A simplified three-dimensional extension of Hoek-Brown strength criterion

The Hoek-Brown(HB) strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress σ_2.Many evidences have demonstrated that the rock strength is dependent on σ_2. Thus it is necessary to extend the HB criterion into a three-dimensional(3D) form.In this study,the effect of σ_2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.     

Shear banding in torsion shear tests on cross-anisotropic deposits of fine Nevada sand

A series of torsion shear experiments was performed on large hollow cylinder specimens of Fine Nevada sand with major principal stress directions relative to vertical, α, varying from 0° to 90° and with the intermediate principal stress, σ₂, varying from σ₃ to σ₁ as indicated by b=(σ₂–σ₃)/(σ₁–σ₃). The Fine Nevada sand was deposited by dry pluviation, thus producing a sand fabric with horizontal bedding planes and cross-anisotropic characteristics. The various stress conditions were achieved by varying the pressures inside and outside the hollow cylinder specimen relative to the shear stress and the vertical deviator stress according to a pre-calculated pattern. All stresses and all strains were determined from careful measurements so that analysis of the soil behavior could be made reliably. The soil behavior was determined for a pattern of combinations of α varying with increments of 22.5° from 0° to 90° and b varying with increments of 0.25 from 0.0 to 1.0. Thus, 25 test locations were established, but many tests were repeated to study the consistency of the results. The friction angles varied considerably with α and b, thus indicating the importance of the intermediate principal stress and the principal stress directions relative to the horizontal bedding planes. The observed shear bands essentially followed the expected directions, but due to the cross-anisotropy shear bands were also observed in the direction of the major principal stress in regions with high b-values. The strength variation was also influenced by the flexibility of the boundaries in these regions.     

Effects of principal stress rotation on stress–strain behaviors of saturated clay under traffic–load–induced stress path

A series of cyclic torsional shear tests using hollow cylinder apparatus (HCA) were performed to investigate the effect of principal stress rotation (PSR) on the stress–strain behaviors of saturated soft clay. The traffic–load–induced shear stress path was used in the cyclic test and the investigation mainly concerned the influence of PSR on the shear stiffness and non-coaxiality. It indicated that the effects of PSR substantially depends on the magnitude of deviatoric stress (q?=?{[(σ₁???σ₂)²?+?(σ₂???σ₃)²?+?(σ₁???σ₃)²]/2}^1/2) as well as the intermediate principal stress ratio (b?=?(σ₂???σ₃)/(σ₁???σ₃)). At low deviatoric stress, the trajectory envelope of deviatoric strain path translates with a nearly constant size, showing constant shear stiffness and strong non-coaxiality. However, at high deviatoric stress, the trajectory envelope of deviatoric strain rapidly expands towards instability, showing degenerating shear stiffness and weak non-coaxiality. Moreover, the excess pore water pressure increases and the shear stiffness decreases more rapidly as b value increases. The results can provide an experimental basis for constitutive modelling of clays under traffic–induced loadings.     

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional(3D) hybrid finite-discrete element method(FDEM) to investigate the development of an excavation damaged zone(EDZ) around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibrated against standard laboratory experiments, including Brazilian disc test and uniaxial compression test. The effect of increasing confining pressure on the mechanical response and fracture propagation of the rock was quantified under triaxial compression tests. Polyaxial(or true triaxial) simulations highlighted the effect of the intermediate principal stress(s2) on fracture directions in the model: as the intermediate principal stress increased, fractures tended to align in the direction parallel to the plane defined by the major and intermediate principal stresses. The peak strength was also shown to vary with changing σ2.     

Use of polyethylene terephthalate fibres for mitigating the liquefaction-induced failures

The presence of non-biodegradable plastic waste is a serious concern for the health of endangered species. The present study is based on the sustainable utilisation of polyethylene terephthalate (PET) fibres obtained from waste plastic bottles to enhance the liquefaction resistance of fine sand. After performing a series of stress-controlled cyclic triaxial tests, the cyclic behaviour of PET-fibre reinforced sand has been investigated. The application of PET fibres was found to be more satisfactory in medium dense sand than that in loose sand as observed by residual excess pore water curves. In medium dense sand with 0.6% PET-fibres, the number of cycles to reach liquefaction was about 4 times that of the unreinforced sand. Using the dynamic shear modulus (G), the degradation index was calculated for both reinforced and unreinforced soils to assess stiffness characteristics. After nearly 50 loading cycles, the value of G/G_max increased 2.55 times with the addition of 0.4% PET fibres in unreinforced sand. Based on the results obtained, a regression model has been developed for the calculation of number of liquefaction failure cycles (N_cyc,L) in correlation with several parameters, namely, relative density (D_r), fibre content (FC) and σ_d/σ_c′ (σ_d = deviator stress, σ_c′ = effective confining stress).     

