Fracture toughness study for a brittle rock subjected to mixed mode I/II loading

A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K_I, K_II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens.     

Shear strength response of some geological materials in triaxial compression

The shear strength of geological materials, like soils and rocks, is often represented either by Coulomb or Mohr–Coulomb theory. It is assumed to vary linearly with the applied stress through two shear strength parameters commonly known as the cohesion intercept and the angle of shearing resistance/friction. In reality, whenever these materials are tested to high stresses, a non-linear shear strength response is observed. The effective cohesion intercept continues to increase while the effective angle of shearing resistance decreases with the increase of effective stress. These strength parameters, therefore, cannot be considered as constants in the analysis of soils and rocks. A more realistic and responsive shear strength criterion, involving only two different strength parameters, that remain practically constant with the applied stress, is advocated to represent non-linear response that minimizes the drudgery by conducting a number of triaxial tests on the material. This criterion has been verified with the experimental data of 41 different soils from clay to rockfill and with the data of a number of intact rocks, jointed rocks and rock-like materials tested in the axisymmetric triaxial compression exhibiting either brittle or ductile response. One of the strength parameters enables to define the brittle–ductile boundary. A boundary between rock and soil has been suggested on the basis of modulus ratio and also on the basis of a weakness factor in a jointed rock, named joint factor, representing the combined influence of joint frequency, inclination of the sliding joint and the strength on the sliding joint. When the joint factor is applied to the compressive strength or the modulus of an intact specimen, it provides the corresponding values of the jointed mass in uniaxial compression and also enables to estimate the two strength parameters, for use in the strength criterion applicable to the mass. The modulus ratio is also linked to the failure axial strain of jointed rocks when tested in uniaxial compression.     

Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock

A series of dynamic uniaxial and triaxial compression, uniaxial tension and unconfined shear tests were conducted on the Bukit Timah granite of Singapore. The results are analyzed in this paper in order to examine the validity and applicability of the Mohr–Coulomb and the Hoek–Brown criteria to the rock material strength properties subjected to dynamic loads. The study indicates that rock material strength under dynamic loads can be approximately described by the Mohr–Coulomb criterion, at low confining pressure range. The change of strength is primarily due to the variation of cohesion with loading rate. The rock material strength under dynamic loads is better described by the Hoek–Brown criterion. Assessment of the Hoek–Brown criterion shows that the uniaxial compressive strength increases with increasing loading rate, and the parameter m appears unaffected by the loading rate.     

A Hoek–Brown criterion with intrinsic material strength factorization

Probably the most common failure criterion for rock masses is the Hoek–Brown (HB) failure criterion. The HB criterion is an empirical relation that extrapolates the strength of intact rock to that of rock masses. For design purposes, the HB criterion is often fitted using equivalent Coulomb failure lines. However, equivalent Mohr–Coulomb (MC) shear strength parameters cannot yield the same failure characteristics as the HB criterion. The curvilinear HB criterion automatically accommodates changing stress fields; the MC criterion does not. The extended HB criterion proposed in this paper provides a solution to this problem by incorporating an intrinsic material strength factorization scheme. The original HB criterion is additionally enhanced by adopting the spatial mobilized plane (SMP) concept, first introduced by Matsuoka and Nakai (MN). The SMP concept accounts for the experimentally proven, influence of intermediate principal stresses on failure, which is disregarded in the original HB criterion. A small set of examples provided at the end of the article gives a good indication of the merits of using the extended HB criterion in practical applications.     

New calculation schemes for the "building-base" system in conditions of collapsing loess soils

New calculation schemes are suggested for the "building—loess collapsing base" system, with the help of which it is possible to obtain values of the forces and movements occurring in a building as a result of collapses of bases that are close to the real ones in the nature of moistening and deformations of loess strata.Samarkand Architectural Construction Institute. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, pp. 19–22, November–December, 1993.     

