Failure Depth Research Articles

Analytical stress analysis method of interbedded coal and rock floor over confined water: a study on mining failure depth

Deep mining commonly causes redistribution of the stress-strain field for coal seam floor strata. The study of this distribution law was of great significance to analyzing the characteristics of floor deformation and failure and predicting the risk of floor water inrush. In this paper, the damage of a coal seam floor with strong water pressure in the Junggar Basin in western China was examined, and the stress analytical formula for every point of floor confined aquifer was constructed using a stress model in the direction of coal seam strike. Combined with Mohr-Coulomb failure criterion, the maximum depth of floor failure was 17.5 m. According to geological and stratigraphic data of the stope floor, a 3D numerical model of fluid-structure coupling was built. Simulation results showed that under a 1.5 MPa water pressure, the maximum floor failure depth was 18 m. The internal stress of the coal-rock interface and soft rock increases significantly, and the weak coal seam intensifies the transfer of stress and strain at depth to some extent. Water pressure had a certain influence on floor deformation and failure. The joint simulation results of stress-seepage-fracture were closer to the real stope measurements. In the boreholes, two types of sensors, distributed fiber and electrodes were arranged. When the coal floor broke, the compressive strain increased with a peak of 4152 με. Meanwhile, the apparent resistivity of the rock seam reached 500–700 Ω•m. The comprehensive analysis showed that: the floor failure depth in the monitoring area of the 61,303 working face was −18 m, and the floor failure disturbance depth was −35 m. The results presented in this contribution can provide reference for future examinations of coal and rock interbedded floor failure over deep confined water.

Research on calculation of contact fatigue life of rough tooth surface considering residual stress

Grinding and shot peening produce large residual stresses on the gear teeth. Research on the calculation of contact stress and fatigue life of rough gear teeth considering the residual stress has not been published in the literature. The influence of residual stress and rough surface on contact fatigue is difficult to be ignored, so the research of the paper is of significance. Based on the finite element modeling method of rough surface contact and multiaxial fatigue criterion, the gear contact stress and fatigue life under the action of rough surface and residual stress is obtained. The study found that residual compressive stress can reduce the high stress area of the near-surface and lead to a low-stress area between the near-surface and the sub-surface. In addition, residual compressive stress can reduce the near-surface fatigue failure depth (NFFD) and make the sub-surface fatigue failure area tend to be deeper while increasing the contact stiffness of the tooth surface. The logarithmic value log10(2Nf) of the sub-surface fatigue life is quantitatively related to the roughness Sq and the residual stress amplitude σrs, and the fitting polynomial of the three variables is obtained, which provides a theoretical reference for the prediction and calculation of the contact fatigue life of the tooth sub-surface.

Comprehensive Monitoring Research on the Effect of Roof Cutting and Pressure Release: A Case Study of the Jiulishan Coal Mine in China

The longwall panel of the Jiulishan coal mine is affected by floor-confined water, while the roof rock weighting makes the production management of some longwall panels difficult. This has caused engineering methods of roof cutting and pressure release to be considered. To explore the dynamic effects of roof cutting and pressure release method, the 14141 longwall panel was taken as the test point, and a variety of monitoring methods were used to comprehensively analyze the characteristics of roof rock weighting, front abutment pressure, and floor mining failure. The main results are as follows: first, the weighting interval, the weighting intensity distribution, and the gateway deformation are asymmetrical. Second, the peak point of the front abutment pressure is approximately 6 m away from the coal wall, the peak stress is 7.02 MPa, the concentration coefficient is 1.54, the range of the pressure increasing area is approximately 16.4 m, and the farthest end of the front abutment pressure effect area is 22.4 m away from the coal wall. Furthermore, the maximum depth of the floor failure is at the No.17 measuring point (A117) position under the condition of one electrode distance. The maximum damage depth is 9.8 m, and the horizontal distance between the location of the maximum failure depth and the working face is 4.1~10.3 m. Finally, compared with the formula calculation value without considering the effect of roof cutting and pressure release or the adjacent 14121 longwall panel, the weighting interval and the weighting intensity, the gateway deformation, the degree of coal wall spalling, the influence range of the front abutment pressure, and the degree of floor mining failure are significantly reduced. The research results provide scientific and technological support for roof cutting and pressure release as a technical method to prevent floor water inrush and reduce the roof rock weighting intensity on the longwall panel.

