Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A Multiscale Method for Damage Analysis of Quasi-Brittle Heterogeneous Materials

A novel multiscale algorithm based on the higher-order continuum at both micro-and macrostructural level is proposed for the consideration of the quasi-brittle damage response of heterogeneous materials.Herein,the microlevel damage is modelled by the degradation of the homogenized stress and tangent stiffness tensors,which are then upscaled to govern the localization at the macrolevel.The C^1 continuity finite element employing a modified case of Mindlin’s form II strain energy density is derived for the softening analysis.To the authors’knowledge,the finite element discretization based on the strain gradient theory is applied for the modeling of damage evolution at the microstructural level for heterogeneous materials for the first time.The advantage of the novel C1 finite element formulation in comparison with the standard finite element discretization in terms of the regularization efficiency as well as the objectivity has been shown.An isotropic damage law is used for the reduction of the constitutive and nonlocal material behaviour,which is necessary for the physically correct description of the localization formation in quasi-brittle materials.The capabilities of the derived finite element to capture the fully developed localization zones are tested on a random representative volume element(RVE)for several different loading cases.By employing the conventional second-order computational homogenization,the microstructural material constitutive response is averaged over the whole RVE area.In order to model the loss of structural integrity when sharp localization is formed across RVE,the specific conditions which detect a completely formed localization zone are developed.A new failure criterion at the microstructural level has been proposed.The derived finite element formulation,as well as the multiscale damage algorithm,are implemented into the finite element program ABAQUS.The capabilities of the presented multiscale scheme to capture the effects of the deformation localization are demonstrated by few benchmark numerical examples.

Mechanical responses and acoustic emission behaviors of coal under compressive differential cyclic loading(DCL):a numerical study via 3D heterogeneous particle model

The stability of coal walls(pillars)can be seriously undermined by diverse in-situ dynamic disturbances.Based on a 3D par-ticle model,this work strives to numerically replicate the major mechanical responses and acoustic emission(AE)behaviors of coal samples under multi-stage compressive cyclic loading with different loading and unloading rates,which is termed differential cyclic loading(DCL).A Weibull-distribution-based model with heterogeneous bond strengths is constructed by both considering the stress-strain relations and AE parameters.Six previously loaded samples were respectively grouped to indicate two DCL regimes,the damage mechanisms for the two groups are explicitly characterized via the time-stress-dependent variation of bond size multiplier,and it is found the two regimes correlate with distinct damage patterns,which involves the competition between stiffness hardening and softening.The numerical b-value is calculated based on the mag-nitudes of AE energy,the results show that both stress level and bond radius multiplier can impact the numerical b-value.The proposed numerical model succeeds in replicating the stress-strain relations of lab data as well as the elastic-after effect in DCL tests.The effect of damping on energy dissipation and phase shift in numerical model is summarized.

Analysis of structural behavior during collision event accounting for bow and side structure interaction

The main goal of this study was to investigate the effects of selected ship collision parameter values on the characteristics of the absorbed energy in several ship collision scenarios. Non-linear simulations were performed using a finite element method （FEM） to obtain virtual experiment data. In the present research, the size of the side damage from a collision phenomenon were measured and used to verify the numerical configuration together with the calculation results using an empirical equation. Parameters in the external dynamics of a ship collision such as the location of the contact point and velocity of the striking ship were taken into consideration. The internal energy and deformation size on the side structure were discussed further in a comparative study. The effects of the selected parameters on several structural behaviors, namely energy, force, and damage extent were also observed and evaluated in this section. Stiffener on side hull was found to contribute significantly into resistance capability of the target ship against penetration of the striking bow. Remarkable force during penetration was observed to occur when inner shell was crushed as certain velocity was applied in the striking bow.

Fracture development around deep underground excavations: Insights from FDEM modelling

Over the past twenty years, there has been a growing interest in the development of numerical modelsthat can realistically capture the progressive failure of rock masses. In particular, the investigation ofdamage development around underground excavations represents a key issue in several rock engineeringapplications, including tunnelling, mining, drilling, hydroelectric power generation, and the deepgeological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finitediscreteelement method （FDEM） code to simulate the fracturing mechanisms associated with theexcavation of underground openings in brittle rock formations. A brief review of the current state-of-theartmodelling approaches is initially provided, including the description of selecting continuum- anddiscontinuum-based techniques. Then, the influence of a number of factors, including mechanical and insitu stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for threedifferent geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropicrock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy onthe development of an excavation damaged zone （EDZ） around a tunnel excavated in a layered rockformation is considered. Finally, the interaction mechanisms between two large caverns of an undergroundhydroelectric power station are investigated, with particular emphasis on the rock mass responsesensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEMsimulations can provide unique geomechanical insights in cases where an explicit consideration offracture and fragmentation processes is of paramount importance. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in sp Pillar Stability Experiment (APSE)

