Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

Finite element analysis of overlay incorporating stress absorbing membrane interlayers against reflective cracking

A wheel tracking test was modelled to gain better understanding of the deflection and stress-strain distribution in an overlaid cracked pavements with and without membrane interlayer （SAMI）. For this purpose, commercial finite element software Abaqus 6.7-1 was used. Two different models were considered, one incorporating stress absorbing membrane interlayers （SAMIs） and the other without SAMI. In the study, full bond condition was assumed for the boundaries between the layers, and a linear elastic model was used for the analysis. The results show that introduction of SAMI caused greater deflection of the pavement. It is found that although with SAMIs, low stiffness is required, a very low stiffness may yield undesirable results. The results show that the introduction of SAMIs results in high strain concentration around the crack region, whilst the strain in the overlay is smaller than the values predicted in the models without SAMIs.

Effect of Strain Rate on Compression Behavior of Vinyl Ester Resin Casting

Quasi-static and high strain rate compressive experiments on vinyl ester casting were carried out by means of MTS (Material Test System) and Hopkinson bar. The behaviors of the compressed unstable and fracture of the resin casting at different strain rates were investigated.The results indicate that the response behavior of the resin casting is controlled by different mechanisms at different strain rate, and some mechanical properties of vinyl ester casting are rate-dependent: the casting are destroyed in toughness model under strain rate 3.3×10 -4～6.6×10 -3/s, while the casting are destroyed in brittleness model under strain rate 950～5800/s. The yield stress, yield strain energy density are all increased with the increasing strain rates at quasi-static as well as at high strain rates. What is interesting is that the yield strain decreased with the strain rates increasing at quasi-static while increased at high strain rates. It is considered that the casting occurred forcing high elastic deformation at high strain rates. The damage of the specimens is mainly controlled by axial stress before unstable deformation, while mainly controlled by shear stress after unstable deformation, and then developed to fracture finally. This progress is rate-dependent: the development of the cracks inside the castings increased with the strain rate increasing.

AN APPROACH TO THE ELASTIC-PLASTIC ANALYSIS OF THE PLANE STRAIN MODE-I CRACK

This paper presents an approach to the solution of the approximate elastic-plastic analysis for the plane strain mode-1 crack.

Investigation of cracking mechanism of the first tunnel lining during double-arch tunnel construction

To solve the engineering problem of the first tunnel lining cracking caused by the second tunnel construction of double-arch highway tunnels,a research method combining distributed optical-fibre monitoring,inversion analysis and numerical simulation that can reflect lining cracking was presented.Optical fibres were laid on opposite sides of the steel arches inside the first tunnel lining.Embedded optical-fibre monitoring was conducted continuously during the second tunnel driving.Based on the fibre-optic strain profile,the lining cracking was deduced and warned in time.The mechanical behaviour of the steel arch was investigated by the inversion analysis,which took into consideration the integrated impact of axial force and flexural moment.A two-dimensional(2D)load-structure method–based numerical model was established,considering the influence of different load distributions in each construction condition.The total strain rotating crack constitutive model was applied to reflect the cracking behaviour of concrete lining in the simulation,and the model was calibrated and verified in the laboratory.Comparative analysis between the simulated strain distribution and the distributed optical-fibre monitoring results was carried out.The deformation mode and crack distribution of the lining were analysed.The cracking mechanism was explained.Specifically,the second tunnel construction led to the loading at the top of the middle partition wall and the release of rock pressure in the first tunnel.Under these load changes,the secondary lining of the first tunnel cracked on the inner side of the top of the middle partition wall owing to tension,and compression-bending failure occurred near the right arch foot.Finally,the influence of the parameters on the lining force was analysed,and a construction optimisation scheme was proposed.

Crack evolution behavior of rocks under confining pressures and its propagation model before peak stress

The understanding of crack propagation characteristics and law of rocks during the loading process is of great significance for the exploitation and support of rock engineering.In this study,the crack propagation behavior of rocks in triaxial compression tests was investigated in detail.The main conclusions were as follows:1)According to the evolution characteristics of crack axial strain,the differential stress?strain curve of rocks under triaxial compressive condition can be divided into three phases which are linear elastic phase,crack propagation phase,post peak phase,respectively;2)The proposed models are applied to comparison with the test data of rocks under triaxial compressive condition and different temperatures.The theoretical data calculated by the models are in good agreement with the laboratory data,indicating that the proposed model can be applied to describing the crack propagation behavior and the nonlinear properties of rocks under triaxial compressive condition;3)The inelastic compliance and crack initiation strain in the proposed model have a decrease trend with the increase of confining pressure and temperature.Peak crack axial strain increases nonlinearly with the inelastic compliance and the increase rate increases gradually.Crack initiation strain has a linear relation with peak crack axial strain.

