Investigation of block foundations resting on soil–rock and rock–rock media under coupled vibrations

In the present study,the dynamic response of block foundations of different equivalent radius to mass(R_o/m) ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.     

Dynamic fragmentation of microwave irradiated rock

The microwave-assisted rock fragmentation has been proven to be a promising approach in reducing cutting tools wear and improving efficiency in rock crushing and excavation.Thus,understanding the influence of damage induced by microwave irradiation on rock fragmentation is necessary.In this context,cylindrical Fangshan granite(FG)specimens were exposed to microwave irradiation at a power of 6 kW for different durations up to 4.5 min.The damages of the specimens induced by irradiation were quantified by using both X-ray micro-CT scanning and ultrasonic wave measurement.The CT value and Pwave velocity decreased with increase of irradiation duration.The irradiated specimens were then tested using a split Hopkinson pressure bar(SHPB)system to simulate rock fragmentation.A momentum-trap technique was utilized to ensure single-pulse loading on the specimen in SHPB tests,enabling valid fragment size distribution(FSD)analysis.The dependence of dynamic uniaxial compressive strength(UCS)on the irradiation duration and loading rate was revealed.The dynamic UCS increased with increase of loading rate while decreased with increase of irradiation duration.Using the sieve analysis,three fragmentation types were proposed based on FSD,which were dictated by both loading rate and irradiation duration.In addition,an average fragment size was proposed to quantify FSD.The results showed that the average fragment size decreased with increase of loading rate.A loading rate range was identified,where a dramatic reduction of the average fragment size occurred.The dependence of fragmentation on the irradiation duration and loading rate was also discussed.     

Simulations of explosion-induced damage to underground rock chambers

A numerical approach is presented to study the explosion-induced pressure load on an underground rock chamber wall and its resultant damage to the rock chamber.Numerical simulations are carried out by using a modified version of the commercial software AUTODYN.Three different criteria,i.e.a peak particle velocity (PPV) criterion,an effective strain (ES) criterion,and a damage criterion,are employed to examine the explosion-induced damaged zones of the underground rock chamber.The results show that the charg...     

Fracture initiation and propagation in intact rock—A review

The initiation and propagation of failure in intact rock are a matter of fundamental importance in rock engineering. At low confining pressures, tensile fracturing initiates in samples at 40%-60% of the uniaxial compressive strength and as loading continues, and these tensile fractures increase in density, ultimately coalescing and leading to strain localization and macro-scale shear failure of the samples. The Griffith theory of brittle failure provides a simplified model and a useful basis for discussion of this process. The Hoek-Brown failure criterion provides an acceptable estimate of the peak strength for shear failure but a cutoff has been added for tensile conditions. However, neither of these criteria adequately explains the progressive coalition of tensile cracks and the final shearing of the specimens at higher confining stresses. Grain-based numerical models, in which the grain size distributions as well as the physical properties of the component grains of the rock are incorporated, have proved to be very useful in studying these more complex fracture processes.     

Applications of rock failure process analysis （RFPA） method

Brittle failure of rocks is a classical rock mechanical problem.Rock failure not only involves initiation and propagation of single crack,but also is associated with initiation,propagation and coalescence of many cracks.The rock failure process analysis(RFPA)tool has been proposed since 1995.The heterogeneity of rocks at a mesoscopic level is considered by assuming that the material properties follow the Weibull distribution.Elastic damage mechanics is used for describing the constitutive law of the meso-le...     

Risk assessment and management in underground rock engineering——an overview

This paper attempts to provide an overview of risk assessment and management practice in underground rock engineering based on a review of the international literature and some personal experience. It is noted that the terminologies used in risk assessment and management studies may vary from country to country. Probabilistic risk analysis is probably the most widely-used approach to risk assessment in rock engineering and in geotechnical engineering more broadly. It is concluded that great potential exists to augment the existing probabilistic methods by the use of Bayesian networks and decision analysis techniques to allow reasoning under uncertainty and to update probabilities, material properties and analyses as further data become available throughout the various stages of a project. Examples are given of the use of these methods in underground excavation engineering in China and elsewhere, and opportunities for their further application are identified.     

