Experimental Investigation on the Strength, Deformability, Failure Behavior and Acoustic Emission Locations of Red Sandstone Under Triaxial Compression

Conventional triaxial compression and “reducing confining pressure” experiments were carried out for red sandstone by an MTS815 Flex Test GT rock mechanics experimental system. Our results show that the post-peak axial deformation characteristics of red sandstone changed as the confining pressure was increased from 5 to 65?MPa. Young’s modulus of red sandstone increased nonlinearly with increasing confining pressure, but Poisson’s ratio remained unaffected. Using our new data, the compactive and dilatant behavior, strength and failure characteristics of sandstone under triaxial compression are further discussed. For our data, the nonlinear Hoek-Brown criterion better reflects the peak strength properties than the linear Mohr-Coulomb criterion. However, the residual strength shows a clear linear relationship with confining pressure, which can be best described using the linear Mohr-Coulomb criterion. The peak and residual strengths were not directly related to the two different loading paths. The onset of dilatancy (C′), the switch from compaction-dominated to dilatant-dominated behavior (D′) and the stress at zero volumetric strain all increased linearly with the confining pressure. In our conventional triaxial compression experiments, the failure mode changed from mixed tension and shear fracture (single shear fracture) to shear fracture with double slippage planes with increasing confining pressure. However, the failure mode in our “reducing confining pressure” experiments was more complicated and results mainly from the unstable failure characteristics of the rock during the reduction in confining pressure. Finally, based on our acoustic emission (AE) locations, at a confining pressure of 35?MPa, a detailed analysis of the evolutionary process of internal cracks is presented for the entire loading process.     

Impacts of karst phenomena on engineering properties of limestone foundation bed,Ar Riyadh,Saudi Arabia

Evaluation of mechanical and petrophysical properties of the karst limestone became essential to avoid future risks in the construction of new urban cities built on limestones. Therefore, this study aims to evaluate the impact of karsts phenomena on engineering properties of limestone foundation bed at Ar Riyadh in Saudi Arabia. Three hundred core plugs were obtained by rotary drilling at depths ranging from the ground surface to 20 m collected from 24 boreholes in two sites: (1) karst limestone (KL) at Al Aziziyah district and (2) massive hard limestone (HL) at Hittin district in Ar Riyadh city, Saudi Arabia. Petrographic, SEM, EDX, and XRD analyses are used to identify the mineralogical composition and microstructures of limestone samples. The petrophysical properties included the ovendry density, P-wave, and porosity where the mechanical properties covered the uniaxial compressive strength (UCS), point load strength index (PLI), and rock quality designation (RQD) for the karst and hard limestone samples. KL is characterized by 17.11% total porosity, 14.71% water absorption, 32.1 MPa UCS, 1.70 g/cm³ ovendry density (γ dry), 51% weathered RQD, 5.49 MPa medium shear strength, and low modulus of deformation of the plate loading test. HL showed 11.63% total porosity, 9.45% water absorption 43.1 MPa UCS, 2.50 g/cm³ ovendry density (γ dry), 78% hard to fresh rock affinity RQD, and 9.93 MPa high strength and high modulus of deformation of the plate loading test. For the water absorption (%), KL at Al Aziziyah district showed a range of 12.85–17.80% averaged 14.71%. HL at Hittin district varied between 7.04 and 11.29% with an average of 9.45%. KL proved to be dense with ovendry density (γ dry) averaged at 1.70 g/cm³ while HL showed very dense affinity of 2.50 g/cm³. KL clarified a UCS range from 22.5 to 40.1 MPa and an average of 32.1 MPa while HL showed a range from 35.4 t o 48.1 MPa with an average of 43.1 MPa. KL is moderately weathered with RQD average of 51% while HL showed a hard to fresh rock affinity of 78%. Point load test clarified a medium shear strength with 5.49 MPa for KL and high strength of 9.93 MPa for HL. Plate loading tests indicated low and high modulus of deformation for KL and HL, respectively. Results of petrographical analyses and XED of limestone samples showed that the strength parameters of samples mostly composed of micrite (mudstone/wackestone) and dolomite in hard limestone of Hittin district. In Al Aziziyah district (KL), the samples mostly consist of foraminifera and high amount of calcite as in karst limestone (wackestone/packstone). Rock mechanical tests with combination of fabric analyses have shown that strength parameters depend not only on the amount of karst but also on the amount of allochem. Major geomechanical differences between the two types of limestone provide the proper base for prioritizing areas to alleviate future risks and sustainable urban planning for decision makers. The karstic limestone, therefore, is considered as an acceptable foundation bed for light engineering structures. However, for heavy structures and buildings, improving the foundation bed strength by grouting, cement injection, and mat foundations is necessary to avoid future failure risks.     