Strength and failure characteristics of jointed marble under true triaxial compression

The rock structure and three-dimensional stress state play a vital role in the mechanical behaviour of rock masses. Here, a series of true triaxial compression tests (σ₁ > σ₂ > σ₃) are conducted on jointed marble (50 × 50 × 100 mm³) containing a natural stiff joint, taken from the China Jinping Underground Laboratory (CJPL-II) project. The purposes of this study are to investigate the joint effect and estimate the stress dependency of jointed marble. The test results show that jointed marble can fail in four distinct forms, namely, splitting or shearing of intact marble, opening of the joint or sliding along the joint, and these failure modes are influenced by the joint configuration and the minimum and intermediate principal stresses. Generally, jointed marble has more brittle post-peak behaviour than intact marble. The linear Mogi-Coulomb failure criterion can be modified to describe the strength of the jointed marble under true triaxial compression. The jointed marble strength is more sensitive to the minimum principal stress than to the intermediate principal stress. A maximum decline of 25% in strength is observed, which corresponds to a joint dip angle of 60° at σ₂ = 60 MPa and σ₃ = 30 MPa. The link between the experimental results and in situ fracturing at CJPL-II is also demonstrated.

     

Three-dimensional drained behavior of normally consolidated anisotropic kaolin clay

A series of consolidated-drained true triaxial tests with a constant mean effective stress and constant Lode angles during shear is performed on cross-anisotropic kaolin clay. All tests are performed in a fully automated true triaxial testing apparatus. The relative magnitude of the intermediate principal stress, expressed in terms of the b-value, and initial cross-anisotropy show significant influence on the stress–strain, strength, and shear band formation characteristics of the clay. Shear bands form and appear to cause failure in all true triaxial tests performed, except in triaxial compression. The initiation and development of shear bands is observed to take place, when the clay undergoes volumetric contraction. The lower strength exhibited in the shear bands is caused by alignment of the clay particles. This shear band mechanism is different from that observed in granular materials, in which the lower shear strength is reached due to dilation in the shear bands.     

Discussion on “A generalized three-dimensional failure criterion for rock masses”

There are many methods to construct true triaxial strength criteria for rocks.Jaiswal and Shrivastva(2012)proposed a strength criterion,named J–S criterion,in the deviatoric plane,which provides nearly the same misfts for true triaxial test data as the exponential criterion.It is diffcult to calculate the strength at given2and3using the J–S criterion,and the multiple solutions to the nonlinear equation may induce confusion and mistake.Strength envelopes in deviatoric planes are not geometric similar;therefore,true triaxial test data cannot be grouped in the mean stress to check strength criteria in the deviatoric plane.     

Development of high-pressure low-temperature plane strain testing apparatus for methane hydrate-bearing sand

A high-pressure low-temperature plane strain testing apparatus was developed for visualizing the deformation of methane hydrate-bearing sand due to methane hydrate production. Using this testing apparatus, plane strain compression tests were performed on pure Toyoura sand and methane hydrate-bearing sand with localized deformation measurements. From the results, it was observed that the methane hydrate-free specimens, despite their relatively high density, showed changes in compressive volume. Marked increases in the initial stiffness and strength of the methane hydrate-bearing sand were observed (methane hydrate saturation of S_MH=60%). Moreover, the volumetric strain changed from compressive to dilative. For the specimens with methane hydrate, a dilative behavior above S_MH=0% was observed. An image analysis showed that the shear bands of the methane hydrate-bearing sand were thinner and steeper than those of the host sand. In addition, the dilative volumetric strain in the shear band increased markedly when methane hydrate existed in the pore spaces.     