Failure behavior and dynamic monitoring of floor crack structures under high confined water pressure in deep coal mining: A case study of Hebei, China

The coal mining process may make cracks in the floor to connect the confined aquifers, causing water inrush from the coal seam floor. Through the inclusion theory and compression failure criterion, the failure model of floor crack structures in deep mining is built by adding the additional water pressure. Under the compressive stresses, the additional water pressure in the cracks increases linearly as the mining-induced stress and the mining depth increase. As the confined water pressure rises, the failure strength of the floor crack structures decreases linearly, while the growth length increases nonlinearly. Yet, the failure strength first decreases and then increases as the angle of crack structures increases, and the dominant failure angles of crack structures in the floor range from 30 to 70°. Thus, the various dynamic monitoring technologies of crack structures, such as water-rich area detection, hydrological and micro-seismic monitoring, and failure depth exploration in the floor, are improved on the mining site. And these technologies are combined to establish a reliable early warning system for floor water inrush, and provide a safe guarantee for deep mining under high confined water pressure.

Roof Bolting Anchoring Performance Research on the Entry under the Gob of Close-Distance Coal Seam

Seam spacing plays a crucial role in selecting roof bolting of the close-distance coal seam. This work utilized three methods to determine the minimum roof bolting seam spacing of the lower coal seam (LCS) entry after the upper coal seam (UCS) mining. Based on the entry of the No.3-2 coal seam (LCS) in Chaili Coal Mine in China, theoretical analysis, pull-out bolt test, and numerical simulation were performed to calculate the maximum floor failure depth of the UCS and to determine the minimum seam spacing of the roof bolting. The maximum floor failure depth of the UCS determined through theoretical analysis and numerical simulation is 3.2 m and 3.3 m, respectively. In general, the anchorage length of rock bolting is less than 2.4 m, so the minimum seam spacing is 5.6 m or 5.7 m. To further determine the anchorage performance of the roof, the pull-out test was employed on the entry roof of the LCS. When the seam spacing is no less than 6 m, the test results show that the pull-out force of the bolt is more significant than 30kN; in addition, the numerical simulation results indicate that the roof-to-floor and rib-to-rib convergence are relatively small. Therefore, the LCS entry’s minimum roof bolting seam spacing can be determined as 6 m. This study could be used to select and design roof bolting under similar close-distance coal seam conditions.

Effect of Partial Saturation on Ultimate Bearing Capacity of Skirted Foundations

Skirted foundations are one of the solutions proposed to increase the bearing capacity of the soil. They assist in increasing the load and depth of failure in weak ground or soils with low shear resistance and reducing the foundation settlement if a soil improvement method cannot be applied or the cost of implementing deep foundations increases. This study examined and investigated the extent of soil bearing of skirted foundations on sandy soils and studied the effect of soil saturation cases and three cases of water content reduction to measure the matric suction value of unsaturated soil. A physical model was created to simulate the strip foundation and compare these cases (dry-fully saturated-partially saturated). It was found that the soil load carrying capacity in the case of unsaturated soil is the highest, where matric suction is at a depth of 450 mm, followed by the dry case and then the saturated case as it represents the weakest state of the soil.

Research on roof damage mechanism and control technology of gob-side entry retaining under close distance gob

With the increase in energy demand and in mining intensity, the phenomenon of multiple coal seam mining has appeared in major coal mining countries. While the downward mining method is generally adopted and under the damage of the upper coal seam, the structure and stress environment of the coal roof are very different from those of a single coal seam in remining. The rock layer between the two coal seams is affected by repeated mining and is prone to rotation instability, which makes it more difficult to reserve gob-side entries along the gob in the lower coal seams. This article mainly targets the case of the gob in the Panel #11426 of Xieqiao Mine, and studies the failure mechanism and control technology of the gob-side entry retaining in short-distance coal seam. First, the floor stress distribution law after mining in the upper coal seam is calculated according to the elastic theory, and verified by FLAC3D numerical simulation; secondly, the floor failure depth after the upper coal seam is calculated according to the elastic–plastic theory. Based on the “block-dispersions” structure, the failure process of the roof of the roadway under close gob is analyzed. Further, it is proposed during the roadway excavation, to adopt support methods such as erecting U-steel retractable supports and back-wall filling; during the mining and before the gob-side entry retaining, the installation of roof bolts (cables), the reinforcement of the roof of the area to be filled and the in-wall filling techniques etc. to control the surrounding rock of gob-side entry. The engineering test was carried out along the track at the Panel #11426 of Xieqiao Mine. The onsite monitoring showed that: the maximum subsidence of the reserved gob-side entry roof along the gob was 180 mm, and the maximum approaching distance of the two banks was 328 mm, which met the engineering requirements. The research results can provide guidance for the design gob-side entry retaining along gobs under similar mining geological conditions.