人工单节理砂岩的三轴试验研究

采用云石胶黏结岩块的方法制备人工节理面,通过直剪试验获得人工节理面的抗剪强度特性,基于完整和单节理砂岩的常规三轴试验,分析不同倾角（0°,30°,60°,90°）对单节理岩体试样力学响应的影响。结果表明:人工节理面在直剪试验中呈现脆性破坏,其抗剪强度符合M-C准则;不同围压下（2.5,5 0和7.5 MPa）完整砂岩的破坏形态和弹性模量基本相同,峰值强度随围压增大;相同围压下（2.5 MPa）不同倾角单节理岩体的破坏形态、弹性模量、峰值强度均不相同,单节理岩体试样的峰值强度-倾角曲线呈反对号“”形,节理倾角对岩体力学性质的影响明显,其中60°节理岩体试样的强度最低,仅为完整岩石强度的19.7%。推导了过圆柱体试样中心任意斜截面内力的三维计算公式,根据其理论预测所得完整岩石的破裂面角度和60°节理试样的破坏方式均与试验结果相符,其吻合度较传统的二维分析更高。     

Influence of Loading Rate on Deformability and Compressive Strength of Three Thai Sandstones

Uniaxial and triaxial compressive strength tests have been performed using a polyaxial load frame to assess the influence of loading rate on the strength and deformability of three Thai sandstones. The applied axial stresses are controlled at constant rates of 0.001, 0.01, 0.1, 1.0 and 10 MPa/s. The confining pressures are maintained constant at 0, 3, 7 and 12 MPa. The sandstone strengths and elastic moduli tend to increase exponentially with the loading rates. The effects seem to be independent of the confining pressures. An empirical loading rate dependent formulation of both deformability and shear strength is developed for the elastic and isotropic rocks. It is based on the assumption of constant distortional strain energy of the rock at failure under a given mean normal stress. The proposed multiaxial criterion well describes the sandstone strengths within the range of the loading rates used here. It seems reasonable that the derived loading rate dependent equations for deformability and shear strength are transferable to similar brittle isotropic intact rocks.     

The strength of ruby from X-ray diffraction under non-hydrostatic compression to 68 GPa

Polycrystalline ruby (α-Al₂O₃:Cr³⁺), a widely used pressure calibrant in high-pressure experiments, was compressed to 68.1 GPa at room temperature under non-hydrostatic conditions in a diamond anvil cell. Angle-dispersive X-ray diffraction experiments in a radial geometry were conducted at beamline X17C of the National Synchrotron Light Source. The stress state of ruby at high pressure and room temperature was analyzed based on the measured lattice strain. The differential stress of ruby increases with pressure from ~3.4 % of the shear modulus at 18.5 GPa to ~6.5 % at 68.1 GPa. The polycrystalline ruby sample can support a maximum differential stress of ~16 GPa at 68.1 GPa under non-hydrostatic compression. The results of this study provide a better understanding of the mechanical properties of this important material for high-pressure science. From a synthesis of existing data for strong ceramic materials, we find that the high-pressure yield strength correlates well with the ambient pressure Vickers hardness.     

Displacement velocity effects on rock fracture shear strengths

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15 × 10⁻⁵ to 1.15 × 10⁻² mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.     

Effects of linking up of discontinuities on fracture growth and groundwater transport

