Testing and modeling of cyclically loaded rock anchors

The Norwegian Public Roads Administration(NPRA) is planning for an upgrade of the E39 highway route at the westcoast of Norway. Fixed links shall replace ferries at seven fjord crossings. Wide spans and large depths at the crossings combined with challenging subsea topography and environmental loads call for an extension of existing practice. A variety of bridge concepts are evaluated in the feasibility study. The structures will experience significant loads from deadweight, traffic and environment. Anchoring of these forces is thus one of the challenges met in the project. Large-size subsea rock anchors are considered a viable alternative. These can be used for anchoring of floating structures but also with the purpose of increasing capacity of fixed structures. This paper presents first a thorough study of factors affecting rock anchor bond capacity. Laboratory testing of rock anchors subjected to cyclic loading is thereafter presented. Finally, the paper presents a model predicting the capacity of a rock anchor segment, in terms of a ribbed bar, subjected to a cyclic load history. The research assumes a failure mode occurring in the interface between the rock anchor and the surrounding grout. The constitutive behavior of the bonding interface is investigated for anchors subjected to cyclic one-way tensile loads. The model utilizes the static bond capacity curve as a basis, defining the ultimate bond sbuand the slip s1 at τ. A limited number of input parameters are required to apply the model. The model defines the bond-slip behavior with the belonging rock anchor capacity depending on the cyclic load level(τcy/τ), the cyclic load ratio(R= τcy/τcy), and the number of load cycles(N). The constitutive model is intended to model short anchor lengths representing an incremental length of a complete rock anchor.

Experimental study of hollow rectangular bridge column performance under vertical and cyclically bilateral loads

To investigate the seismic performance of hollow reinforced concrete （RC） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges （JTG/T B02-01-2008）. The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Damage evolution of rock-encased-backfill structure under stepwise cyclic triaxial loading

Rock-encased-backfill(RB)structures are common in underground mining,for example in the cut-andfill and stoping methods.To understand the effects of cyclic excavation and blasting activities on the damage of these RB structures,a series of triaxial stepwise-increasing-amplitude cyclic loading experiments was conducted with cylindrical RB specimens(rock on outside,backfill on inside)with different volume fractions of rock(VF=0.48,0.61,0.73,and 0.84),confining pressures(0,6,9,and 12 MPa),and cyclic loading rates(200,300,400,and 500 N/s).The damage evolution and meso-crack formation during the cyclic tests were analyzed with results from stress-strain hysteresis loops,acoustic emission events,and post-failure X-ray 3D fracture morphology.The results showed significant differences between cyclic and monotonic loadings of RB specimens,particularly with regard to the generation of shear microcracks,the development of stress memory and strain hardening,and the contact forces and associated friction that develops along the rock-backfill interface.One important finding is that as a function of the number of cycles,the elastic strain increases linearly and the dissipated energy increases exponentially.Also,compared with monotonic loading,the cyclic strain hardening characteristics are more sensitive to rising confining pressures during the initial compaction stage.Another finding is that compared with monotonic loading,more shear microcracks are generated during every reloading stage,but these microcracks tend to be dispersed and lessen the likelihood of large shear fracture formation.The transition from elastic to plastic behavior varies depending on the parameters of each test(confinement,volume fraction,and cyclic rate),and an interesting finding was that the transformation to plastic behavior is significantly lower under the conditions of 0.73 rock volume fraction,400 N/s cyclic loading rate,and 9 MPa confinement.All the findings have important practical implications on the ability of backfill to support underground excavations.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Dynamic failure process of expanded polystyrene particle lightweight soil under cyclic loading using discrete element method