粗砂不排水剪切的真三轴试验研究

通过对福建标准砂进行不同围压、不同中主应力系数下的不排水真三轴剪切试验,分析砂土在不排水状态下的应力与应变特性、强度与变形特性,并研究偏应力、孔隙水压力、应力比、有效主应力比随中主应力系数的变化规律。     

Mechanical Properties of Lightweight Treated Soil Cured in Water Pressure

An artificial lightweight soil has been developed as a backfill to reduce the earth pressure behind port and harbor structures. To reduce the unit weight lightening ingredient such as air foam or EPS beads is mixed within slurry of dredged soft clay, while cement is used as stabilizer to warrant compressive strength. This experimental study aims to characterize the strength and deformation properties of lightweight treated soil cured in water pressure. Samples of two types of lightweight treated soil mixed with air foam or EPS were cured under various pressures, and subjected to undrained shearing tests on triaxial apparatus modified to detect volumetric change. Though high pressures inevitably compress lightener and consequently incur increment in unit weight, pressured curing did not reduce the compressive strength, q_max = (σ_a-σ_c)_max. It was also found that the deformation modulus E₅₀ greatly decreases with relative confining pressure σ_c/q_max. The lightweight soils maintained relatively large residual strengths, showing no significant sign of brittle failure as often confronted in unconfined compression test. It was observed that the critical state line exists when subjected to ultimate strains, and that the peak deviator stress envelop was identified in effective stress path plane for air foam mixed cases alone. K₀-consolidation tests were conducted on modified triaxial apparatus, showing that K₀ values from the quasi one dimensional tests decline to as small as 0.1 to 0.15 around axial strain of 0.5~1% at near yielding points. Poisson's ratios based on both undrained shearing and K₀-consolidation are compared in consistent tendency with minimal values of 0.1 to 0.2 near the identical yielding points. Yet it is revealed from the obtained compression curves that the compressibility increases drastically by some 100-fold when comparing before and after yielding for lightweight treated soil. This fact strikes the importance of not overloading lightweight treated soil by its compressive strength.     

Relationship between Shear Wave Velocity and Stresses at Failure for Weakly Cemented Sands During Drained Triaxial Compression

Small strain shear modulus (G_max) has been a parameter of choice used to assess the strength and deformation behavior of cemented and other sensitive soils. The influence of density, effective confining stress, stress anisotropy, and cement content on shear wave velocity (v_s)/shear modulus has been studied extensively and published. There are, however, very few studies on the effects of cement/strength degradation during shear on the shear wave velocity/shear modulus, which may be important for reliable and accurate prediction of mechanical behavior of cemented sands. The objective of this study is to evaluate the effect of cement degradation on shear wave velocity/shear modulus by measuring continuously the shear wave velocity during shear. A laboratory testing program was performed using samples of silty sand artificially cemented with Ordinary Portland Cement (OPC). Shear wave velocity was measured continuously within the triaxial cell during the shear phase using torsional ring transducers. G_max was calculated using the shear wave velocity and the corresponding density during shear. Results from this study suggest that G_max reaches a peak value before σ′₁ reaches a failure stress and this behavior is believed to be an indicator of bond breakage or destructuring. G_max calculated at various stages during shear showed that the cement and modulus degradation can be represented by a simple index using G_max. The results of this study suggest that there may be a unique relationship between small strain shear modulus and effective stresses at failure for dilative soils implying that in situ shear wave velocity measurements may be used to estimate effective stress strength parameters or as a precursor to failure in weakly cemented soils.     

Feasible method,utilizing density changes,for estimating in situ dynamic strength and deformation properties of sand samples

Laboratory tests and design reliability are directly controlled by sample quality. The frozen sampling (FS) method is useful for dynamic strength and deformation tests of undisturbed clean sand. However, it is very expensive and requires considerable equipment. The sample quality of Toyoura sands obtained from 48 mm and 75 mm samplers are scrutinized based on void ratio, dynamic strength and deformation properties through model and cyclic undrained triaxial tests. A conventional method for estimating in-situ dynamic strength and deformation properties of sand samples utilizing density changes is examined and the applicability of the proposed method is discussed for the samples obtained from Niigata sand deposits.The main conclusions obtained from this study are summarized as follows:(1) A conventional method for estimating in-situ void ratio (e₀), D_r, stress ratio (R_L20) in a 20 cyclic time frame and the initial modulus of rigidity (G₀) of sand samples utilizing density changes is proposed.(2) The in-situ R_L20 and G₀ estimated from the proposed method for sand samples from tube samplers were similar to those of frozen sampling and the in-situ modulus of initial rigidity was calculated from the secondary wave velocity for Niigata sand deposits.Therefore, dynamic strength and deformation properties changes, caused by sampling, can be modified appropriately to an in-situ condition by this proposed method.     