Floor Disturbance and Failure Characteristics of Super-Large Mining Height Working Face

The failure depth of the working face floor caused by mining is a key parameter to predict water inrush from the working face floor. Extensive research has been conducted on the floor failure zone of the working face. However, in recent years, there have been few studies on the floor failure law of the working face with a super-large mining height (over 20 m) in the western mining area of China. In this paper, the working face with a super-large mining height of 24 m in Longwanggou Coal Mine was studied. Electrical monitoring and numerical simulation of the working face floor were carried out. The measured floor failure depth of the working face is 15 m while the average numerical simulation result is 11 m. When compared with the calculation results of the statistical analysis formulas, the floor failure depth of the working face with a super large mining height obtained from field measurement and numerical simulation is smaller. The reason for the smaller failure zone of the floor of the super large mining height working face is that the falling roof inhibits the pressure relief of the floor, the large mining height reduces the advance pressure, and the shear stress of the floor decreases. The research methods and findings are of great significance to the prediction of floor failure and water inrush in working face with a super-large mining height, the prevention and control of water disasters in coal seam roof and the monitoring of mine pressure.

Application and Research of Gangue Partial-Filling Mining Method in Preventing Water Inrush from Floor

Coal gangue produced during coal production not only poses a serious threat to the ground environment but also imposes serious economic burdens on the mine. The partial-filling mining (PFM) method proposed in this paper can make full use of coal gangue and is of great significance to the prevention and control of water disasters at the working face. The specific process used to implement this method is to first divide the working face into several narrow working faces and then fill the filling body into part of the goaf. The ability of PFM to restrain floor water inrush is analyzed by physical simulation, and the field application research is carried out at the No. 9211 mining face of Bucun Coal Mine in Shandong, China. The physical simulation results show that the failure depth of this layer is less than 5 m. The field measurements reveal that the maximum compression deformation of the filling body is 89.1 mm, and the maximum floor failure depth of the floor is only 8.6 m. Comparative analysis indicates that the floor failure depth of the No. 9211 working face with the local filling method is 4.6 m lower than that of the No. 9110 working face with the strip mining method. In addition, no water inrush accident occurs at the No. 9211 working face during mining. Therefore, PFM not only controls the floor damage depth effectively but also consumes coal gangue to protect the mine environment.

Dynamic Monitoring and Research on the Evolution of the Damage of Weakly Consolidated Coal Floor under Dynamic Pressure Using Distributed Optical Fiber

During the extraction of coal seam, the evolution pattern of the rock is an important element for controlling the rock seam and preventing water damage to mine. In order to obtain the deformation and damage of weakly cemented coal seam footings under dynamic pressure, the stability of the footings was studied using a combination of various methods, including rock mechanics testing, field testing, and numerical simulations. By sticking distributed optical fiber on the surface of rock samples, the degree and location of rupture on the surface of rock samples could be obtained using the strain response correlation for optical fiber. Two monitoring holes were arranged in the bottom plate of coal seam at 12307 working face of a mine in Ordos Basin, China. Moreover, a distributed optical fiber sensor was implanted in the hole. The results show that the failure depth was 16.5 m. On the other hand, the numerical simulation results show that the failure depth of the bottom plate was 16.0 m, which agreed well with the measured value. The distribution characteristics of the maximum principal stress of the bottom slab during the advancement of working face were obtained using three-dimensional (3D) numerical model. Based on the distributed optical fiber strain tests in the two boreholes in the same vertical profile and combined with the natural proximal interpolation method, the interhole strain increment distribution profile was obtained. The research results provide a reference for the safe mining of coal resources and the prevention and control of water damage in the mine floor.

