Reinforcement Strength Research Articles

Experimental, Numerical, and Analytical Investigation of the Reinforced Concrete Hidden and Wide Beams

AbstractThis research presents an experimental, analytical, and numerical study to predict the flexural behavior of reinforced concrete hidden and wide beams embedded in slabs. The experimentally studied parameters of testing eight specimens include beam depth, beam width, and beam eccentricity from the column. The obtained test results were compared to the predictions of finite element analysis using the ANSYS program. A numerical parametric study was conducted by the ANSYS program to explore other parameters affecting the ultimate flexural strength of beams. The studied parameters encompass concrete compressive strength, steel reinforcement strength, bottom reinforcement ratio, top-to-bottom reinforcement ratio, and web reinforcement ratio. The results revealed that an increase in beam depth led to higher ultimate load and secant stiffness, along with a decrease in deflection. The increase in beam width significantly affected beam depth, resulting in increased ultimate load and secant stiffness and a slight decrease in deflection. The increase in beam eccentricity from the column resulted in a decrease in ultimate load and secant stiffness while increasing the deflection. Comparisons between experimental and numerical results were made against calculations based on the ECP 203-2017 and ACI 318-19 codes, and the comparison yielded satisfactory results.

Influence of diagonal reinforcement in grouted vertical joints between precast concrete wall panels, part I: Experimental investigation

AbstractMulti‐storeyed buildings are constructed using precast concrete large panels. Although the resistance to lateral loads during an earthquake can be provided by the walls, the vertical joints between the panels remain the weak links. Conventionally, a grouted vertical joint between precast panels is achieved using minimum number of overlapping transverse horizontal U‐bars or looped wire ropes from the adjacent panels, with a holder bar at the overlap, and subsequent grouting of the gap. It was observed that under in‐plane lateral loads, the shear behavior of such joints, especially those with looped wire ropes, is brittle. This paper presents a study to improve the behavior of conventional joints by introducing diagonal reinforcement (DR). Toward this, 13 specimens were tested under monotonic loading and 2 specimens were tested under quasi‐static cyclic loading. The parameters investigated were the types of transverse joint reinforcement, types and strengths of diagonal reinforcement. The compressive strengths of panel concrete and joint grout were kept similar to industry practice. The specimens with DR showed substantial increase of the shear strength and load retention beyond the peak. The presence of conventional transverse joint reinforcement in addition to DR, increases the retention capacity of the joint. Thus, the behavior of a joint with DR was found to be stronger and more ductile.

Mechanical model analysis of column-footing joints with combined socket-corrugated pipe connection

The socket connection method is widely used in precast column, particularly in seismic regions. However, reducing the socket-depth to lower costs may lead to shear failure in the socketed part of the columns. To address this issue and achieve cost objectives, a new approach combines shallow sockets with corrugated pipes for column-footing joints. Comparative tests were conducted to investigate failure in columns with socket-corrugated pipe connections (SCPC), shallow sockets (SSC), and cast-in-place (CIP). Furthermore, finite element models were employed to validate the experimental and simplified model results. The findings suggest potential shear failure in shallow socket connections, which can be mitigated by using the combined socket-corrugated pipe method that alters force transmission paths. As the axial load ratio increases, both the ultimate lateral load capacity of the specimen and the local stresses at the column base increase. In addition, the ultimate lateral load capacity of the column and the stress of the connection reinforcement are increased by increasing the strength of the longitudinal reinforcement, consequently amplifying the extent of joint area damage. Finally, a simplified strut-and-tie model of the SCPC, validated against numerical and experimental data, accurately represents force paths, ultimate lateral load capacity and failure modes in socket joints.

Bond‐slip behavior between polypropylene fiber concrete and corroded reinforcement

AbstractIn this paper, the bond‐slip behavior and bond‐slip constitutive model of corroded reinforcement embedded in polypropylene fiber‐reinforced concrete (PFRC) were investigated. The central pullout test was conducted for 36 specimens. The effects of the corrosion level of reinforcement and the volume fraction of polypropylene (PP) fibers in concrete on the damage mode and bond‐slip process between reinforcement and concrete were studied. Based on the experimental data, a modified bond‐slip constitutive model considering the corrosion level of reinforcement and the volume fraction of PP fibers in concrete was proposed, and the proposed modified bond‐slip constitutive model was used in finite element analysis. The results showed that the addition of PP fibers effectively improved the ultimate bond strength, peak slip and bond toughness of reinforcement and concrete. The enhancement of the bonding properties of the specimens by the PP fibers remained significant after the reinforcement was corroded. The proposed modified bond‐slip constitutive model agreed well with the experimental results. The validity of the proposed model was further verified by finite element analysis.

