Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.

Development of multi-functional anchorage support dynamic-static coupling performance test system and its application

In underground engineering with complex conditions,the bolt(cable)anchorage support system is in an environment where static and dynamic stresses coexist,under the action of geological conditions such as high stresses and strong disturbances and construction conditions such as the application of high prestress.It is essential to study the support components performance under dynamic-static coupling conditions.Based on this,a multi-functional anchorage support dynamic-static coupling performance test system(MAC system)is developed,which can achieve 7 types of testing functions,including single component performance,anchored net performance,anchored rock performance and so on.The bolt and cable mechanical tests are conducted by MAC system under different prestress levels.The results showed that compared to the non-prestress condition,the impact resistance performance of prestressed bolts(cables)is significantly reduced.In the prestress range of 50–160 k N,the maximum reduction rate of impact energy resisted by different types of bolts is 53.9%–61.5%compared to non-prestress condition.In the prestress range of 150–300 k N,the impact energy resisted by high-strength cable is reduced by76.8%–84.6%compared to non-prestress condition.The MAC system achieves dynamic-static coupling performance test,which provide an effective means for the design of anchorage support system.

Stress Analysis of New Type Pre-Stressed Anchor Bearing Plate Combining Stamping with Welding Forming and Its Anchorage Zone

An anchor bearing plate transfers the anchoring force from anchor plate to the concrete and the pre-stress is formed in the concrete structure. Currently, the main type of anchor bearing plate is cast iron. It is brittle during transportation and tension process. This paper presents a new type of anchor bearing plate combined stamping with welding forming. The structure of the new type anchor bearing plate is introduced. The stress states of the anchor bearing plate and anchorage zone under work are studied. Various specifications of anchor bearing plate are studied by ANSYS finite element analysis software following the AASHTO specification. The analysis results are compared with the results of the same type of OVM round-shaped anchor plate. The study results show that the new pre-stressed anchor plates combined stamping with welding forming are feasible and more sturdy which can meet the engineering demand.

Effects of anti-pull ties on the bearing behaviors of shallow tunnel-type anchorages in soft rock

Tunnel-type anchorages(TTAs)installed in human gathering areas are characterized by a shallow burial depth,and in many instances,they utilize soft rock as the bearing stratum.However,the stability control measures and the principle of shallow TTAs in soft rock have not been fully studied.Hence,a structure suitable for improving the stability of shallow TTAs in soft rock strata,named the anti-pull tie(APT),was added to the floor of the back face.Physical tests and numerical models were established to study the influence of the APT on the load transfer of TTAs,the mechanical response of the surrounding rock,the stress distribution of the interface,and the failure model.The mechanical characteristics of APTs were also studied.The results show that the ultimate bearing capacity of TTAs with an APT is increased by approximately 11.8%,as compared to the TTAs without an APT.Also,the bearing capacity of TTAs increases approximately linearly with increasing height,width,length,and quantity of APTs,and decreases approximately linearly with increasing distance from the back face and slope angle of the tie slope.The normal squeezing between the tie slope and the surrounding rock increases the shear resistance of the interface and expands the range of the surrounding rock participating in bearing sharing.Both tension and compression zones exist in the APT during loading.The tension zone extends from the tie toe to the tie bottom along the tie slope.The range of the tie body tension zone constantly expands to the deep part of the APT with an increasing load.The peak tensile stress value is located at the tie toe.The distribution of compressive stress in the tie body is the largest at the tie top,followed by the tie slope,and then the tie bottom.

Numerical simulation study on shear resistance of anchorage joints considering tensile-shear fracture criterion of 2G-NPR bolt

2G-NPR bolt (the 2nd generation Negative Poisson’s Ratio bolt) is a new type of bolt with high strength, high toughness and no yield platform. It has signifcant efects on improving the shear strength of jointed rock mass and controlling the stability of surrounding rock. To achieve an accurate simulation of bolted joint shear tests, we have studied a numerical simulation method that takes into account the 2G-NPR bolt's tensile–shear fracture criterion. Firstly, the indoor experimental study on the tensile–shear mechanical properties of 2G-NPR bolt is carried out to explore its mechanical properties under diferent tensile–shear angles, and the fracture criterion of 2G-NPR bolt considering the tensile–shear angle is established. Then, a three-dimensional numerical simulation method considering the tensile–shear mechanical constitutive and fracture criterion of 2G-NPR bolt, the elastoplastic mechanical behavior of surrounding rock and the damage and deterioration of grouting body is proposed. The feasibility and accuracy of the method are verifed by comparing with the indoor shear test results of 2G-NPR bolt anchorage joints. Finally, based on the numerical simulation results, the deformation and stress of the bolt, the distribution of the plastic zone of the rock mass, the stress distribution and the damage of the grouting body are analyzed in detail. The research results can provide a good reference value for the practical engineering application and shear mechanical performance analysis of 2G-NPR bolt.