A simplified approach to directly consider intact rock anisotropy inHoekeBrown failure criterion

Many rock types have naturally occurring inherent anisotropic planes, such as bedding planes, foliation,or flow structures. Such characteristic induces directional features and anisotropy in rocks＇ strength anddeformational properties. The HoekeBrown （HeB） failure criterion is an empirical strength criterionwidely applied to rock mechanics and engineering. A direct modification to HeB failure criterion toaccount for rock anisotropy is considered as the base of the research. Such modification introduced a newdefinition of the anisotropy as direct parameter named the anisotropic parameter （Kb）. However, thecomputation of this parameter takes much experimental work and cannot be calculated in a simple way.The aim of this paper is to study the trend of the relation between the degree of anisotropy （Rc） and theminimum value of anisotropic parameter （Kmin）, and to predict the Kmin directly from the uniaxialcompression tests instead of triaxial tests, and also to decrease the amount of experimental work.
2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.     

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.     

Engineering rock mechanics practices in the underground powerhouse at Jinping Ⅰ hydropower station

Based on the analyses of data obtained from the underground powerhouse at Jinping Ⅰ hydropower station,a comprehensive review of engineering rock mechanics practice in the underground powerhouse is first conducted.The distribution of strata,lithology,and initial geo-stress,the excavation process and corresponding rock mass support measures,the deformation and failure characteristics of the surrounding rock mass,the stress characteristics of anchorage structures in the cavern complex,and numerical simulations of surrounding rock mass stability and anchor support performance are presented.The results indicate that the underground powerhouse of Jinping Ⅰ hydropower station is characterized by high to extremely high geo-stresses during rock excavation.Excessive surrounding rock mass deformation and high stress of anchorage structures,surrounding rock mass unloading damage,and local cracking failure of surrounding rock masses,etc.,are mainly caused by rock mass excavation.Deformations of surrounding rock masses and stresses in anchorage structures here are larger than those found elsewhere:20%of extensometers in the main powerhouse record more than 50 mm with the maximum at around 250 mm observed in the downstream sidewall of the transformer hall.There are about 25%of the anchor bolts having recorded stresses of more than 200 MPa.Jinping Ⅰ hydropower plant is the first to have an underground powerhouse construction conducted in host rocks under extremely high geo-stress conditions,with the ratio of rock mass strength to geo-stress of less than 2.0.The results can provide a reference to underground powerhouse construction in similar geological conditions.     

Norwegian oil and gas storage in rock caverns-Technology based on experience from hydropower development

Underground storage in rock caverns is widely used in Norway for many different petroleum products,such as crude oil,fuel,propane and butane.Basically,the caverns for such storages are unlined,i.e.containment is ensured without using any steel lining or membrane.The main basis for the storage technology originates from the extensive hydropower development in Norway.As part of this activity,about 4500 km of tunnels and shafts have been excavated,and around 200 large powerhouse caverns have been constructed.The hydropower tunnels are mainly unlined,with hydrostatic water pressure on unlined rock of up to 1000 m.Some of the projects also include air cushion chambers with volumes of up to 1×10⁵m³and air pressure up to 7.7 MPa.Many lessons which are valuable also for underground oil and gas storage have been learnt from these projects.For a storage project to become successful,systematic,well planned design and ground investigation procedures are crucial.The main steps of the design procedure are first to define the optimum location of the project,and then to optimize orientation,shape/geometry and dimensions of caverns and tunnels.As part of the procedure,ground investigations have to be carried out at several steps integrated with the progress of design.The investigation and design procedures,and the great significance of these for the project to become successful will be discussed.Case examples of oil and gas storage in unlined rock caverns are given,illustrating the relevancy of experience from high-pressure hydropower projects for planning and design of unlined caverns for oil and gas storage.     