Strip foundations with intermediate earth-pile pads

Conclusions 1. It was found that an intermediate pad of variable rigidity (in the form of earth piles) improves the operation of the soil base and of the foundation itself.2. When use is made of an intermediate pad of variable rigidity under the center of a foundation, a region of increased compaction of the soil is formed which is less deformable in comparison with the surrounding soil.3. When a pad is constructed redistribution of the pressure occurs — under the foundation center it increases by 25–40% and under the edges it decreases by 30%. The effect of the pad on the stress conditions of the soil base decreases with depth and is limited to a depth equal to 1.5 b.4. As a result of use of an intermediate pad in the form of earth piles, the bending moment in the design section of the foundation is reduced, which yields a saving of 25–27%.Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, pp. 12–14, November–December, 1991.     

A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory

Generalized beam theory—GBT—is among the most adequate tools for the analysis of thin-walled prismatic elements. It enables the analysis of the distortion of the element cross-section and local buckling of individual walls in a unified manner that incorporates the results from classical bending theory. The basis of this theory was developed in the 1960s by Schardt for first and second order elastic behaviour of thin-walled members.Open and closed thin-walled members present the distinctive difference of the unknown shear flow that characterizes the latter. More specifically, shear strains must follow an elasticity law, as opposed to the simplifying assumptions for open cross-sections.It is the purpose of the present paper to present a unified energy formulation for the non-linear analysis of both open and closed sections in the framework of GBT, able to deal with all modal interaction phenomena between local plate behaviour, distortional behaviour and the more classical global (flexural, torsional and flexural–torsional) response. Finally, an application to the stability analysis of a compressed thin-walled column is presented and discussed.     

Semi-analytical postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending

A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh–Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises’ yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer program based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.     

Evaluation of the damping factor of foundation bases subjected to vertical vibrations

Conclusions 1. The damping factor b depends on the elastic properties of the soil base and the dimensions of the lower surface of the foundation. Hence, one of the values — the coefficient of uniform elastic compression C_z — makes it possible to find both the elastic and damping characteristics of the soil base. To evaluate the damping characteristics, it is expedient to use the specific damping factor introduced in this article.2. To find the maximum amplitudes of unsteady vibrations of massive foundations under the action of an instantaneous impulse, use can be made of Eqs. (21)–(23), which determine the factor b_z if the limit from which the elastic waves may be reflected (rock, soil layer with higher wave velocities, etc.) is located below the lower surface of the foundation at a depth greater thanl/2,l being calculated from Eq. (16). To find the parameters of steady vibrations of massive foundations, the damping properties of the soil base are determined by the factor b_z, calculated from Eqs. (12)–(15).3. The equations for the factor b_z are related to the mean soil conditions; however, the effect of the characteristics of the geologic morphology is exerted on this factor more strongly than on the rigidity modulus of the soil base; hence, it is desirable to gather experimental data for the systematization and processing of which use can be made of the relations obtained in this article.Scientific-Research Institute of Bases and Underground Structures. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 5, pp. 15–18, September–October, 1981.     

Prospects for the use of heavy-duty dual-mass tampers for the compaction of soils

Conclusions 1. It is expedient to increase the weight of a tamper with given lower-surface dimensions and drop height to a certain limit, the excedence of which may lead to the development of shear strains and, correspondingly, to heaving and loosening of the soil around the tamper without a significant increase in the effect of its compaction outside the bounds of this zone.2. In many cases, the weights of the single-mass tampers employed at the present time exceed those limiting values for which heaving and loosening of the surface layer of the soil is possible. In cases where dual-mass tampers are employed, the probability of the development of soil heaving and loosening is significantly reduced. The volume of tamped-in soil is 25–30% higher for a dual- than a single-mass tamper.3. At a drop height of 8–10 m and 6–8 blows, a heavy-duty 10-ton dual-mass tamper may compact saturated sands at a depth of 4.5–5.5 m to a dense composition.Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 4, pp. 9–12, July–August, 1990.     