Optimization of anchorage support parameters for soft rock tunnel based on displacement control theory

In the construction of a soft rock tunnel,it is critical to accurately estimate the pre-stressed anchor support parameters for surrounding rock reinforcement;otherwise,engineering disasters may occur.This paper presents a support parameter selection method that aims to allow deformation as a control objective,which was applied to the tunnel located in Muzailing Highway,Min County,Dingxi City,Gansu Province,China.Through theoretical analysis,we have identified five factors that influence pre-stressing anchorages.The selection of mechanical parameters for the rock mass was carried out using an inverse analysis method.Compared with the measured data,the maximum displacement error of the numerical simulation results was only 0.07 m.The length of anchor cable,circumferential spacing of anchor cable,longitudinal spacing,and pre-stress index are adopted as the input parameters for the support vector machine neural network model based on particle swarm optimization(PSO-LSSVM).Besides,the vault subsidence and the maximum deformation of surrounding rock are considered as output values(performance indices).The goodness of fit between the predicted values and the simulated values exceeds 0.9.Finally,all support parameters within the acceptable deformation range are calculated.The optimal support variables are derived by considering the construction cost and duration.The field application results show that it is feasible to construct the sample database utilizing the numerical simulation approach by taking the displacement as the control target and using the neural network to specify the appropriate support parameters.

Test analysis of stress characteristics on reinforcing rock slope with group anchorage cable

To research the reinforcement effect of a rock slope with group anchorage cables and the stress characteristics of pre-stressed anchorage cables in the fractured surface, the rock slope calculated model of a wedge block within the double-slide face was established by using the finite difference software according to the actual slope project combined with indoor model test. The pre-stress loss rule of the anchorage cable and the distribution of axial force and the force-transferring mechanism of the anchorage cable were analyzed during simulation. Also, based on the displacement contour and the safety factor of the calculated results, the quantitative analysis for the reinforcement ef- fect of the rock slope with group pre-stressed anchorage cable was discovered. The results computed by the software conform with the data in the experiment, which can prove the effectiveness and correctness of parameter selection and model building. Keywords group anchorage reinforcement, rock slope, joint fissure, pre-stressed anchorage cable, stress characteristics

Reliability analysis for anchorage of reinforced concrete beams with longitudinal cracks due to corrosion at anchorage zone

An anchorage reliability analysis approach for simply supported reinforced concrete beams under corrosion attack in the anchorage zone is developed.The first-order second-moment method is employed to analyze the effects of various factors on the anchorage reliability.These factors include both the length and width of cover cracking due to reinforcement corrosion,the cover thickness,the anchorage length,and the stirrup ratio.The results show that the effect of corrosion-induced crack length on the reliability index for anchorage,β0,is negligible when the crack on the concrete surface is just appearing,but with the crack widening,the β0 value is reduced significantly;the considerable changes in β0 result from a variation in cover depth and anchorage length;the effect of changes in the diameter or space of stirrups on the anchorage resistance is very limited,and the variation in β0 is also very low.

Intrusion of Overerupted Maxillary Molars with Miniscrew Implant Anchorage: A Radiographic Evaluation

The aim of this retrospective study was to quantitatively evaluate the treatment effects of in- trusion of overerupted maxillary molars using miniscrew implant anchorage and to investigate the apical root resorption after molar intrusion. The subjects included 30 patients whose average ages were 35.5±9.0 years. All patients had received intrusion treatments for overerupted maxillary molars with miniscrew anchorage. There were 38 maxillary first molars and 26 maxillary second molars to be in- truded. Two miniscrews were inserted in the buccal and palatal alveolar bone mesial to the overerupted molar. Force of 100-150 g was applied by the elastic chains between screw head and attachment on each side. Lateral cephalograms and panoramic radiographs taken before and after intrusion were used to evaluate dental changes and root resorption of molars. Only 6 of the 128 miniscrews failed. The first and second molars were significantly intruded by averages of 3.4 mm and 3.1 mm respectively （P〈0.001）. The average intrusion time was more than 6 months. The crown of the molars mesially tilted by averages of 3.1 degrees and 3.3 degrees （P〈0.001） for first and second molars. The amounts of root resorption were 0.2-0.4 mm on average. The intrusion treatment of overerupted molars with miniscrew anchorages could be used as an efficient and reliable method to recover lost restoration space for pros- thesis. Radiographically speaking, root resorption of molars was not clinically significant after applica- tion of intrusive forces of 200 to 300 g.