Floor Failure Characteristics in Deep Island Longwall Panel: Theoretical Analysis and Field Verification

Floor failure in deep coal mining above confined aquifers with high-water pressure may induce floor water inrush disasters. Considering the effects of mining stress and nonuniformly distributed water pressure, a mechanical calculation model of the island longwall panel in up-dip mining was established, and the stress distribution and floor failure characteristics were analyzed. The failure characteristics of the floor at NO. 2129 panel in Xingdong coal mine were detected by the borehole televiewer and microseismic monitoring system to validate the theoretical model. The results indicated that the floor failure characteristics along the strike and inclination of the island longwall panel in up-dip mining were “asymmetric inverted saddle-shaped” and “spoon-shaped,” respectively. The maximum floor failure depths before and after roof hydraulic fracturing (RHF) were 45.7 m and 29.1 m, respectively. The theoretical calculation results of the maximum depths of floor failure were 45.1 m and 29.9 m, respectively. The theoretical failure characteristics were consistent with those measured on site. The stress concentration magnitude and floor failure depth on the side of the isolated coal pillar were greater than those of other areas, and the water-inrush-prone zones were concentrated on the side of the isolated coal pillar near the intersection of the working face and the roadway. The research results could provide a certain reference for floor failure and water inrush mechanisms under complex geological conditions in deep mining.

Evaluation of the Depth and Width of Progressive Failure of Breakout Based on Different Failure Criteria, Using a Finite Element Numerical Model

Evaluation of the Depth and Width of Progressive Failure of Breakout Based on Different Failure Criteria, Using a Finite Element Numerical Model

Statistical Damage Model of Rock Structural Plane Considering Void Compaction and Failure Modes

The shear behavior of rock structural planes contains various symmetry laws, and the shear failure can be considered as an asymmetric state of the rock and rock mass. The study of shear deformation and the failure of rock structural planes plays a vital role in ensuring the safety and stability of engineered rock masses. In view of the inability of traditional shear constitutive models to describe the non-linear characteristics of the dilatancy stage and the single applicable failure form, firstly, we discuss, in depth, the law and mechanism of shear deformation and failure of structural planes, and introduce the compaction index α to measure the non-linear characteristics of shear stress–shear displacement caused by compaction of microcracks and internal pores of structural planes, and the structural plane damage model, considering the void compaction and failure mode, was established. Then, the statistical damage theory was introduced, and the strength and failure of the microunits of the rock structural plane were assumed to obey the Weibull distribution. Based on the Mohr-Coulomb strength criterion to measure the strength of the microunits of the rock structure surface, a statistical damage model of structural planes, which can describe void compaction and failure modes, was established. Finally, a comparative analysis was carried out with the test curve, and the results showed that: the calculation curve of the structural plane statistical damage model established, considering the void compaction and failure modes, has the same trend as the structural plane shear test curve, which can better describe the shear stress– shear displacement at the dilatancy stage, as well as the shearing stage and sliding stage in different failure modes. The changing law of shear displacement reflects the rationality and accuracy of the constructed constitutive model. The research results can provide a theoretical basis for the shear deformation and failure of rock structural planes.

Characteristics of Stress Field and Damage Law of Coal Rock in Residual Pillar of Top Slice and Its Application

This article presents a theoretical analysis and numerical simulation studies to determine the suitable position for the lower slice roadway in a residual pillar area after top slicing a thick coal seam. We considered the load concentration on the coal pillar, the goaf floor, and the stress distribution characteristics of the coal pillar area before and after the top slice. With a mechanical model built of the residual pillar load propagation in the floor and the failure model of the floor surrounding rock, the analytical formula we deduced for the coal pillar floor stress and the expression of the floor failure depth of the roadway provides a basis for the reasonable determination of the position of the lower slicing roadway. Studies proved that after mining the top slice working face, the floor stress field of the residual pillar area presented characteristics of the non-uniform distribution. The stress concentration occurred below the coal pillar. The stress variation area appeared at the edge of the coal pillar, with a stable stress area appearing far away from the coal pillar area. Therefore, the roadway layout should avoid the areas below the coal pillar and the coal pillar edge with high stress levels and a large stress variation gradient. High stress concentration formed on the coal pillar transferred to the lower layered coal and floor strata, and decreased the stress concentrations layer by layer. However, mining of the top-layered working face affected the coal, and rock mass damaged the coal pillar floor area and weakened the mechanical properties, which was not conducive to the control of the roadway surrounding rock. The research results applied to No. 30117 working face of the lower slice of the Shancheng Coal Industry, and the proper position of the return airway of the working face was determined to be 8 m outside the east side of the residual pillar in the top slice, achieving a good surrounding rock control effect.