Mechanical Behavior of Bentonite-Sand Mixtures as Buffer Materials

For the purpose of establishing the method for estimating in-situ mechanical behavior of artificial buffer materials, stress-deformation behavior of bentonite-sand mixtures were investigated through oedometer test, consolidated undrained triaxial compression test and expansive stress-strain measuring test by changing the clay content as 30, 50, 70 and 100%, and by changing the range of initial dry density of mixture from 1.4 to 1.8 g/cm³. Oedometer test results suggest that the magnitude of consolidation yield stress almost coincides with the maximum expansive stress (p′_s)_max irrespective of bentonite-sand mix proportion, initial density of mixture and the magnitude of molding stress at the specimen making. Strong correlation between consolidation stress and initial tangent modulus during undrained triaxial compression test is observed, and it is found that the reduction rate of rigidity is hardly dependent on the specimen making method, molding stress and the consolidation stress. From the two series of expansive stress-strain measuring tests, it is recommended to perform the measurement of expansive stress by feed back system with the load cell installed at the base of the specimen. A unique relationship is found between the maximum expansive stress (p′_s)_max versus bentonite specific volume v_b, which is defined as the specific volume calculated by excluding the volume of sand particles. The line showing the unique log v_b versus log (p′_s)_max relationship can be recognized as the state boundary line prescribing one-dimensional expansive stress-strain behavior of the bentonite-sand mixtures.     

一室四腔刚-柔加载机构真三轴仪的改进与强度试验——西安理工大学真三轴仪

土的真三轴仪是研究不同应力路径等复杂应力条件下土力学性质的重要仪器。与国内外已有真三轴仪的加载机构比较,西安理工大学真三轴仪具有一室四腔、竖向和水平面内正交两向分别呈刚性和柔性加载机构的特征。试样的竖向采用刚性板加载,侧向正交双轴分别采用两组内置于压力腔的液压囊加载。针对试样上下端部刚性板的约束作用,增大了试样的竖向尺寸,研制了高宽比为2∶1的压力室;针对立方体试样侧面正交双轴的液压囊体积变化量测侧向变形的不足,研制了穿越液压囊的变形量测机构;针对自动控制系统信号波动变化较大,稳定性差等不足,开发了自动控制系统及多种应力路径和控制方式的控制程序。通过饱和砂土、非饱和土和原状黄土的试验,测试了各种土的强度变化规律,验证了改进真三轴仪的性能。     

True-triaxial strength criteria for rock

This paper reviews some strength criteria which include the role of the intermediate principal stress, and proposes a new criterion. Strength criteria of the form σ_oct=f_N(σ_oct), such as Drucker–Prager, represent a rotation surface in the principal stress space, symmetric to the line σ₁=σ₂=σ₃ in the meridian plane. Because σ_oct=f_N(σ_oct) must fit the pseudo-triaxial compressive strength, it will have a non-physical outcome for triaxial extension. Mogi's criteria, σ_oct=g₁(σ_m,2) and σ_max=g₂(σ_β) are able to fit experimental data reasonably well, but the prediction of strength is not good and sometimes problematic. Strength criterion with the form λ(σ₁, σ₂, σ₃)=F[η(σ₁, σ₂, σ₃)], or a curve of two variables which can be decided by fitting pseudo-triaxial experimental data, is not expected to describe the strength under various stress states, no matter how high the correlation coefficient of λ and η is, or how low the misfit of the equation λ=F(η) is, as these seemingly good correlations usually result from the dominant influence of the maximum principal stress in the metrics of λ and η. The intermediate principal stress may improve the strength of rock specimen, but its influence will be restricted by σ₃. Also when σ₂ is high enough to cause failure in the σ₂–σ₃ direction, the strength will decrease with the increasing σ₂. The new strength criterion with exponent form has just such a character, and gives much lower misfits than do all seven criteria discussed by Colmenares and Zoback [Colmenares LB, Zoback MD. A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 2002;39:695–729].     

Effect of Curing Stress and Period on the Mechanical Properties of Cement-Mixed Sand