In this paper, the coupled thermo-mechanical （TM） processes in the AEspoe Pillar Stability Experiment （APSE） carried out by the Swedish Nuclear Fuel and Waste Management Company （SKB） were simulated using both continuum and discontinuum based numerical methods. Two-dimensional （2D） and three- dimensional （3D） finite element method （FEM） and 2D distinct element method （DEM） with particles were used. The main objective for the large scale in situ experiment is to investigate the yielding strength of crystalline rock and the formation of the excavation disturbed/damaged zone （EDZ） during excavation of two boreholes, pressurizing of one of the boreholes and heating. For the DEM simulations, the heat flow algorithm was newly introduced into the original code. The calculated stress, displacement and temperature distributions were compared with the ones obtained from in situ measurements and FEM simulations. A parametric study for initial microcracks was also performed to reproduce the spalling phenomena observed in the APSE.

Damage identification method of girder bridges based on finite element model updating and modal strain energy

A timely and accurate damage identification for bridge structures is essential to prevent sudden failures/collapses and other catastrophic accidents.Based on response surface model(RSM)updating and element modal strain energy(EMSE)damage index,this paper proposes a novel damage identification method for girder bridge structures.The effectiveness of the proposed damage identification method is investigated using experiments on four simply supported steel beams.With Xiabaishi Bridge,a prestressed continuous rigid frame bridge with large span,as the engineering background,the proposed damage identification method is validated by using numerical simulation to generate different bearing damage scenarios.Finally,the efficiency of the method is justified by considering its application to identifying cracking damage for a real continuous beam bridge called Xinyihe Bridge.It is concluded that the EMSE damage index is sensitive to the cracking damage and the bearing damage.The locations and levels of multiple cracking damages and bearing damages can be also identified.The results illuminate a great potential of the proposed method in identifying damages of real bridge structures.

Experimental research and numerical simulation of RC beams strengthened with bonded steel plates

It is a common method to strengthen the damaged RC structures with bonded steel plates. At present the ultimate bearing ca- pacity of RC structures strengthened with bonded steel plates is calculated mostly using the theory based on the test. Four beams, including one reference beam, two strengthened concrete beams in primary force and secondary force respectively, and one strengthened concrete beam which was not anchored enough, were tested under four-point bending (4PB) in order to get the data of strain of longitudinal bars, bonded bottom steel plate in tension and deflection of beams in the middle span. The experimental program was supported by a three-dimensioned finite analysis using ABAQUS. At the end of experiments and finite analysis, it is concluded that the investing strengthening technique can significantly improve the load-carrying capacity and the phenomenon of stress concentration at the end of interface, as well as the damage at interface, can be well simulated with cohesive element provided by ABAQUS.

Multiaxial fatigue life prediction of composite materials

In order to analyze the stress and strain fields in the fibers and the matrix in composite materials,a fiber-scale unit cell model is established and the corresponding periodical boundary conditions are introduced.Assuming matrix cracking as the failure mode of composite materials,an energy-based fatigue damage parameter and a multiaxial fatigue life prediction method are established.This method only needs the material properties of the fibers and the matrix to be known.After the relationship between the fatigue damage parameter and the fatigue life under any arbitrary test condition is established,the multiaxial fatigue life under any other load condition can be predicted.The proposed method has been verified using two different kinds of load forms.One is unidirectional laminates subjected to cyclic off-axis loading,and the other is filament wound composites subjected to cyclic tension-torsion loading.The fatigue lives predicted using the proposed model are in good agreements with the experimental results for both kinds of load forms.

Oxidative capacities of size-segregated haze particles in a residential area of Beijing

The frequent haze days around the Chinese capital of Beijing in recent years have aroused great attention owing to the detrimental effects on visibility and public health. To discover the potential health effects of the haze, oxidative capacities of airborne particles collected in Beijing during haze and clear days were comparably assessed by a plasmid scission assay. Eleven water-soluble trace elements （As, Cd, Cr, Cu, Mn, Ni, Pb, V, Se, T1, and Zn） in the size-segregated airborne particles were quantitatively analyzed by inductively coupled plasma mass spectrometry, and most of the water- soluble trace elements were found to mainly concentrate in the fine particle size of 0.56-1.0 μm. In comparison with clear days, the mass concentrations of 11 analyzed water-soluble trace elements remarkably increased during haze days, and the oxidative capacities determined by the plasmid scission assay were markedly elevated accordingly during the haze days under the same dosage of particles as for those during clear days. Water-soluble trace elements in airborne particles, such as Cu, V, and particularly Zn, were found to have significantly positive correlations with the plasmid DNA damage rates. Because Cu, V, and Zn have been considered as bioavailable elements, the evident increase of these elements during haze days may be greatly harmful to human health.