It is proposed that the growth of fractures is the basic process for generating and maintaining permeability in solid rock (bedrock). Many extension fractures grow as hydrofractures, whereas many shear (and extension) fractures grow through the formation of transverse fractures that connect the adjacent tips of existing fractures. In a boundary-element analysis, the hydrofractures are modeled as being driven open by a fluid overpressure that varies linearly from 10 MPa at the fracture centre to 0 MPa at the fracture tip. The host rock has a uniform Young's modulus of 10 GPa, a Poisson's ratio of 0.25, and is dissected by vertical joints and horizontal contacts, each of which is modeled as an internal spring of stiffness 6 MPa m⁻¹. The number of joints and contacts, and their location with respect to the hydrofracture tip are varied in different model runs. The results of the analyses indicate that the tensile stresses generated by overpressured hydrofractures open up joints and contacts out to considerable distances from the fracture tip, so that they tend to link up to form a hydraulic pathway. Using the same Young's modulus, Poisson's ratio, and internal spring constant for joints as in the hydrofracture models, boundary-element models were made to study the interaction stresses that cause neighbouring joints to become interconnected through the growth of linking transverse fractures that, ultimately, may evolve into shear fractures. The models were subjected to tensile stress of 6 MPa acting normal to the joint planes as the only loading. The offset (horizontal distance) and underlap (vertical distance) between the adjacent tips of the joints were varied between model runs. The results show a concentration of tensile and shear stresses in the regions between the neighbouring tips of the joints, but these regions become smaller when the underlap of the joints decreases and changes to overlap. These stress-concentration regions favour the development of transverse (mostly shear) fractures that link up the nearby tips of the joints, so as to form a segmented shear or extension fracture. Analytical results on aperture variation of a hydrofracture in a homogeneous, isotropic rock are compared with boundary-element results for a hydrofracture dissecting layered rocks. The aperture is larger where the hydrofracture dissects soft (low Young's modulus) layers than where it dissects stiff layers. Aperture variation may encourage subsequent groundwater-flow channeling along a pathway generated by a hydrofracture in layered rocks. Electronic Publication     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。     

Limits on strength and deformation properties of jointed basaltic rock masses

Summary A study of strength and deformation measurements for basaltic rocks, along with consideration of the influence of fracturing using a rock mass classification system, documents the range of brittle response for basaltic rock masses. Although basalts vary widely in composition and other physical factors, many of the properties of a basaltic rock mass appear to vary within a factor of about 10. Typical values of strength parameters for intact basalt at ambient temperature (20°C) and negligible confining pressure are Young's modulus, 78±19 GPa; Poisson's ratio, 0.25±0.05; tensile strength, –14.5±3.3 MPa; unconfined compressive strength, 266±98 MPa; and conhesion, 66 MPa. Corresponding values for a basaltic rock mass that incorporate the weakening effects of scale are deformation modulus, 10–40 GPa; Poisson's ratio, 0.3; tensile strength, –0.1 to –2.5 MPa; uniaxial compressive strength, 10–90 MPa; and cohesion, 0.6–6 MPa. A measured deformation modulus for ambient pressure in the vertical direction, 20 GPa, is 1.5–3 times larger than that in the horizontal directions, 13.5 and 6.5 GPa, reflecting strength anisotropy due to column or block geometry for one particular basalt. Values of tensile and cohesive strength for the basaltic rock mass are generally one to two orders of magnitude lower than corresponding values for intact basalt. The shear strength of joints appears to vary considerably from flow to flow.     

Effect of Strain Rate on the Strength Characteristics of Soil–Lime Mixture

The effects of rate of strain on strength and deformation characteristics of soil–lime were investigated. Five strain rates (0.1, 0.8, 2.0, 4.0 and 7.0 %/min), five lime contents (0, 3, 6, 9 and 12 %) by dry soil weight and three cell pressures (100, 200 and 340 kN/m²) were carried. Triaxial tests, under unconsolidated condition, were used to study the effect of strain rate on strength and initial modulus of elasticity of soil and soil–lime mixture after two curing periods 7 and 21 days, respectively. A total of 405 triaxial specimens have been tested, where 225 specimens have been tested with first curing period (7 days). The testing program includes nine specimens for each strain rate, and each lime content was carried out, including natural soil with zero lime content. Another set of triaxial tests with a total of 180 specimens for the second curing period (21 days) was prepared at optimum moisture content, and the corresponding maximum dry density was also tested. The effects of strain rate and curing period on each of stress–strain behavior, type of failure, deviator stress at failure, cohesion and angle of internal friction and initial modulus of elasticity were studied thoroughly for the natural soil as well as soil–lime mixtures. For natural soil, the test results showed that the undrained shear strength, the initial modulus of elasticity and the cohesion increase significantly as the strain rate increase, while for soil–lime mixture at different curing periods, the undrained shear strength, initial modulus of elasticity and the cohesion increases to a maximum and then decreases as the strain rate and lime content increase. Also, the same variables and angle of internal friction increase with increasing curing period.     

