应力张量方差空间分布特征;采用云南地区2013~2022年M≥3.0地震震源机制解结果分析震源区附近震源机制一致性参数的时序变化特征。结果表明:漾濞6.4级地震性质为右旋走滑型,矩震级M_(W)6.03,矩心深度5.8 km,节面Ⅰ走向39°、倾角75°,滑动角-16°;节面Ⅱ走向133°、倾角75°、滑动角-164°。应力张量方差空间演化特征显示,漾濞6.4级地震震源区附近应力张量方差经历了一个低值-显著升高-震前下降形成新低值-震后显著升高的变化过程。应力张量方差时间演化特征显示,漾濞6.4级地震震源区附近应力张量方差在地震前1~2 a达到最高值,后持续下降,下降至最低值后发生转折并趋势回升,整体呈正“V”字型,地震发生在正“V”字型转折后趋势回升阶段。应力张量方差的时空演化特征具有一致性。

钙质砂三轴排水试验围压与剪切速率对应力特性影响研究

以海南省三沙市西沙群岛钙质砂为研究对象开展不同剪切速率的三轴固结排水试验,研究钙质砂剪切应力特性。试验结果表明:围压越大偏应力峰值出现的越晚,相同围压剪切速率越快应力峰值越大,应力下降也越快应力下降比越大,剪切速率对应力的峰值大小及残余剪切强度有一定影响,低围压下剪切速率对偏应力峰值影响更大。围压越小偏应力比越大,相同围压剪切速率越大偏应力比增长越快,当剪切速率低于一定速度时,偏应力比的变化并不受剪切速度的影响。相同围压条件下,由于排水剪切时围压和孔压保持不变,偏应力和平均有效应力关系为斜率3的直线,不同剪切速率破坏线趋势相同,剪切速率越大破坏线角度越大,但相差不大,破坏线为接近斜率1.75的直线,钙质砂内摩擦角为42°。剪切过程平均有效应力先增大后减小,剪切过程表现出剪缩到剪胀的变化过程,剪缩阶段不同剪切速率下孔隙比下降速率相近,剪切速率在剪胀阶段对孔隙比影响较大,剪切速率越大,孔隙比变化越大。

中间主应力系数对页岩气渗流特性及气体滑脱效应的影响

页岩气的渗流特性极大地影响着采收率,但对页岩气渗流特性的研究大多是在不同围压条件下开展的,其结果尚不能揭示中间主应力对渗透率的影响。因此,选用涪陵页岩气区块志留系龙马溪组页岩露头立方体岩石试件,采用自主研发的“多功能真三轴流固耦合试验系统”开展了页岩真三轴流固耦合试验,利用Klinkenberg方程拟合试验数据分析不同中间主应力系数对页岩气渗流特性和气体滑脱效应的影响。试验结果表明:①当偏应力较小时,中间主应力对页岩渗透率演化的影响较小,而当偏应力增加时,其影响越大且越不可忽略;②滑脱系数—固有渗透率的关系式与试验数据的拟合结果显示二者具有良好的相关性,可用于对同区块页岩滑脱系数的预测;③当偏应力小于或等于35 MPa时,滑脱效应贡献率保持在65%以上,表明此时滑脱效应主导着页岩中气体的渗流。

不同应力养护条件对水泥土力学性能影响试验研究

为更好地了解水泥土在养护时期所受应力大小对其后期力学性能的影响,研发恒温等压或偏压条件下水泥土试样的养护装置和相应的试验方法。基于改制的恒温恒压水泥土试样养护装置,制作等压和偏压养护条件下不同龄期的水泥土试样。通过无侧限压缩试验(UCT),获得等压和偏压养护条件下水泥土试样的应力-应变曲线及其无侧限抗压强度(UCS)和变形模量E_(50)随龄期的演化规律。试验结果表明:等压养护时围压σ_(c)从0.1 MPa增加到0.3 MPa,水泥土试样在龄期为7 d和14 d时的无侧限抗压强度和变形模量E_(50)均随着围压的增加而增大,但28 d龄期水泥土样的UCS和E_(50)随围压σ_(c)的增长而减小,甚至0.3 MPa围压养护试样的UCS已低于无围压养护试样的UCS,水泥土存在“高围压养护长期强度降低效应”;不同轴压比λ下偏压养护的水泥土样,其60 d龄期的UCS在偏压较小(即λ<λ_(c),λ_(c)为临界轴压比)时逐渐增加,而在偏压较大(即λ>λ_(c))时逐渐下降,即水泥土又存在“小偏压养护强度增加,大偏压养护强度降低的效应”。通过对试验结果进行回归分析,分别建立等压养护下计入围压参数σ_(c)的水泥土UCS和E_(50)的演化方程、偏压养护下水泥土UCS和E_(50)与轴压比λ的经验关系式。研究成果对于深刻理解环境条件对水泥土力学性能的影响机制和指导工程实践,具有较好的理论和工程实际意义。

反压诱导有效应力增生模式与土体强度关联机制研究

反压施加是提高土体饱和度的常用有效方法,但易引起土体强度参数表观偏离。采用标准球形玻璃珠砂,开展基准固结不排水(consolidated undrain,CU),固结排水(consolidated drained,CD)及干样试验,对偏应力与孔压(或体积应变)数据进行实时精准测记与对比分析,借助p′-q应力路径图,显著呈现并定量分析了反压施加对土体力学特性的影响规律,初步厘清了反压施加对土体强度的影响机制。反压设置对CU试验结果影响显著,孔压发展形态控制着偏应力发展的形态,最终影响强度参数的确定,但应力路径始终约束在修正类剑桥模型的框架范围内。孔压发展模式和速率主要受限于反压设置大小及试样相对密实度,反压越大,孔压潜在变化幅度越大,进而导致偏应力变化区间增大;相对密实度越大,孔压发展速率越大,偏应力增速渐大。初始状态相同时,CU试验孔压发展与CD试验体积应变发展趋势高度一致,展示了试样体积应变势在不同边界条件下的共同本质。初步给出了临界状态时CU残余强度定量预测公式,根据相对密实度及反压值可初步定量评定残余孔压值,进而可确定CU残余强度。

高偏应力煤巷围岩拉剪破裂特征及分区控制方法研究

为获得高偏应力巷道围岩拉剪破裂特征并提出优化支护方案,以山西某矿孤岛工作面为背景,采用理论分析、数值模拟、相似模拟相结合的研究手段,分析了高偏应力条件下巷道围岩拉剪破裂分布特征及演化规律,揭示了托顶煤巷道围岩拉剪破裂机制,提出了高偏应力条件下巷道围岩沿掘进方向的全长分区控制方法。研究结果表明:(1)当侧压系数λ为0.60时,巷道围岩两帮呈“楔形”破坏,顶底出现明显卸荷并在巷道围岩四角点处产生应力集中;侧压系数λ逐渐减小至0.24的过程中,巷道围岩以两帮破坏为基础,在剪切应力作用下“蝶叶”逐渐发育,并最终形成蝶形破裂。(2)开挖破坏区围岩的浅部存在拉剪混合破裂区域,以张拉破裂为主;围岩深部为剪切破裂。围岩破裂演化过程可划分为3个阶段,分别为环自由面的自身破坏阶段、“蝶叶”孕育扩展阶段和“蝶叶”扩展稳定阶段。(3)定义了基于巷道全长分区的应力阈值,提出了掘进巷道全长分区支护方法,可为后续采煤工作面巷道的差异化支护提供理论参考。