A non-Archimedean number system to characterize the structurally inhomogeneous rock behavior nearby a tunnel

The development of mathematical models of structurally inhomogeneous media leads to the necessity to consider structure of space itself where deformation occurs, i.e. change of mathematical apparatus itself. The space, whose coordinate axes are non-Archimedean straight lines, has been considered. Refusing the fulfillment of Archimedes's law allows to describe multi-scaling of the space, and so to consider deformation processes on different scale levels. The construction of two-scale mathematical model of ro...     

Dynamic distinct-element analysis of the 800 m high Åknes rock slope

The seismic stability of the Åknes rock slope, western Norway, was analysed by using the distinct element code UDEC (Universal Distinct Element Code). The slope poses a threat to the region as a sudden failure may cause a destructive tsunami in the fjord. The dynamic input was based on earthquakes with return periods of 100 and 1000 years, and in most models the input shear wave was a harmonic function (sine wave). Models with depths of the sliding surface up to 200 m and with ground water conditions derived from site investigations were analysed, as well as models with ground water conditions assumed from possible future draining of the slope. The analyses indicate that an earthquake with a return period of 1000 years is likely to trigger sliding to great depth in the slope at the present ground water conditions and that the slope will be stable if it is drained. The analyses also indicate that sliding is not likely to be triggered by an earthquake with a return period of 100 years at the present ground water conditions.     

Dynamic compression characteristics of layered rock mass of significant strength changes in adjacent layers

Layered rock mass of significant strength changes for adjacent layers is frequently observed in underground excavation,and dynamic loading is a prevalent scenario generated during excavation.In order to improve the driving efficiency and reduce engineering accidents,dynamic compression characteristics of this kind of rock mass should be understood.The dynamic properties of a layered composite rock mass are investigated through a series of rock tests and numerical simulations.The rock mass is artificially made of various proportions of sand,cement and water to control the distinct strength variations at various composite layers separated by parallel bedding planes.All rock specimens are prefabricated in a specially designed mould and then cut into 50 mm in diameter and 50 mm in height for split Hopkinson pressure bar(SHPB)dynamic compression testing.The test results reveal that increasing strain rate causes the increases of peak strength,σ_p,and the corresponding failure strain,ε_p,while the dynamic elastic modulus,E_d,remains almost unchanged.Interestingly,under the same strain rates,Ed of the composite rock specimen is found to decline first and then increase as the dip angle of bedding plane increases.The obtained rock failure patterns due to various dip angles lead to failure modes that could be classified into four categories from our dynamic tests.Also,a series of counterpart numerical simulations has been undertaken,showing that dynamic responses are in good agreement with those obtained from the SHPB tests.The numerical analysis enables us to Iook into the dynamic characteristics of the composite rock mass subjected to a broader range of strain rates and dip angles than these being tested.     

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

General:Jaiswal and Shrivastva(2012)proposed the mathematical formulations,i.e.the J–S criterion for converting generalized H-B failure criterion into 3D smooth convex failure criterion at deviatoric plane.The J–S strength criterion is in two versions:uniform and variable extension ratio.It has been observed from the analysis that at uniform extension ratio,the required strength parameters are only UCS and m(other parameters such as Ls,a,b and c are related with m).In the case of variable extension ratio,extra parameter f is required along with UCS and m.Thus,it has minimal strength parameters compared to You strength criterion.Furthermore,You strength criterion does not obey the smooth convex condition at deviatoric plane.     