Expanded polystyrene(EPS)particle-based lightweight soil,which is a type of lightweight filler,is mainly used in road engineering.The stability of subgrades under dynamic loading is attracting increased research attention.The traditional method for studying the dynamic strength characteristics of soils is dynamic triaxial testing,and the discrete element simulation of lightweight soils under cyclic load has rarely been considered.To study the meso-mechanisms of the dynamic failure processes of EPS particle lightweight soils,a discrete element numerical model is established using the particle flow code(PFC)software.The contact force,displacement field,and velocity field of lightweight soil under different cumulative compressive strains are studied.The results show that the hysteresis curves of lightweight soil present characteristics of strain accumulation,which reflect the cyclic effects of the dynamic load.When the confining pressure increases,the contact force of the particles also increases.The confining pressure can restrain the motion of the particle system and increase the dynamic strength of the sample.When the confining pressure is held constant,an increase in compressive strain causes minimal change in the contact force between soil particles.However,the contact force between the EPS particles decreases,and their displacement direction points vertically toward the center of the sample.Under an increase in compressive strain,the velocity direction of the particle system changes from a random distribution and points vertically toward the center of the sample.When the compressive strain is 5%,the number of particles deflected in the particle velocity direction increases significantly,and the cumulative rate of deformation in the lightweight soil accelerates.Therefore,it is feasible to use 5%compressive strain as the dynamic strength standard for lightweight soil.Discrete element methods provide a new approach toward the dynamic performance evaluation of lightweight soil subgrades.

Effect of NaCl Concentration on the Cumulative Strain and Pore Distribution of Clay under Cyclic Loading

Clay,as the most common soil used for foundationfill,is widely used in various infrastructure projects.The phy-sical and mechanical properties of clay are influenced by the pore solution environment.This study uses a GDS static/dynamic triaxial apparatus and nuclear magnetic resonance experiments to investigate the effects of cyclic loading on clay foundations.Moreover,the development of cumulative strain in clay is analyzed,and afitting model for cumulative plastic strain is introduced by considering factors such as NaCl solution concentration,con-solidation stress ratio,and cycle number.In particular,the effects of the NaCl solution concentration and con-solidation stress ratio on the pore distribution of the test samples before and after cyclic loading are examined,and the relationship between microscopic pore size and macroscopic cumulative strain is obtained accordingly.Our results show that as the consolidation stress ratio grows,an increasing number of large pores in the soil samples are transformed into small pores.As the NaCl solution concentration becomes higher,the number of small pores gradually decreases,while the number of large pores remains unchanged.Cyclic loading causes the disappearance of the large pores in the samples,and the average pore size before cyclic loading is posi-tively correlated with the axial cumulative strain after cyclic loading.The cumulative strain produced by the soil under cyclic loading is inversely proportional to the NaCl solution concentration and consolidation stress ratio.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Strength and damage evolution mechanism of rock mass with holes under cyclic loading

The damage and failure law of rock mass with holes is of great significance to the stability control of roadways. This study investigates the mechanical properties and failure modes of porous rock masses under cyclic loading, elucidates the acoustic emission (AE) characteristics and their spatial evolution, and establishes the interrelation among AE, stress, strain, time, and cumulative damage. The results reveal that the rock mass with holes and the intact rock mass show softening and hardening characteristics after cyclic loading. The plastic strain of the rock mass with holes is smaller than that of the intact rock mass, and the stress −strain curve shows hysteresis characteristics. Under uniaxial compression, the pore-bearing rock mass shows the characteristics of higher ringing count, AE energy, b-value peak, and more cumulative ringing count in the failure stage, while it shows lower characteristics under cyclic action. At the initial stage of loading, compared with the intact rock mass, the pore-containing rock mass shows the characteristics of a low b-value. The AE positioning and cumulative damage percentage are larger, and the AE positioning is denser around the hole. The specimen with holes is mainly shear failure, and the complete specimen is mainly tensile shear failure.

Mechanical behavior of red sandstone under cyclic point loading

The mechanical properties of red sandstone subjected to cyclic point loading were investigated. Tests were conducted using MTS servohydraulic landmark test system, under cyclic loadings with constant amplitudes and increasing multi-level amplitudes. The frequencies range from 0.1 to 5 Hz and lower limit load ratios range from 0 to 0.60. Laboratory investigations were performed to find the effect of the frequency and the lower limit load ratio on the fatigue life and hysteresis properties of sandstone. The results show that the fatigue life of sandstone decreases first and then increases with the increase of frequency and lower limit load ratio. Under the same cycle number, the spacing between hysteresis loops increases with rising frequency and decreasing lower limit load ratio. The existence of “training” and “memory” effects in red sandstone under cyclic point loading was proved.