砂岩Ⅰ型断裂韧度及其与强度参数的相关性研究

岩石的破坏和断裂是密切相关的,岩石强度准则的材料参数和断裂理论的断裂韧度是存在特定关系的,基于此,设计了紧凑的试验方案,对干燥和饱水状态下的砂岩试样进行了3点弯曲断裂韧度试验和抗压、抗拉强度试验,试验结果表明,饱水后,砂岩的Ⅰ型断裂韧度软化效应明显,饱水试样和干燥试样的 比值与砂岩抗压强度的软化系数相近,具有相似的软化效应。同时,从理论上分析了岩石I型断裂韧度与抗拉强度之间的关系,并结合大量的试验数据进行了验证,相关结论为以往的岩石I型断裂韧度与抗拉强度之间的数据统计拟合公式提供了理论基础。最后,统计分析了砂岩Ⅰ型断裂韧度与抗压强度、黏聚力、内摩擦角等强度参数之间的关系。研究成果对于把握砂岩Ⅰ型断裂韧度及其与强度参数的相关性具有较大的参考价值,相关的分析结论、试验方法和试验结果也可以为其他类型岩石的研究提供有益的参考。     

Experimental and Numerical Studies on Determination of Indirect Tensile Strength of Rocks

Indirect tension tests using Brisbane tuff Brazilian disc specimens under standard Brazilian jaws and various loading arcs were performed. The standard Brazilian indirect tensile tests caused catastrophic, crushing failure of the disc specimens, rather than the expected tensile splitting failure initiated by a central crack. This led to an investigation of the fracturing of Brazilian disc specimens and the existing indirect tensile Brazilian test using steel loading arcs with different angles. The results showed that the ultimate failure load increased with increasing loading arc angles. With no international standard for determining indirect tensile strength of rocks under diametral load, numerical modelling and analytical solutions were undertaken. Numerical simulations using RFPA^2D software were conducted with a heterogeneous material model. The results predicted tensile stress in the discs and visually reproduced the progressive fracture process. It was concluded that standard Brazilian jaws cause catastrophic, crushing failure of the disc specimens instead of producing a central splitting crack. The experimental and numerical results showed that 20° and 30° loading arcs result in diametral splitting fractures starting at the disc centre. Moreover, intrinsic material properties (e.g. fracture toughness) may be used to propose the best loading configuration to determine the indirect tensile strength of rocks. Here, by using numerical outcomes and empirical relationships between fracture toughness and tensile strength, the best loading geometry to obtain the most accurate indirect tensile strength of rocks was the 2α?=?30° loading arc.     

岩石受热后的强度,变形破坏特性的微观研究

本文对砂岩、灰岩、大理岩在不同温度条件下的单轴抗压强度进行了实验研究,并对岩石在各种温度下结构变化进行了镜下分析,探讨了岩石受热后的破裂机理,定性定量地分析了岩石裂纹随温度变化而发展的规律。研究和分析结果表明:在热应力和外应力的作用下,随着温度增加,砂岩单轴抗压强度有增加的趋势,而灰岩、大理石的强度则有所降低。温度对这几种岩石的变形和破坏特性也有很大影响。     

Variation of mechanical properties of granite after high-temperature treatment

Variations in the mechanical properties (compressive strength, elastic modulus, tensile strength, and fracture toughness) of granite were analyzed as functions of temperature. It was found that above 200 °C, tensile strength and fracture toughness tended to decrease with temperature, while variations in the compressive strength and elastic modulus demonstrated decreasing trends when the heating temperature exceeded 400 °C. The temperature ranges of room temperature—200 and above 600 °C—corresponded to an undamaged state and strongly/completely damaged state, respectively. It is suggested that 400 °C might be a critical threshold of thermal damage to granite. Based on results of statistical tests, a sharp decrease in mechanical properties can be recognized, accompanied by a drastic growth in peaking strain and acoustic emission rate. This phenomenon may be associated with the α/β phase transition of quartz.     

Finite volume–based modeling of flow‐induced shear failure along fracture manifolds

In this paper, a numerical model to predict flow‐induced shear failure along pre‐existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence.     

断续三裂隙砂岩强度破坏和裂纹扩展特征研究

利用岩石力学伺服试验机,对尺寸为80 mm×160 mm×30 mm的断续三裂隙砂岩试样进行了单轴压缩试验,研究了岩桥倾角? 2对断续三裂隙砂岩（? = 30°和? 1 = 60°）强度破坏和裂纹扩展特征的影响规律。与完整砂岩试样相比,断续三裂隙砂岩试样应力-应变曲线显示了较多的应力跌落,其峰值强度也呈显著降低趋势,但降低程度与? 2密切相关,随着? 2从75°增加到90°,峰值强度从82.04 MPa 降低到77.82 MPa,而当? 2从90°增加到120°,其峰值强度无明显变化。完整砂岩试样呈现轴向劈裂脆性破坏,而断续三裂隙砂岩试样是由许多从裂隙尖端产生的裂纹扩展与汇合,导致了其失稳破坏。通过照相量测技术,探讨了? 2对断续三裂隙砂岩试样裂纹扩展特征的影响：? 2为75°、90°和105°的断续三裂隙试样中裂隙①、③和②、③之间均出现了贯通,而裂隙①、②之间无任何贯通;? 2为120°的断续三裂隙试样中裂隙①、③和①、②之间均出现了贯通,而②、③之间无任何贯通。最后给出了断续三裂隙砂岩试样宏观变形特性与裂纹扩展过程之间的关系。     