Seismic behavior of prefabricated lightweight steel composite frame-sandwich wall with enhanced border structure

An innovative prefabricated lightweight steel composite frame-sandwich wall with an enhanced border structure (LSCF-SW), suitable for low-energy consumption low-rise residences, is proposed. Low cyclic loading experiment were conducted to study its seismic behavior. The main parameters include wallboard border type (composite border, mixed border) and steel reinforcement strength (HRB450, HRB500). One full-scale LSCF specimen and four full-scale LSCF-SW specimens are prepared, and their seismic behavior is investigated in terms of failure mode, hysteretic characteristics, ultimate bearing capacity, stiffness degradation, deformation capacity, energy dissipation, and strain characteristics. The results revealed that the sandwich wall (SW) with an enhanced border and lightweight steel composite frame (LSCF) is the primary and secondary seismic fortification lines of the structure, respectively. The LSCF-SW structure exhibited a damage evolution process with four stages. The failure mode involving concrete crushing at the bolted connection area is observed in the specimens with composite bordered sandwich walls (LSCF-SWC), and dense diagonal cracks are discovered in the specimens with mixed bordered sandwich walls (LSCF-SWM). Compared to LSCF-SWC specimens, the ultimate load of LSCF-SWM specimens increases by 23.0 %–50.3 %, and the initial stiffness improves by 16.3 %–42.3 %. The deformation capacity of LSCF-SWC specimens is superior to that of LSCF-SWM specimens. As the steel reinforcement strength increases, the ultimate bearing capacity and initial stiffness of the LSCF-SW also rise. A shear model for the bolt group and a local bending model for the wallboard border are proposed, establishing an ultimate bearing capacity calculation method for LSCF-SW. The calculation results closely align with the experimental results.

Effect of temperature on creep aging behavior of the nugget zone of AA2195 Al[sbnd]Li alloy produced by friction stir welding

This paper aims to study the effect of temperatures on the creep aging behaviors of the nugget zone (NZ) of AlLi alloy by friction stir welding (FSW). The results suggest that the creep strain of the NZ experiences a significant increase as the temperature rises, surpassing that of the base material (BM) at equivalent temperatures. In the case of NZ, the elevation of temperature from 160 to 190 °C induces a pronounced increase in both the size and volume fraction of the T1 phase, which results in a substantial enhancement in the strength. In contrast, the peak-aged strengths of the BM exhibit minimal variation in this temperature range. As the temperature increases, the time required for the BM to reach its peak aging state significantly decreases, whereas the changes in the NZ are less pronounced. For the NZ, the time required to reach the peak aging state is obviously longer than that for the BM. Although the average length of the T1 phase in the NZ is markedly greater than that in the BM, its volume fraction and number density in the NZ are considerably lower than those in the BM, resulting in inferior strength reinforcement in the NZ compared to the BM after creep aging.

The Application of Machine Learning Algorithms to Bond Strength between Steel Rebars and Concrete Using Bayesian Optimization.

The purpose of this study is to estimate the bond strength between steel rebars and concrete using machine learning (ML) algorithms with Bayesian optimization (BO). It is important to conduct beam tests to determine the bond strength since it is affected by stress fields. A machine learning approach for bond strength based on 401 beam tests with six impact factors is presented in this paper. The model is composed of three standard algorithms, including random forest (RF), support vector regression (SVR), and extreme gradient boosting (XGBoost), combined with the BO technique. Compared to empirical models, BO-XGB`oost was found to be the most accurate method, with values of R2, MAE, and RMSE of 0.87, 0.897 MPa, and 1.516 MPa for the test set. The development of a simplified model that contains three input variables (diameter of the rebar, yield strength of reinforcement, concrete compressive strength) has been proposed to make it more convenient to apply. According to this prediction, the Shapley additive explanation (SHAP) can help explain why the ML-based model predicts the particular outcome it does. By utilizing machine learning algorithms to predict complex interfacial mechanical behavior, it is possible to improve the accuracy of the model.