THE KINEMATIC HARDENING RULES UNDER NONPROPORTIONAL CYCLIC LOADING

A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardening rules. It shows that Mroz and Tseng Lee rule related to a two surface model has the latent potentiality to describe the nonproportional cyclic hardening behaviors, and a simple two surface model is presented.

Dynamic performance of angle-steel concrete columns under low cyclic loading-I:Experimental study

This paper describes low cyclic loading testing of nine angle-steel concrete column （ASCC） specimens. In the tests, the influence of the shear-span ratio, axial compression ratio and shear steel plate ratio on the hysteretic behavior, energy dissipation, strength degradation, stiffness degradation, skeleton curve and ductility of the ASCCs is studied. Based on the test results, some conclusions are presented. The P-A and sectional M -φ hysteretic models for the ASCCs are presented in a companion paper （Zheng and Ji, 2008）.

Accumulative deformation in railway track induced by high-speed traffic loading of the trains

Prediction and control of the permanent settlement of a track caused by traffic loading from trains is crucial to high-speed railway design and maintenance. In this study, a unified prediction model of accumulative deformation of geomaterials used in railway construction subjected to cyclic loadings is introduced and calibrated using physical model testing. Based on this versatile model, a calculation approach to determine the track structure settlement under repeated loadings caused by the movement of the wheel axle of the train is proposed. Regression analysis on the physical model testing is adopted to determine the parameters involved in the computational approach. Comparison of model test data and computed results shows that the parameters obtained from the back-analysis are consistent throughout the various testing conditions, and the proposed calculation approach is capable of satisfactorily predicting the accumulative settlement of the railway roadbed and subgrade soil for various axle loads and loading cycles. A case study of a high-speed railway is performed to demonstrate the feasibility of the proposed approach in realistic engineering applications. The computation results from the settlement development of a roadbed and subgrade soil are presented and discussed.

A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading

Rock engineering is highly susceptible to cyclic loads resulting from earthquakes,quarrying or rockbursts.Acquiring the fatigue properties and failure mechanism of rocks is pivotal for long-term stability assessment of rock engineering structures.So far,significant progress has been gained on the mechanical characteristics of rocks subjected to cyclic loading.For providing a global insight of typical results and main features of rocks under cyclic loading conditions,this study comprehensively reviews the state-ofthe-art of deformation and failure mechanism and fatigue constitutive relationship of rocks subjected to cyclic loading in the past 60 years.Firstly,cyclic tests on rocks are classified into different types based on loading paths,loading parameters,loading types and environment conditions.Secondly,representative results are summarized and highlighted in terms of the fatigue response of rocks,including the deformation degradation,energy dissipation,damage evolution and failure characteristics;both laboratory testing and numerical results are presented,and various measurement techniques such as X-ray microcomputed tomography(micro-CT)and digital image correlation(DIC)are considered.Thirdly,the influences of cyclic loads on the mechanical characteristics of rocks are discussed,including the cyclic stress,frequency,amplitude and waveform.Subsequently,constitutive relationships for rocks subjected to cyclic loading are outlined,in which typical fatigue constitutive models are compared and analyzed,regarding the elastoplastic model,the internal variable model,the energy-based damage model and the discrete element-based model.Finally,some ambiguous questions and prospective research are interpreted and discussed.

Estimation of Undrained Bearing Capacity for Offshore Soft Foundations with Cyclic Load

The degradation strength of soils under cyclic loading is studied and a method for determining the cyclic degradation strength with cyclic triaxial tests is given in the paper. Furthermore, a dum my static method for estimating the undrained bearing capacity for offshore soft foundation under wave loads is developed. It can consider the effect of the difference of cyclic stress for different parts of the foundation on both the degradation strength of the foundation soil and the bearing capacity so that the estimated result can better reflect the real condition of foundation under cyclic loading. The method can be applied to plane and space problem.