Study of failure mechanisms of rock under compressive–shear loading using real-time laser holography

Failure of rock is quite commonly induced by compressive and shear coupling loading. The knowledge of the mechanism and process of deformation and failure of rock under compressive–shear loading condition is an important basis for the study of stability of rock engineering. Based on the principles of laser holographic interferometry, an experimental system with high precision has been established. Through the experiment, the real-time laser holographic interferential fringes under compressive–shear loading are simultaneously observed and recorded. The active fringes can visually display the distribution, mode, moving path and dynamic evolution of deformation and cracking in rock. On the basis of interpretation and quantitative analysis of the active fringes, the whole process of deformation and failure of rock, including time–spatial evolution law of initiating, propagating, growing and closing of cracks in rock, is quantitatively described. From the experimental results, some conclusions on the mechanism and characters of deformation and failure of rock under compressive–shear loading condition are drawn out.     

Rock brittleness indices and their applications to different fields of rock engineering:A review

Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.     

Assessment of the properties of polycrystalline rock salt synthesized under nominally dry and wet conditions

Polycrystalline rock salt’s compression is a function of applied stresses,exposure duration to the applied stresses,ambient temperature,and water content.Rock salt’s compressional behavior under different conditions and its effects on the specimens’mechanical properties have been investigated in the literature.However,the one-dimensional(1D)compression behavior of polycrystalline rock salt at various water contents and how the specimen’s compression at different water contents further affects its physical and mechanical properties are not fully understood yet.In this study,polycrystalline rock salt specimens were prepared under nominally dry and wet conditions and some of the dry and wet specimens were annealed after the preparation.The relationship between the porosity of the specimens and the logarithm of the applied axial stresses during the 1D compression was found to follow a linear relationship after reaching unique critical porosities of 32%and 37%for the dry and wet specimens,respectively.Unloading and reloading the specimens did not result in any major changes in the porosity of the specimens.The specimens compressed under wet condition showed an average final porosity of 2.6%compared to 6.9%for the dry specimens.The dry and wet specimens that were annealed after the compression exhibited a lower porosity in comparison to the dry and wet specimens,respectively.Unconfined compression experiments on the specimens showed dry and wet specimens possess averaged unconfined compressive strengths(σ_u)of 64.3 and 16.2 MPa,respectively.Annealing decreased σ_uof the dry specimens to 39.6 MPa and increased σ_uof the wet specimens to 41 MPa.     

Behavior of noncircular tunnels excavated in stratified rock masses – Case of underground coal mines

The amount of tunnels excavated along stratified/sedimentary rock masses in Quangninh coal mine area,Vietnam, is gradually increasing. Rock mass in Quangninh is characterized by beddings between rock layers. The behavior of stratified rock masses surrounding the tunnels depends on both the intact rock and the beddings between rock layers. The main characteristics of stratified rock masses that need to be considered are their heterogeneity and anisotropy. Depending on the dip angle of rock layers, movements and failure zones developed surrounding the tunnels can be asymmetrical over the vertical axis of tunnel. This asymmetry causes adverse behaviors of the tunnel structures. The objective of this study is to highlight convergences and yielded zones developed in rock masses surrounding noncircular tunnels in Quangninh coal mine area using a finite element method. The presence of bedding joints is explicitly simulated. The numerical results indicated that with the increase in dip angle of bedding joints, the stress asymmetry over the tunnel vertical axis increases. It gradually leads to an asymmetry of the failure zone surrounding the tunnel. An increase of rock mass quality means a decrease of rock mass sensitivity to the discontinuities. In addition,a dip angle of the bedding joints of approximately 45° could be considered as the critical angle at which the rock mass mechanism changes between sliding and bending.     

Ultimate bearing capacity at the tip of a pile in rock—part 1: theory

This paper proposes a method for calculating the ultimate bearing capacity at the tip of a pile that is embedded in rock, according to the theory of plasticity. The non-linear failure criterion of Hoek and Brown (Underground excavation in rock, The Institution of Mining and Metallurgy, London, 1980) is used. The plastified area is analysed as a two-dimensional medium using the characteristic lines method generalised for non-linear failure criteria. The embedment is simulated using the hypothesis proposed by Meyerhof for piles in soils. The results obtained through the calculations are corrected by applying a shape factor in order to take into account the three-dimensional nature of the pile.