Roof Hydraulic Fracturing for Preventing Floor Water Inrush under Multi Aquifers and Mining Disturbance: A Case Study

Water inrush disasters from the coal seam floor occur frequently due to the high water pressure of the Ordovician limestone aquifer, multiple aquifers and strong mining disturbance. We presented a model of water-resisting key strata (WRKS) to investigate the mechanism of floor water inrush from multiple aquifers in deep coal mines. Roof hydraulic fracturing (RHF) for controlling floor water inrush and multi-parameter monitoring were proposed and validated in the Xingdong coal mine in Xingtai, Hebei Province. The results indicated that the periodic weighting step of the test working face after RHF was 9.53 m, which was 61.42% less than that of the working face without RHF (24.7 m). The floor failure depth was 30 m, which was 34.4% less than that of the zones without RHF (45.7 m). Hydraulic fracturing weakened the strength of the overlying strata to control the weighting step and reduce the mining disturbance stress, and the stability of the floor WRKS was enhanced, thereby preventing water inrush from the coal seam floor. The research results provide a solution for preventing floor damage and floor water inrush under strong mining disturbance and in complex hydrogeological environments in deep mining.

Geomechanische Reservoircharakterisierung in Bayern im Rahmen der Geothermie‐Allianz Bayern

AbstractTo increase the use of geothermal energy in Bavaria, the subsurface, which serves as a reservoir, must be explored as precisely as possible. In the projects of the Geothermal‐Alliance Bavaria, the most promising areas for geothermal exploration in Bavaria were characterised based on an extensive geomechanical laboratory testing program which was carried out on both drill cores and analogue samples from quarries. In the North Alpine Foreland Basin (SE Germany), the geomechanical test results on Upper Jurassic carbonate rocks show a high heterogeneity. On the contrary, in the Franconian Basin (NE Bavaria) the geomechanical properties of granite analogues are rather homogenous. For the numerical simulation of the borehole stability, the determined parameters from ultrasonic‐ and compression tests serve as input parameters for different scenarios. For both locations, the determination of the failure depth around the borehole and the stress distribution in the near‐field of the borehole were accomplished. In the North Alpine Foreland Basin, the borehole stability decreases with increasing depth. For all scenarios in NE Bavaria, the borehole stability is very low. In the future, the determined parameter ranges will allow to validate already existing models and to develop new ones. This will enable a better knowledge of the sedimentary and crystalline reservoirs and a more effective use of geothermal energy in Bavaria.

Sequential stress control and delayed support in deep shaft construction

In constructing hard rock mine deep shafts, the failure caused by high stress is a significant problem. A construction section extending from the -930 m to -1271 m level of a 1527 m deep shaft was selected as a case study. Q, RMR, and GSI rock mass quality classifications of the surrounding rock were obtained to determine the shaft’s maximum unsupported sinking cycle height in different construction sections. The potential failure mode, failure zone shape, and failure depth of the surrounding rock shaft under high stress were then analyzed theoretically, empirically, and by numerical simulation, sequential stress control and delayed support technology was proposed according to the results. The temporary and permanent support timing parameters were calculated and verified by the empirical chart, numerical simulation, convergence-confinement theory, and theoretical formula. Results show that the surrounding rock in all the construction sections from -930 m to -1271 m belongs to the mild or severely pressure squeezed strata. The potential failure mode is stress-controlled, and the failure zone of the surrounding rock is “ear” shaped. Temporary support strengthens the rock mass, improves the shear capacity of surrounding rock, and prevents the broken rock from falling but does not release stress. Permanent support, conversely, cannot bear the stress of surrounding rock. The stress and elastic strain energy in rock mass should be released to the greatest extent possible before installing permanent support; it is not advisable to install it too early. The time and cycle height of delayed permanent shaft support were comprehensively determined to be four days and 16 m, respectively. The numerical simulation and safety factor proof show that the sequential stress control process effectively minimizes stress in surrounding rock and ensures long-term shaft stability.