Dynamic performance of angle-steel concrete columns under low cyclic loading-II:parametric study

Tests of nine angle-steel concrete column （ASCC） specimens under low cyclic loading are described in a companion paper （Zheng and Ji, 2008）. In this paper, the skeleton curves from the numerical simulation are presented, and show good agreement with the test results. Furthermore, parametric studies are conducted to explore the influence of factors such as the axial compression ratio, shear steel plate ratio, steel ratio, prismatic concrete compression strength, yield strength of angle steel and shear span ratio, etc., on the monotonic load-displacement curves of the ASCCs. Based on a statistical analysis of the calculated results, hysteretic models for load-displacement and moment-curvature are proposed, which agree well with the test results. Finally, some suggestions concerning the conformation of ASCCs are proposed, which could be useful in engineering practice.

Strength degradation of sandstone and granodiorite under uniaxial cyclic loading

Change in mechanical properties of rocks under static loading has been widely studied and documented.However, the response of rocks to cyclic loads is still a much-debated topic. Fatigue is the phenomenon when rocks under cyclic loading fail at much lower strength as compared to those subjected to the monotonic loading conditions. A few selected cored granodiorite and sandstone specimens have been subjected to uniaxial cyclic compression tests to obtain the unconfined fatigue strength and life. This study seeks to examine the effects of cyclic loading conditions, loading amplitude and applied stress level on the fatigue life of sandstone, as a soft rock, and granodiorite, as a hard rock, under uniaxial compression test. One aim of this study is to determine which of the loading conditions has a stronger effect on rock fatigue response. The fatigue response of hard rocks and soft rocks is also compared. It is shown that the loading amplitude is the most important factor affecting the cyclic response of the tested rocks. The more the loading amplitude, the shorter the fatigue life, and the greater the strength degradation. The granodiorite specimens showed more strength degradation compared to the sandstone specimens when subjected to cyclic loading. It is shown that failure modes of specimens under cyclic loadings are different from those under static loadings. More local cracks were observed under cyclic loadings especially for granodiorite rock specimens.

Seismic performance of interior precast concrete beam-column connections with T-section steel inserts under cyclic loading

An experimental investigation was conducted to study the performance of precast beam-column concrete connections using T-section steel inserts into the concrete beam and joint core,under reversed cyclic loading.Six 2/3-scale interior beam-column subassemblies,one monolithic concrete specimen and five precast concrete specimens were tested.One precast specimen was a simple connection for a gravity load resistant design.Other precast specimens were developed with different attributes to improve their seismic performance.The test results showed that the performance of the monolithic specimen M1 represented ductile seismic behavior.Failure of columns and joints could be prevented,and the failure of the frame occurred at the flexural plastic hinge formation at the beam ends,close to the column faces.For the precast specimens,the splitting crack along the longitudinal lapped splice was a major failure.The precast P5 specimen with double steel T-section inserts showed better seismic performance compared to the other precast models.However,the dowel bars connected to the steel inserts were too short to develop a bond.The design of the precast concrete beams with lap splice is needed for longer lap lengths and should be done at the beam mid span or at the low flexural stress region.

Numerical modeling of centrifuge cyclic lateral pile load experiments

To gain insight into the inelastic behavior of piles, the response of a vertical pile embedded in dry sand and subjected to cyclic lateral loading was studied experimentally in centrifuge tests conducted in Laboratoire Central des Ponts et Chaussees. Three types of cyclic loading were applied, two asymmetric and one symmetric with respect to the unloaded pile. An approximately square-root variation of soil stiffness with depth was obtained from indirect in-flight density measurements, laboratory tests on reconstituted samples, and well-established empirical correlations. The tests were simulated using a cyclic nonlinear Winkler spring model, which describes the full range of inelastic phenomena, including separation and re-attachment of the pile from and to the soil. The model consists of three mathematical expressions capable of reproducing a wide variety of monotonic and cyclic experimentalp-y curves. The physical meaning of key model parameters is graphically explained and related to soil behavior. Comparisons with the centrifuge test results demonstrate the general validity of the model and its ability to capture several features of pile-soil interaction, including： soil plastification at an early stage of loading, ＂pinching＂ behavior due to the formation of a relaxation zone around the upper part of the pile, and stiffness and strength changes due to cyclic loading. A comparison of the p-y curves derived from the test results and the proposed model, as well as those from the classical curves of Reese et al. （1974） for sand, is also presented.