Rock interface strength influences fluid-filled fracture propagation pathways in the crust

Rock interface strengths have often been assumed to be zero in numerical and analogue models of fracture propagation and magma intrusion in the crust. Rock strength tests were performed to explore the role that rock interfaces have on the geometry and propagation dynamics of fluid-filled fractures in the crust. We used a 1 kN test machine to study 5 mm thick cuboidal specimens cut from a sandstone-siltstone rock core, where the strata were known to host magma intrusions and the rock interface between the units was intact. By measuring the load required to grow a crack running along the lithological contact between the layers we calculate its fracture toughness K_c. The siltstone had an average K_c of 0.56 ± 0.03 MPa m^1/2 compared to the sandstone at 0.42 ± 0.02 MPa m^1/2. The rock interface had intermediate average fracture toughness to the parent units at 0.45 ± 0.03 MPa m^1/2. These results have important implications on fracture propagation pathways through rocks, as well as for the geometry and propagation dynamics of magma intrusions in the crust.     

受弯条件下薄层灰岩的力学响应行为试验研究

鉴于薄层岩体在实际地下工程中经常发生弯折破坏,利用三点弯曲试验对单层灰岩及含弱面灰岩试样进行抗弯性能测试,探究岩层受弯作用时的变形及破坏特征。试验结果表明,薄层灰岩的抗弯性能与层厚密切相关,单宽峰值弯矩及峰值力对应的岩梁挠度随层厚变化规律基本符合材料力学理论公式计算结果。薄层灰岩弯折破裂模式呈现多样化,既有垂直切穿层理的I型裂纹,也有在弱面处发生转折并沿弱面扩展的断续裂纹,以及与层理斜交的复合型裂纹等。理论分析表明,薄层岩体中的裂纹扩展路径主要受层面拉、剪强度（或断裂韧度）与岩石抗拉强度（或断裂韧度）的相对大小控制。利用双模量理论结合弯曲试验求解岩石拉伸模量需要进行迭代计算,拉压模量相差越大,迭代次数越多,收敛值越偏离初值。试验所得规律有助于深入理解薄层岩体弯曲变形特征及弯折破坏机制,并可作为对薄层岩体受弯作用理论及数值计算的有益补充。     

Elastic and Seismic Properties of Dabie-Sulu Ultrahigh Pressure Metamorphic Rocks

Lamé modulus (λ) and shear modulus (μ) are among the most important,intrinsic,elastic constants of rocks.Using λ and μ could be much more advantageous than using P- and S-wave velocities (Vp and Vs).He...     

Bearing of structural anisotropy on deformation and mechanical response of rocks: An experimental example of rocksalt deformation under variable compression rates

The deformation and mechanical responses of rocks are prime concern in development of varieties of civil and mining engineering structures. The deformation and mechanical properties of both natural and artificial materials are strongly depend on mineral constituents and their arrangements, temperatures and pressures, stress rates and structural anisotropy. This study elaborates an understanding of structural anisotropy, compression rates and mechanical attributes relationship in rocks with specific examples of deformed rocksalt. The cubical samples (5X5X5 cm³) with three kinds of structural anisotropy were subjected to quasistatic compressive stress at rates 0.00035 MPa/min, 0.0035 MPa/min, 0.035 MPa/min, 0.35 MPa/min, 3.5MPa/min, 5 MPa/ min, 7MPa/min and 9 MPa/min on servo-controlled Material Testing System (MTS). The stress-strain curves prepared from deformation of rocksalt’s samples under different rates of compressions are used to determine major mechanical parameters viz., strengths, strains, and modulus of elasticity. A micromechanical en-echelon crack array model is proposed to explain the influence of structural anisotropy on deformation patterns and mechanical properties of rocksalt.According to the proposed model the deformation progresses due to different proportional contributions of tensile and shear crack arrays under the influence of structural anisotropy. The control of structural anisotropy loses with respect to increment in rate of compression with enhance contribution of shear crack arrays in comparison to tensile crack arrays and ultimately fails in shear where the structurally anisotropic rock show isotropic behaviour.