An atomistic and experimental approach to study the effect of water and nanofillers on the compressive strength of PEGDA hydrogels for cartilage replacement

Polyethylene glycol diacrylate (PEGDA) hydrogel is emerging as a potential candidate for biomedical applications, particularly cartilage replacement. However, due to weak mechanical strength, their applications are still in the infancy for cartilage replacement. In this article, authors have reported the compressive strength of hexagonal boron nitride (h-BN) reinforced PEGDA hydrogels in conjunction with different water content. A combined experimental and atomistic approach (Molecular Dynamics) was employed to explore the compressive strength of nanocomposite hydrogels. It was reported from the experimental analysis that h-BN acts as a superior reinforcement for the compressive strength at lower water content. The Molecular Dynamics (MD) based simulations also predict a similar trend with h-BN and water content. The MD-based study gives insight into scrutinizing the behavior of polymer chains and their entanglement and sheds light on microscale phenomena that are usually inaccessible through experiments alone. It can be concluded from the experiments in conjunction with MD simulations that at higher water content, the contact points between h-BN nanosheets and polymer chains decrease, mitigating the overall compressive strength of PEGDA hydrogels. In summary, this study enables us to obtain meaningful mechanical properties that mimic the strength of human articular cartilage.

Study on the Bond Performance of Epoxy Resin Concrete with Steel Reinforcement

Epoxy resin concrete, characterized by its superior mechanical properties, is frequently utilized for structural reinforcement and strengthening. However, its application in structural members remains limited. In this paper, the bond–slip behavior between steel reinforcement and epoxy resin concrete was investigated using a combination of experimental research and finite element analysis, with the objective of providing data support for substantiating the expanded use of epoxy resin concrete in structural members. The research methodology included 18 center-pullout tests and 14 finite element model calculations, focusing on the effects of variables such as epoxy resin concrete strength, steel reinforcement strength, steel reinforcement diameter and protective layer thickness on bond performance. The results reveal that the bond strength between epoxy resin concrete and steel reinforcement significantly surpasses that of ordinary concrete, being approximately 3.23 times higher given the equivalent strength level of the material; the improvement in the strength of both the epoxy resin concrete and steel reinforcement are observed to marginally increase the bond stress. Conversely, an increase in the diameter of the steel reinforcement and a reduction in the thickness of the protective layer of the concrete can lead to diminished bond stress and peak slip. Particularly, when the steel reinforcement strength is below 500 MPa, it tends to reach its yield strength and may even detach during the drawing process, indicating that the yielding of the steel reinforcement occurs before the loss of bond stress. In contrast, for a steel reinforcement strength exceeding 500 MPa, yielding does not precede bond stress loss, resulting in a distinct form of failure described as scraping plough type destruction. Compared to ordinary concrete, the peak of the epoxy resin concrete and steel reinforcement bond stress–slip curve is more pointed, indicating a rapid degradation to maximum bond stress and exhibiting a brittle nature. Overall, these peaks are sharper than those of ordinary concrete, indicating a rapid decline in bond stress post-peak, reflective of its brittle characteristics.

Axial compressive performance of spirally reinforced high-strength CFST column

The concrete-filled steel tubular (CFST) member using high-strength materials could have less ductility than its counterpart using normal-strength materials. In this study, spiral reinforcement is used to enhance the performance of CFST columns using high-strength materials. Experiments were conducted for spirally reinforced high-strength CFST stub columns. The highest yield strengths of spiral reinforcement and steel tube were 1597.6 MPa and 771.7 MPa, respectively, and the highest compressive strength of concrete was 103.1 MPa. Results showed that the presence of high-strength spiral reinforcement effectively improved both the strength and ductility of composite columns, while the fracture of spiral reinforcement was observed in tests. A numerical study revealed that spiral reinforcement provided effective confinement to the high-strength core concrete. The steel tube and spiral reinforcement reached respective yield strength corresponding to peak load. The spirally reinforced CFST column exhibited higher resistance than the equivalent normal CFST column using a thick tube. A design-oriented strength prediction method was proposed and was validated against the test data. The average ratio of formula-predicted to experimental resistances was 0.934, with a coefficient of variation being 0.079.