Investigation of the bearing capacity of piles driven in plastic frozen soil

Conclusions The bearing capacity of a pile lowered into a borehole whose cross section exceeds the cross section of the pile for the possibility of filling in with slurry (frozen-in, friction, bored-sunk piles) is close to the calculated, but has a greater settlement under a standard load in comparison with a bored-drive pile.The bearing capacity of piles driven by the VMS-1 vibratory hammer into plastic frozen soil (bored-drive piles) is on the average 1.6 times greater than the calculated. Such an excess of the bearing capacity of the piles can be explained by the formation of a new structure and frost texture of the soil within 30–50 mm around the pile skin. A characteristic feature of the newly formed zone of soil is a considerably greater homogeneity and density of the soil than under natural conditions and absence of ice lenses and interlayers directly contacting the pile.The settlements of the pile tested under a standard load were less than the allowable deformations for the bases of the majority of buildings and structures.The cross-sectional area of the pilot hole should be equal to 0.65–0.75 of the pile section in the case of driving it at the time of the maximum depth of thawing of the soil and 0.95 at the time of seasonal freezing of the soil.Restoration of the contact bonds between the soil and pile during its freezing-in after driving into soil with a temperature of -0.5°C and higher can continue for several months.Deceased.Central Scientific-Research Institute of Transport Construction (TsNIIS). Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 1, pp. 19–20, January–February, 1979.     

Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion

This paper applies numerical limit analyses to evaluate the ultimate bearing capacity of a surface footing resting on a rock mass whose strength can be described by the generalised Hoek–Brown failure criterion [Hoek E, Carranza-Torres C, Corkum B. Hoek–Brown failure criterion—2002 edition. In: Proceedings of the North American rock mechanics society meeting in Toronto, 2002]. This criterion is applicable to intact rock or heavily jointed rock masses that can be considered homogeneous and isotropic. Rigorous bounds on the ultimate bearing capacity are obtained by employing finite elements in conjunction with the upper and lower bound limit theorems of classical plasticity. Results from the limit theorems are found to bracket the true collapse load to within approximately 2%, and have been presented in the form of bearing capacity factors for a range of material properties. Where possible, a comparison is made between existing numerical analyses, empirical and semi-empirical solutions.     

Settlements and contact pressures of a nonlinearly deformable foundation bed subject to strip loading

Conclusions 1. Consideration of the nonlinearity, creep, and mutual effect of the invariance of the stress tensor makes it possible to reflect more precisely the real properties of a soil and brings theoretical solutions in line with field data.2. Nonlinearity, creep, and other factors can be accounted for in analytical solutions of the problem of the stress-strain state of a half plane, provided the laws satisfying conditions (5) and (7) are initial laws governing soil deformation. The general solution of this problem is given in the paper; however, selection of the specific form of law governing deformation is established on the basis of tests.3. In the more general case — where the effect of the natural weight of the soil, variation in the type of stress state, the loading scheme and history, etc. are taken into account — solution of the problem is possible using an electronic computer.4. The computational method under consideration can be used for practical bed designs, contributing to realization of the instructions in Construction Norms and Specifications II-15-74 concerning consideration, where necessary, of the nonlinear law governing the strain and creep of the bed soils.Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, pp. 15–20, November–December, 1977.     

Experimental thawing of permafrost soils in bases of reconstructed main building of the Chita-I Thermoelectric Power Plant

Conclusions 1. Compaction of thawed soils takes place directly during the thawing process or in the first 10–35 days after it. The thawed soils do not require subsequent compaction and, as regards the load-carrying properties, they are comparable to similar rocks in a naturally thawed state.2. The specific electric energy consumption for thawing 1 m³ of permafrost soils in bases is 25.2 kWh, and it is a fundamental characteristic in the design of industrial thawing of soil bases for determining the spacing between the heaters their capacity, and the thawing period.3. In test thawing, the number of ground mark vertical lines and the number of marks in each vertical line should be determined from the degree of heterogeneity of the frozen soils as regards the collapsibility in plan and section. For permafrost soil conditions similar to those of the construction site of the Chita-I plant, the optimal solution is to lay one vertical line per 100–120 m² of thawing area, and to use in each vertical line not less than one mark per 5 m of section of thawed permafrost soils."Atomteploelektroproekt" Institute, Novosibirsk. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 5, pp. 9–10, September–October, 1986.     

Use of foundations and artificial bases in punched (tamped-out) trenches in seismic regions (using South Kazakhstan as an example)

Field and experimental investigations as well as full-scale tests of foundations and artificial bases in punched (tamped-out) trenches at specific projects in South Kazakhstan have once again confirmed the effectiveness of their application in seismic regions with similar soil conditions.Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, pp. 37–39, November–December, 1992.     