Anisotropy of crack initiation strength and damage strength of coal reservoirs

The crack volume strain method and acoustic emission(AE)method are used to analyze the anisotropy of the crack initiation strength,damage strength,the failure mode and the AE characteristics of coal reservoir.The results show that coal reservoirs show obvious anisotropic characteristics in compressive strength,cracking initiation strength and damage strength.The compressive strength of coal reservoirs decreases with the increase of bedding angle,but the reservoirs with bedding angles of 450 and 900 differ little in compressive strength.The crack initiation strength and damage strength decrease first and then increase with the increase of bedding angle.The crack initiation strength and damage strength are the highest,at the bedding angle of 0°,moderate at the bedding angle of 90°,and lowest at the bedding angle of 45°.When the bedding angle is 0°,the failure of the coal reservoirs is mainly steady propagation of large-scale fractures.When the bedding angle is 45°,one type of failure is caused by steady propagation of small-scale fractures,and the other type of failure is due to a sudden instability of large-scale fractures.When the bedding angle is 90°,the failure is mainly demonstrated by a sudden-instability of small-scale fractures.Compared with the cumulative count method of the AE,the cumulative energy method is more suitable for determining crack initiation strength and damage strength of coal reservoirs.

An improved elastoplastic model for rocks and application to cyclic loading and unloading triaxial compression tests

The recoverable strain of rock is completely classified as elastic strain in the conventional elastic-plastic theory,which often results in poor agreement between theoretical and experimental curves.This work proposes an improved elastoplastic model of rock materials considering the evolutions of crack deformation and elastic modulus to better characterize the nonlinear mechanical behavior of rock in the post-peak stage.In this model,the recoverable strain is assumed to be a combination of elastic and crack strain,and the constitutive relationship between crack strain and rock stress is deduced.Based on the proposed assumption,the evolutions of the mechanical parameters including strength parameters,elastic,plastic,and crack deformation parameters versus the plastic strain and confining stress were investigated.The developed elastoplastic model was validated by comparing the theoretical values with the results of the triaxial cyclic loading and unloading test.The theoretical calculation results show a good agreement with the laboratory test,which indicates that the improved elastoplastic model can effectively reflect the nonlinear mechanical behavior of the rock materials.The research results are expected to provide a valuable reference for further understanding the evolution of rock crack deformation.

SCC investigation of low alloy ultra-high strength steel 30CrMnSiNi2A in 3.5wt% NaCl solution by slow strain rate technique

To evaluate stress corrosion cracking（SCC） mechanism of low alloy ultra-high strength steel 30CrMnSiNi2 A in environment containing NaCl, SCC behavior of the steel in 3.5wt% NaCl solution is investigated by slow strain rate technique（SSRT） with various strain rates and applied potentials, surface analysis technique, and electrochemical measurements. SCC susceptibility of the steel increases rapidly with strain rate decreasing from 1 · 10 5s 1to 5 · 10 7s 1, and becomes stable when strain rate is lower than 5 · 10 7s 1. SCC propagation of the steel in the solution at open circuit potential（OCP） needs sufficient hydrogen which is supplied at a certain strain rate.Fracture surface at OCP has similar characteristics with that at cathodic polarization 1000 mVSCE, which presents characteristic fractography of hydrogen induced cracking（HIC）.All of these indicate that SCC behavior of the steel in the solution at OCP is mainly controlled by HIC rather than anodic dissolution（AD）.

Calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure

In order to calculate the stress intensity factor(SIF) of crack tips in two-dimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the SIF is proposed. In this paper, the procedure is presented to calculate the SIF of crack tips in mode I cracks, mode II cracks and I+II mixed mode cracks. Meanwhile, the results are compared to those calculated by traditional approaches or other approaches based on strain energy density and verified by theoretical solutions. Furthermore, the effect of mesh density near the crack tip is discussed, and the proper location where the strain energy density factor is calculated is also studied. The results show that the SIF calculated by this procedure is close to not only those calculated by other approaches but also the theoretical solutions, thus it is capable of achieving accurate results.Besides, the mesh density around the crack tip should meet such requirements that, in the circular area created, the first layer of singular elements should have a radius about 0.05 mm and each element has a circumferential directional meshing angle to be15°–20°. Furthermore, for a single element around the crack tip, the strain energy density factor is suggested to be calculated in the location where half of the sector element's radius from the crack tip.

Effect of three dimensional stress state on unstable fracture condition and crack opening level in a new crack growth model

A new model for the analysis of fatigue crack growth in the metal structures was proposed. This model shows a promising capability of explaining various fatigue phenomena. The new crack growth model is further completed by a continuous empirical formula for estimating the value of variable fracture toughness during crack propagation and a modified continuous equation for the crack tip stress/strain constraint factor used to calculate the stress intensity factor at the opening level. The prediction results are proved to agree well with the observed phenomena in test.