Comparative Analysis of the Distribution Characteristics of Floor Stress Field between Gob-Side Entry Retaining with Roof Cutting and Conventional Mining

All coal fields in North China are affected by floor confined water to varying degrees, floor failure and water inrush risk have always been a major problem to baffle coal mining activities. Roof cutting and pressure relief and the lack of protective coal pillar can cause the change of floor stress field, leading to the change of the floor failure depth, stress field of floor is the key to determine the depth of floor failure. In order to deeply study the distribution characteristics of floor stress field in gob-side entry retaining mining with roof cutting, taking the 50107 and 50109 working faces of Dongdong Coal Mine in Chenghe as the research objects, the numerical simulation software is used to simulate the floor stress field distribution of gob-side entry retaining mining with roof cutting and conventional mining. The distribution characteristics of the floor stress field of the working face are compared and analyzed under the three modes of conventional mining of reserved coal pillar, the first mining face of gob-side entry retaining with roof cutting and gob-side entry retaining with roof cutting. The results show that the peak stress concentration in front of the working face all occurs at 10 m under the three mining modes. The stress concentration area in front of conventional working face of reserved coal pillar is mainly in the middle of the working face. The stress concentration area in front of the first working face of gob-side entry retaining with roof cutting (50107) is located in the middle of the working face and the side of the working face of the retaining roadway. The stress concentration area of the working face (50109) is mainly in the middle and the two ends of the working face. The order of the peak value of the maximum concentrated stress in front of the working face is conventional working face of reserved coal pillar > the first working face of gob-side entry retaining with roof cutting (50107) > working face of gob-side entry retaining with roof cutting (50109). There is a stress reduction zone behind the working face, but there is a stress concentration phenomenon extending to the outside of the roadway, and the stress distribution is obviously different. Conventional working face of reserved coal pillar and the first working face of gob-side retaining with roof cutting (50107) show a double peak form of stress concentration on the outside of the two ends of the roadway, and the peak value of the concentrated stress at the rear of the working face is in the following order: On the side close to the transportation roadway, conventional working face of reserved coal pillar = the first working face of gob-side entry retaining with roof cutting (50107) > working face of gob-side entry retaining with roof cutting (50109); on the side close to the return airway, conventional working face of reserved coal pillar > the first working face of gob-side entry retaining with roof cutting (50107) > working face of gob-side entry retaining with roof cutting (50109).

Stress Distribution and Failure Characteristics of Stope Overburden of an Inclined Coal Seam

The stress distribution, failure depth, and shape and range of overlying strata of the stope are important bases for the prevention of roof water hazards and determination of reasonable locations of roof roadways. Based on the hydrogeological data of the E9103 workface, FLAC numerical simulation software was used to establish a numerical calculation model of the overlying strata of the E9103 inclined coal seam, and the stress distribution and failure characteristics of the overlying strata were analyzed. The development height of the caving and water-flowing fractured zones in the overlying strata of the workface was determined. Results showed that the stress reduction area appeared above the goaf in the form of an “arched” distribution, and tensile stress occurred in the local area of the overburden. The overburden relief arch of the workface was symmetrically distributed along the advanced direction and asymmetrically distributed along the inclined direction, with the arch crown deflecting above the workface. The horizontal and vertical displacements of the overlying strata of the stope increased with the advancing distance of the workface. The horizontal displacement in the x -direction presented two obvious regions, and the critical points of the two regions moved forward with the advancement of the workface and showed a certain degree of symmetry. The horizontal displacement in the y -direction presented an “inverted bowl” distribution and increased with the advancement of the workface. The main failure forms of the overlying strata of the workface were a tensile and shear failure, and shear failure was dominant in the upper direction. The height of the overburden caving zone in the workface had little relationship with the advancing distance of the workface and increased slowly as the advancing distance of the workface increased. The development height of the caving zone is 7.2–18.13 m. The development height of the water conduction fissure zone increased rapidly with the increase in the advancing distance of the workface. When the advancing distance was equal to the length of the workface, the development height of the water conduction fissure zone was flat and basically maintained at a stable value. The development height of the water conduction fissure zone is 30.8–62.2 m. These research findings have important engineering importance for ensuring safe and efficient mining of E9103 workface.

Experimental Investigation and Modeling of FRP–Concrete Joint Bond Strength Based on Failure Depth

Abstract The growing interest in fiber-reinforced polymer (FRP) composites in recent years for use in strengthening concrete structures bears witness to their efficiency and ease of use. A major is...