A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock

This paper presents the methodology in which two computer codes—TOUGH2 and FLAC3D—are linked and jointly executed for coupled thermal–hydrologic–mechanical (THM) analysis of multiphase fluid flow, heat transfer, and deformation in fractured and porous rock. TOUGH2 is a well-established code for geohydrological analysis with multiphase, multicomponent fluid flow and heat transport, while FLAC3D is a widely used commercial code that is designed for rock and soil mechanics with thermomechanical and hydromechanical interactions. In this study, the codes are sequentially executed and linked through external coupling modules: one that dictates changes in effective stress as a function of multi-phase pore pressure and thermal expansion, and one that corrects porosity, permeability, and capillary pressure for changes in stress. The capability of a linked TOUGH-FLAC simulator is demonstrated on two complex coupled problems related to injection and storage of carbon dioxide in aquifers and to disposal of nuclear waste in unsaturated fractured porous media.     

Investigations of negative skin friction on piles and suggestions on its calculation

Conclusions The investigations showed that negative frictional forces appear at the time of occurrence of continuous settlement of the soil relative to the pile, but for their maximum development this settlement should be relatively large, of the order of 5 cm and more. In addition, it was established that the negative frictional forces act only during active displacement of the soil surrounding the pile as a result of its consolidation or other causes. After this displacement stops the negative frictional forces practically disappear.The established physical characteristics of the effect of negative frictional forces permitted taking the presence of an excess of the rate of soil settlement over the rate of pile settlement as the criterion of their occurrence. The suggestions on calculating piles worked out with consideration of this criterion allows in a number of cases disregarding the negative frictional forces in the effective design load or taking them to be considerably less than by the previously known calculation methods.Scientific-Research Institute of Bases and Underground Structures. State Planning Institute for General Construction and Sanitary-Engineering Planning of Industrial Establishments, Kiev. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 4, pp. 11–15, July–August, 1974.     

Possibility of reducing the duration of static pile tests

Conclusions 1. The experiments, carried out under different conditions, did not show substantial differences in the limit strengths of prismatic piles tested at the standazd loading rate and by the accelerated method when it is considered that attenuation of the settlement has been reached when it has a rate of 0.1 mm in 15 min. The tests performed by continuous increase in the load over a period of 10–15 min led to overestimation of the limit strengths by 20–30%.2. Under conditions in which the settlements are not the object of special studies, accelerated pile tests (with a settlement stabilization criterion of 0.1 mm in 15 min), in place of standard prismatic piles applicable under the most widespread soil soil conditions (for example, in alluvial, deluvial, and similar deposits). In this case, it is advisable to use the pile limit strength for settlements which are smaller by a factor of two than for the standard tests.NIIpromstroi Institute. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 1, pp. 9–12, January–February, 1987.     

Deformations of brick buildings on collapsing soils of the Zeravshan oasis

The reasons for damage to frame and brick buildings in soil conditions of the first and second types with respect to collapsibility are analyzed. Ways of stabilizing the deformations of loess soils are discussed. Recommendations are suggested that make it possible to decrease the probability of damage to buildings from uneven moistening of bases composed of collapsing loess soils.M. Ulugbek Samarkand State Architectural Construction Institute. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, pp. 23–26, November–December, 1993.     

Influence of constitutive model on numerical simulation of EPS seismic buffer shaking table tests

The paper describes two constitutive models for the simulation of expanded polystyrene (EPS) seismic buffer shaking table tests previously reported by the writers. The first model is linear elastic–plastic with Mohr–Coulomb criterion and Rayleigh damping. The second is called the equivalent-linear method (ELM) which incorporates hysteretic load–unload cycles using Masing-type functions and strain-dependent shear modulus and damping ratio functions. The constitutive models were applied to both the geofoam buffer and sand backfill in both approaches. Both models are shown to capture qualitative features of measured peak load-time response of the physical tests. The advanced ELM model gave predictions that were closer to the measured results for the seismic buffer test with the most compressible EPS when model accelerations and total wall forces were greatest. However, the simpler model is judged to be sufficiently accurate for practical purposes when the dynamic force increment is considered only.