Deformation and failure characteristics of anchorage structure of surrounding rock in deep roadway

This paper investigated the stress evolution,displacement field,local deformation and its overall distribution,and failure characteristics of the anchorage structure of surrounding rock with different rockbolt spacing through the model experiments.The influences of the pre-tightening force and spacing of rockbolt on the support strength of the anchorage structure of surrounding rock were analyzed by the simulation using FLAC3D numerical software.The support scheme of the excavated roadway was then designed,and the effectiveness of this support scheme was further verified by the displacement measurement of the roadway.The results showed that the maximum displacement between the roof and floor of the west wing track roadway in Kouzidong coal mine,China is about 42 mm,and the maximum displacement between its both sides is about 72 mm,indicating that the support scheme proposed in this study can ensure the stability and safety of the excavated roadway.

Mechanical properties and reinforcement effect of jointed rock mass with pre-stressed bolt

Pre-stressed bolt anchorage is the key technology for jointed rock masses in rock tunnelling,slope treatment and mining engineering.To investigate the mechanical properties and reinforcement effect of jointed rock masses with pre-stressed bolts,in this study,uniaxial compression tests were conducted on specimens with different anchoring types and flaw inclination angles.ABAQUS software was used to verify and supplement the laboratory tests.The laws of the uniaxial compressive strength(UCS)obtained from the numerical simulations and laboratory tests were consistent.The results showed that under the same flaw angle,both the UCS and elastic modulus of the bolted specimens were improved compared with those of the specimens without bolts and the improvements increased with an increase in the bolt pre-stress.Under the same anchoring type,the UCS and elastic modulus of the jointed specimens increased with an increase in the flaw angle.The pre-stressed bolt could not only restrain the slip of the specimens along the flaw surface but also change the propagation mode of the secondary cracks and limit the initiation of cracks.In addition,the plot contours of the maximum principal strain and the Tresca stress of the numerical models were influenced by the anchoring type,flaw angle,anchoring angle and bolt position.

Finite difference method for dynamic response analysis of anchorage system

Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.

Bearing mechanism of a tunnel-type anchorage in a railway suspension bridge

A tunnel-type anchorage(TTA)is one of the main components in suspension bridges:the bearing mechanism is a key problem.Investigating the deformation characteristics,development law,and failure phenomenon of a TTA under load can provide the theoretical basis for a robust design.Utilizing the TTA of the Jinsha River suspension bridge at Lijiang Shangri-La railway as a prototype,a laboratory model test of the TTA was carried out for three different contact conditions between the anchorage body and the surrounding rock.The stress and deformation distribution law of the anchorage body and its surrounding rock were studied,and the ultimate bearing capacity and failure mode of the TTA were analyzed.The test results show that the compressive stress level is highest at the rear part of the anchorage body.Moving away from the rear portion of the body,the stress decays in a negative exponential function.Based on the load transfer curve,the calculation formula for the shear stress on the contact surface between the anchorage body and the surrounding rock was derived,which shows that the distribution of the shear stress along the axial direction of the anchorage body is not uniform.The distance from the maximum value to the loading surface is approximately 1/3 of the length of the anchorage body,and the stress decreases as the distance from the loading surface increases.Furthermore,the contact condition between the anchorage body and surrounding rock has a great influence on the bearing capacity of the TTA.The increase in the anti-skid tooth ridge and radial anchor bolt can improve the cooperative working capacity of the anchorage body and the surrounding rock,which is approximately 50%higher than that of the flat contact condition.The main function of the anchor bolt is to increase the overall rigidity of the TTA.The contact condition between the anchorage body and the surrounding rock will lead to a change in the failure mode of the TTA.With an increase in the degree of contact,the failure mode will change from shear sliding along the interface to trumpet-shaped inverted cone-shaped failure extending into the surrounding rock.