Cement mixing is one of the popular ground improvement technologies in geotechnical engineering practice. In order to effectively and confidently design cement-mixed soil structures for specific purposes, its stress-strain behavior needs to be well understood. Though there have been many studies on cement-mixed soils using different types of soils, their behaviors have not been generalized yet. As is the case with concrete materials, the hydration of cement in cement-mixed soil continues with time, thereby improving the strength and deformation characteristics of cement-mixed soil over time. In the field, the cementation bonds are formed under stress in case of in-situ soil. However, in the usual testing techniques, cementation bonds under stress has not been a point of consideration in most of the previous studies. This has led to an underestimation of the stress-strain behavior of cement-mixed soil. On the other hand, soils are subjected to confining stress during loading which has also some effect on the strength and deformation characteristics of soil which has not been considered yet in the case of cement-mixed sand. This study investigates the effect of curing stress and period on the strength and deformation characteristics of cement-mixed sand. The effect of confining stress in the triaxial test is also investigated in another series of specimens. A series of consolidated drained (CD) triaxial compression (TC) tests were done along with the small strain cyclic loading and bender element tests during monotonic loading to determine the small strain Young's modulus (E_v) and shear modulus (G_vh) respectively. The effect of the curing period is significant in the peak strength, stiffness, E_v, G_vh and also in the post peak regime. The curing stress also has a significant effect on the peak strength, E_v and G_vh. The confining stress has an effect on the peak strength, stiffness and in the post peak regime. However, the effect is small compared to clean sand.     

Triaxial Strength Properties of Natural Deposits at K0 Consolidation State Using a Precision Triaxial Apparatus with Small Size Specimens

The strength properties of undisturbed Japanese, Korean and United Kingdom deposits and their remolded soils are examined through K₀ consolidated-undrained triaxial compression and extension tests by a new precision triaxial test apparatus (PTA) using small specimens 15 mm in diameter and 35 mm in height. The effect of sample disturbance on the coefficient of earth pressure at rest (K₀) under K₀ consolidation was quantitatively examined. The K₀ value can be explained by the equation, K₀ = 0.003 + 0.302I_p, under the normally consolidated region (NC). The K₀ values under the effective overburden pressure (σ'_VO) were (6∼15)% smaller than those of the NC. The rate of strength increase (c_u/p) under σ'_VO were in the range of 0.4 to 0.7 and those under the NC were 0.3 to 0.4. The effective angle of friction (φ') obtained from the strain rate of 1%/min was 10% smaller than that of 0.05%/min. The K₀ values for the undisturbed soils were 0.07 greater than those using Jaky's formula and the K₀ value can be explained by the equation, K₀ = 0.912-0.012φ'. Brooker and Ireland and Yamanouchi and Yasuhara's equations can explain the K₀ values for the remolded soils. The PTA effectively measured the engineering strength properties of natural soil deposits and their remolded samples. Therefore, it is a valuable tool in diagnosing soil samples and analyzing triaxial strength properties, thus leading to improvements in the accuracy of engineering design.     

Undrained Shear Characteristics of Saturated Sand Under Anisotropic Consolidation

A series of undrained triaxial compression tests was performed on Toyoura sand in order to investigate the behavior of sand under large deformation. The present study focuses on the effects of anisotropic consolidation on the undrained behavior of sand. A wide range of initial states of sand is covered and taken into account with the behavior of sand varying from contractive to dilative. Different states of consolidation stress were shown to affect the stress-strain behavior of sand and the development of excess pore water pressure up to an axial strain of 5%. Beyond a strain in excess of 10%, the behavior of sand was shown to become independent of the stress state at consolidation. Consequently, the relation between void ratio and confining stress at steady state and quasi-steady state are independent of the extent of anisotropic consolidation. Moreover, the initial dividing curve between dilative and contractive behaviors in an e ~ p' diagram was shown to move down as the sand is more anisotropically consolidated.     

A unified approach to link small-strain shear modulus and liquefaction resistance of pumiceous sand

Natural pumiceous (NP) sands containing pumice particles, a type of volcanic soil, are commonly found in the central part of the North Island in New Zealand. The pumice particles are highly crushable, compressible, lightweight and angular, making engineering assessment of their properties problematic. In this paper, several series of bender element and undrained cyclic triaxial tests were performed on reconstituted and undisturbed NP sands to determine their small-strain shear modulus (G_max) and cyclic resistance ratio (CRR). Furthermore, similar tests were also conducted on normal hard-grained sands (e.g., Toyoura sand) for the purpose of comparison. The results showed that the NP sands have considerably lower G_max compared to normal sands, resulting in their higher deformability during the initial stages of the cyclic loading test. The high angularity of NP sands play an important role toward the end of the cyclic loading and contributed to their higher CRR. Next, the ratio of CRR/G_max for each sample was correlated to a level of strain denoted as cyclic yield strain (ε_ay), which was found to be significantly dependent on the percentages of pumice particles present in the natural soils. On the other hand, the ε_ay was found to be less sensitive to the consolidation stress (σ′_c) and the relative density (Dr) of the materials. For example, over different values of σ′_c and Dr, NP sands have substantially higher values of cyclic yield strain due to their lower G_max and higher CRR when compared with those of ordinary sands.