Wire laser additively reinforced blanks: Effect of the laser power on the bending strength of a single layer reinforcement

This study investigates the application of Wire Laser Metal Deposition (w-LMD), a form of Directed Energy Deposition (DED) additive manufacturing, to enhance the production process of automotive components, specifically through the development of patchwork blanks with localized reinforcements. The research focuses on reinforcing 22MnB5 steel sheets with beads of 316L steel using a laser beam at various power levels, aiming to achieve maximum strength with minimal use of material. The resulting components, referred to as wire-Laser Additively Reinforced Blanks (w-LARB), demonstrated a substantial increase in strength, up to 87%, as verified by bending tests. Notably, the study reveals that a relatively low laser power can still yield significant mechanical improvements, underlining the efficiency of the process in terms of material usage and energy consumption. Furthermore, the high repeatability of the w-LMD process confirms its potential for widespread industrial adoption in automotive manufacturing.

Experimental study on mechanical properties and breakage of high temperature carbon fiber-bar reinforced concrete under impact load

To investigate the effects of high temperature and carbon fiber-bar reinforcement on the dynamic mechanical properties of concrete materials, a muffle furnace was used to treat two kinds of specimens, plain and carbon fiber-bar reinforced concrete, at high temperatures of 25, 200, 400 and 600 °C. Impact compression tests were carried out on two specimens after high-temperature exposure using a Hopkinson pressure bar (SHPB) test setup combined with a high-speed camera device to observe the crack extension process of the specimens. The effects of high temperature and carbon fiber-bar reinforcement on the peak stress, energy dissipation density, crack propagation and fractal dimension of the concrete were analyzed. The results showed that the corresponding peak strengths of the plain concrete specimens at 25, 200, 400, and 600 °C were 88.37, 93.21, 68.85, and 54.90 MPa, respectively, and the peak strengths after the high-temperature exposure first increased slightly and then decreased rapidly. The mean peak strengths corresponding to the carbon fiber-bar reinforced concrete specimens after high-temperature action at 25, 200, 400, and 600 °C are 1.13, 1.13, 1.21, and 1.19 times that of plain concrete, respectively, and the mean crushing energy consumption densities are 1.27, 1.31, 1.73, and 1.59 times that of plain concrete, respectively. The addition of carbon fiber-bar reinforcement significantly enhanced the impact resistance and energy dissipation of the concrete structure, and the higher the temperature was, the more significant the increase. An increase in temperature increases the number of crack extensions and width, and the high tensile strength of the carbon fiber-bar reinforcement and the synergistic effect with the concrete material reduce the degree of crack extension in the specimen. The fractal dimension of the concrete ranged from 1.92 to 2.68, that of the carbon fiber-bar reinforced concrete specimens ranged from 1.61 to 2.42, and the mean values of the corresponding fractal dimensions of the plain concrete specimens after high-temperature effects at 25, 200, 400, and 600 °C were 1.19, 1.21, 1.10, and 1.11 times those of the fiber-reinforced concrete specimens, respectively. The incorporation of carbon fiber-bar reinforcement reduces the degree of rupture and fragmentation of concrete under impact loading and improves the safety and stability of concrete structures.

Regression prediction model for shear strength of cold joint in concrete

The shear resistance of cold joint in concrete is influenced by various design parameters. Traditional mechanical models typically consider only a limited number of parameters to predict the shear strength of cold joints. This research aims to explore the complex nonlinear relationship between design parameters and cold joint shear strength using statistical method and machine learning technology. The goal is to develop a more accurate, reliable, and engineering applicable regression model for predicting shear strength. A dataset of 546 Z-shaped shear specimens characterizing cold joint in concrete was constructed, involving a total of 16 variables that may affect shear performance. Correlation analysis and recursive elimination were adopted to eliminate correlated and insignificant variables based on their importance. Multiple linear regression (MLR), random forest regression (RFR), and support vector machine regression (SVR) prediction models for cold joint shear strength were established based on rigorously screened variables and comprehensively evaluated using multiple methods. It was found that the most significant factors influencing the shear strength of cold joints are concrete strength, interface shear key, product of interface reinforcement strength and its reinforcement ratio, normal stress, fiber length of new concrete, casting method of the new concrete, and product of the fiber length and its tensile strength of old concrete. The MLR, SVR, and RFR models all exhibited superior performance relative to traditional mechanics-based models with regard to shear strength prediction of cold joints. The RFR model is recommended for predicting the shear strength of cold joints due to its superior evaluation indexes in comparison to the MLR and SVR models, and variable sensitivity analysis shows that it does not yield common-sense errors.