RC beam strengthened with pre-stressed CFP under the secondary load

Feasibility of using pre-stressed carbon fiber plates to strengthen reinforced concrete beams was studied. Based on the characteristics of carbon fiber plates, we developed a pre-stress clamp and a device for applying the pre-stress. Contrast tests were conducted between ordinary carbon fiber plates and a pre-stressed carbon fiber plate and between secondary loaded carbon fiber plates and a concrete beam strengthened with a secondary loaded carbon fiber plate. On this basis, we analyzed the failure pattern, the width of cracks and their distribution, the cracking load, the yield load, the limit load and the relation between load and deflec- tion. The results indicate that using pre-stressed carbon fiber plates to strengthen concrete beams is feasible and effective.

Strength weakening effect of high static pre-stressed granite subjected to low-frequency dynamic disturbance under uniaxial compression

This study aimed to elucidate the strength weakening effect of high static pre-stressed rocks subjected to low-frequency disturbances under uniaxial compression.Based on the uniaxial compressive strength(UCS)of granite under static loading,70%,80%,and 90%of UCS were selected as the initial high static pre-stress(σ_(p)),and then the pre-stressed rock specimens were disturbed by sinusoidal stress with amplitudes of 30%,20%,and 10%of UCS under low-frequency frequencies(f)of 1,2,5,and 10 Hz,respectively.The results show that the rockburst failure of pre-stressed granite is caused by low-frequency disturbance,and the failure strength is much lower than UCS.When theσp or f is constant,the specimen strength gradually decreases as the f or σ_(p) increases.The experimental study illustrates the influence mechanism of the strength weakening effect of high static pre-stress rocks under low-frequency dynamic disturbance,that is,high static pre-stress is the premise and leading factor of rock strength weakening,while low-frequency dynamic disturbance induces rock failure and affects the strength weakening degree.

Flexural Property of String Beam of Pre-Stressed Glulam Based on Influence of Regulation and Control

Applying pre-stress in glulam beam can reduce its deformation and make full use of the compressive strength of wood.However,when the glulam with low strength and the pre-stressed steel with high strength form combined members,materials of high strength can’t be fully utilized.Therefore,this study puts forward the idea of regulating and controlling string beam of pre-stressed glulam.By regulating and controlling the pre-stress,a part of the load borne by the wood is allocated to the pre-stressed tendon,which is equivalent to completing a redistribution of internal force,thus realizing the repeated utilization of the wood strength and the full utilization of the strength of the high-strength pre-stressed tendon.The bending experiments of 10 beams under 5 working conditions are carried out.The failure mode,bearing capacity and deformation of the beams are analyzed.The results show that 90%of beams are deformed under compression.The ultimate load of the regulated and controlled beam is obviously larger than that of the unregulated beam,and the ultimate load of the beam increases with the increase of the degree of regulation and control.Compared with that of the unregulated beams,the ultimate load of beams regulated by 7.5%-30%increases by 25.42%-65.08%,and the regulated and controlled effect is obvious.With the increase of the regulation and control amplitude of pre-stress,the stiffness of string beam of pre-stressed glulam increases.In addition,with the increase of the regulation and control amplitude,the compression height of the beam increases before the failure,and it reaches the state of full-section compression at the time of failure,giving full play to the compressive property of the glulam.At the end of the experiment,the constitutive relation which can reflect the anisotropy of the wood is established combined with the experimental data.The finite element analysis of the beam under 7 working conditions is carried out by using ABAQUS finite element program,and the influence of the regulation and control amplitude on the stress distribution and ultimate bearing capacity of the beam is discussed.

Influence of anchorage length and pretension on the working resistance of rock bolt based on its tensile characteristics

In coal mining roadway support design,the working resistance of the rock bolt is the key factor affecting its maximum support load.Effective improvement of the working resistance is of great significance to roadway support.Based on the rock bolt’s tensile characteristics and the mining roadway surrounding rock deformation,a mechanical model for calculating the working resistance of the rock bolt was established and solved.Taking the mining roadway of the 17102(3)working face at the Panji No.3 Coal Mine of China as a research site,with a quadrilateral section roadway,the influence of pretension and anchorage length on the working resistance of high-strength and ordinary rock bolts in the middle and corner of the roadway is studied.The results show that when the bolt is in the elastic stage,increasing the pretension and anchorage length can effectively improve the working resistance.When the bolt is in the yield and strain-strengthening stages,increasing the pretension and anchorage length cannot effectively improve the working resistance.The influence of pretension and anchorage length on the ordinary and high-strength bolts is similar.The ordinary bolt’s working resistance is approximately 25 kN less than that of the high-strength bolt.When pretension and anchorage length are considered separately,the best pretensions of the high-strength bolt in the middle of the roadway side and the roadway corner are 41.55 and 104.26 kN,respectively,and the best anchorage lengths are 1.54 and 2.12 m,respectively.The best anchorage length of the ordinary bolt is the same as that of the high-strength bolt,and the best pretension for the ordinary bolt in the middle of the roadway side and at the roadway corner is 33.51 and 85.12 kN,respectively.The research results can provide a theoretical basis for supporting the design of quadrilateral mining roadways.

Numerical experimental study on optimum design of anchorage system for Xiashu loess slope

In FLAC ^(3D),cable element or modified pile element can be used to build slope anchoring model.However,the difference between the two structural elements and their influence on the calculation results have not been studied in depth.In order to solve this problem,the Xiashu loess slope anchoring models based on cable element and modified pile element were constructed respectively.A variety of anchoring schemes were designed by orthogonal experiment method,and then they were brought into the model for calculation and the calculation results were analyzed by range analysis and variance analysis.The results show that the modified pile element can bear the bending moment and reflect the strain softening property of the grout.From the perspective of slope safety factor,the anchorage length and anchor bolt spacing are the main factors affecting the stability of the slope,and the anchorage angle is the secondary factor.The grout in cable element is assumed to be an elastic-perfectly plastic material,so the safety factor of the slope can be significantly increased by increasing the length of the anchor bolts.This will bring potential risks to the slope treatment project.Therefore,in the calculation of the slope anchoring model,the modified pile element is more suitable for simulating the anchor bolt.

Evaluation of Long-term Stability of Vertical Control in Hyperdivergent Patients Treated with Temporary Anchorage Devices

This study aims to evaluate,the long-term stability of vertical control in hyperdivergent patients treated with temporary anchorage devices.The sample included 20 hyperdivergent patients without anterior open bite.The temporary anchorage devices were used to intrude the upper incisor and molars for vertical control.Lateral cephalograms were established prior to treatment,immediately after treatment,and during retention. The upper molars and incisors were intruded by 1.33 mm and 1.41 mm after treatment (P<0.05).U6-PP increased by 0.11 mm and 0.23 mm during the first and second stages of retention (P>0.05).U1-PP was found to possess a significant extrusion of 1.2 mm during the first stage (P<0.05),which increased by 0.68 mm during the second stage (P>0.05). The mandibular plane angle (MP-SN)decreased by 2.58 degrees following treatment, and underwent a relapse of 0.51 degree and 0.42 degree during the first and second stages of retention respectively (P>0.05).No significant soft tissue changes occurred,with the exception of increased upper lip length during the second stage (P<0.05).Maxillary anterior and posterior intrusions,counter clockwise rotation,of the mandibular plane,and improved profiles can be successfully achieved following treatment with vertical control. During the first stage of retention (less than three years),intruded molars and incisors both exhibited some extrusion,and molars had better long-term stability than incisors. During the second stage of retention (three to six years),the therapeutic effects appeared stable,with the exception of some increase in upper lip length.Rotated mandibular plane remained stable during the entire retention period.

Mechanical properties and failure characteristics of fractured sandstone with grouting and anchorage

Based on uniaxial compression experimental results on fractured sandstone with grouting and anchorage, we studied the strength and deformation properties, the failure model, crack formation and evolution laws of fractured sandstone under different conditions of anchorage. The experimental results show that the strength and elastic modulus of fractured sandstone with different fracture angles are significantly lower than those of intact sandstone. Compared with the fractured samples without anchorage,the peak strength, residual strength, peak and ultimate axial strain of fractured sandstone under different anchorage increase by 64.5–320.0%, 62.8–493.0%, and 31.6–181.4%, respectively. The number of bolts and degree of pre-stress has certain effects on the peak strength and failure model of fractured sandstone. The peak strength of fractured sandstone under different anchorage increases to some extent, and the failure model of fractured sandstone also transforms from tensile failure to tensile–shear mixed failure with the number of bolts. The pre-stress can restrain the formation and evolution process of tensile cracks, delay the failure process of fractured sandstone under anchorage and impel the transformation of failure model from brittle failure to plastic failure.