Characterization and properties of porous red mud–based geopolymer composites reinforced with carbon fiber powders

To obtain porous composites with high porosity and improved performance, porous geopolymer composites (CFP/RMG) were fabricated using alkali-excited red mud and carbon fiber powders (CFPs) using the foaming method. The synergistic effects of CFPs and H2O2 on the microstructure, pore structure, strength, and thermal properties of the porous samples were systematically investigated. CFPs were uniformly distributed on the pore walls of the samples. The total porosity decreased with CFPs and increased with H2O2, the density of CFP/RMG samples ranged from 0.57 ± 0.01 to 1.71 ± 0.05 g/cm3. The compressive strength of the composite samples increased from 0.54 ± 0.09 to 4.16 ± 0.24 MPa with an increase in CFPs from 0 to 12.5 wt%, and it decreased from 4.06 ± 0.23 to 0.47 ± 0.06 MPa with 1–5 wt% H2O2. Fiber bridging and fiber pullout contributed to the strength reinforcement of the whole composite. The porous composites also showed low thermal conductivity (0.176–0.680 W/(m·K)), which revealed that it had potential applications in the field of building materials in the future.

Flexural behavior of reinforced concrete beams externally strengthened with ECC and FRP grid reinforcement

To prevent premature delamination of FRP sheets in strengthened concrete structures, this study explores a novel method of laying a composite layer of fiber reinforced polymer (FRP) grid reinforced with engineering cementitious composite (ECC), designated as FGRE, and applied at the soffit of reinforced concrete (RC) beams to improve its flexural performance. Experimental studies were conducted on RC beams with different strengthening configurations to validate the effectiveness of the proposed strengthening method. In addition, analysis on the working mechanism and a parametric analysis were performed for the composite strengthened beam using nonlinear finite element modeling. The experimental results showed that FGRE composite layers can significantly improve the bearing capacity of RC beams. Compared with the control RC beam, the FGRE composite strengthening technique significantly increased the cracking load, yield load, and ultimate load of the beam specimens up to 28, 11, and 12 %, respectively. The ECC grout layer maintained a good bonding performance with the concrete substrate until beam failure. The flexural capacity of RC beams with the proposed FGRE strengthening systems is determined by the thickness of the ECC layer. In addition, the effect of strengthening on the flexural capacity was more significant when the yield and tensile strength of the steel reinforcement were lower. Moreover, the prediction deviation from the experimental data of the FE models and analytical models for the ultimate load-bearing capacity were less than 2 and 7 %, respectively. It can be concluded that the proposed FGRE system is a viable solution to enhance the flexural capacity of RC beams.

Dynamic behaviors of bridge with corroded RC piers under barge collisions

Reinforced concrete (RC) bridge piers located in navigable waterways are susceptible to chloride-induced corrosion, which may cause severe damage or even entire collapse of bridge under potential barge collisions. The present study aims to examine the failure patterns and dynamic responses of typical simply supported girder bridge with corroded RC piers under barge collisions. Firstly, nine RC column specimens with three designed corrosion degrees and two corrosion strategies were prepared using the impressed anodic current technique. Secondly, the drop hammer impact and axial compression tests were successively performed to examine the residual axial load bearing capacities of both unimpacted and impacted specimens. Furthermore, by comprehensively considering the effects of corrosion-induced deteriorations on the effective cross-sectional area and yield strength of reinforcements, concrete strength, as well as the rebar-concrete bond-slip relationship, the refined finite element (FE) models of specimens were established and validated. Finally, the dynamic behaviors of a prototype simply supported girder bridge with corroded RC piers under barge collisions at different service lives, i.e., 0–60 years, were numerically assessed. It indicates that: (i) under drop hammer impact, six specimens all exhibit global flexure failure, and relatively severe concrete cracking and spalling occur in the specimens with 15 % designed corrosion degree; (ii) the axial load bearing capacities of specimens with 5 % and 15 % designed corrosion degrees are reduced by 15.46 % and 34.86 % compared to the unimpacted non-corroded specimen, and 11.29 % and 43.30 % compared to the impacted non-corroded specimen; (iii) the transverse impact resulted in 25.93 %, 22.27 % and 35.53 % reductions in axial load bearing capacities for 0 %, 5 % and 15 % designed corrosion degree, respectively; (iv) for the prototype barge-bridge collision scenario, the failure patterns vary from minor bending cracks to remarkable flexural failure as the service live increases from 0 to 60 years. The corrosion-induced degradations of bridge performance should be concerned for the vessel collision-resistant design of bridge.

Data-driven predicting of bond strength in corroded BFRP concrete structures

The mechanical properties of basalt fiber-reinforced polymer (BFRP) concrete structures in corrosive environments are largely dependent on the bonding performance between the BFRP reinforcement and concrete. An accurate and convenient method for calculating the bonding strength is crucial for engineering design. However, experimental methods and existing empirical models are insufficient to encompass the intricate interdependencies among the bonding factors. This study proposed a machine learning (ML)-based bonding strength prediction method, which utilizes random forests (RF) and adaptive boosting (AdaBoost) algorithms to predict the interfacial bond strength of BFRP reinforcement in corroded concrete. The model was trained on a dataset of 355 samples, effectively quantifying the relationships between the BFRP reinforcement parameters, concrete parameters, corrosion factors, and bonding strength. The performance of the two algorithms was evaluated using R2, RMSE, and MAE indicators, and the prediction results were explained using the SHAP method. The results show that the predicted results of the machine learning model are highly consistent with the experimental results, with the AdaBoost model achieving an R2 of 0.925 on the test set, demonstrating high predictive performance. Among the various factors, the corrosion factor has the most significant impact on bonding strength, followed by concrete compressive strength and BFRP bar yield strength. Ultimately, the model was juxtaposed against traditional empirical formulas, affirming its efficacy and dependability. The research presents a novel approach to predicting bond strength in corroded BFRP bar-concrete systems.

Neural Slicer for Multi-Axis 3D Printing

We introduce a novel neural network-based computational pipeline as a representation-agnostic slicer for multi-axis 3D printing. This advanced slicer can work on models with diverse representations and intricate topology. The approach involves employing neural networks to establish a deformation mapping, defining a scalar field in the space surrounding an input model. Isosurfaces are subsequently extracted from this field to generate curved layers for 3D printing. Creating a differentiable pipeline enables us to optimize the mapping through loss functions directly defined on the field gradients as the local printing directions. New loss functions have been introduced to meet the manufacturing objectives of support-free and strength reinforcement. Our new computation pipeline relies less on the initial values of the field and can generate slicing results with significantly improved performance.

Flexural behavior and serviceability of steel fiber-reinforced lightweight aggregate concrete beams reinforced with high-strength steel bars

Six beams reinforced with HRB600 bars and one reinforced with HRB400 bars fabricated using steel fiber-reinforced lightweight aggregate concrete (SFLWAC) were tested under a four-point bending load to investigate the load-carrying capacity and service performance, with different reinforcement ratios, clear span lengths, concrete strengths, and reinforcement strengths. The test results showed that cracks ran through lightweight aggregates and developed rapidly without an aggregate interlocking mechanism, and the specimens eventually failed in the mode that the compressive concrete was crushed following longitudinal bars yielded, with 3 ∼ 4 major cracks. The specimens satisfied the allowable deflection and crack width required in the codes, with a ductility coefficient exceeding 4.5, and 1/150 of the span length was recommended to be the maximum deflection at the serviceability limit state. Generally, the increasing reinforcement ratio significantly improved the flexural strength and serviceability but reduced the ductility, the linear stiffness decreased with the growing span length, and the SFLWAC strength mainly affected the cracking moment and ductility. Replacing HRB400 bars with equal strength of HRB600 bars led to a substantial drop in serviceability, while an equal area of HRB600 bars improved the ultimate moment by 38.7 %. The calculation results indicated that by neglecting the residual tensile strength, fracture characteristics, and bond properties of SFLWAC, the prediction equations in the Chinese, American, and European codes underestimated the ultimate moment and overestimated the crack width, and the Chinese code yielded the conservative deflection prediction. The analytical flexural models for HRB600-reinforced SFLWAC beams were derived by incorporating the effects of steel fibers, lightweight aggregate concrete, and bond stress, exhibiting accurate predictions.

Recent advances in stability analysis and design of 3D slopes

Slope failures in nature and engineering are typically three-dimensional (3D). The rotational failure mechanism derived from the variational limit equilibrium (LE) method shows superior performance in the stability analysis of the 3D slope. In contrast to the traditional LE methods, it avoids arbitrary kinematical and statical assumptions. Stability charts obtained by the variational LE method are used to derive explicit expression equations of the safety factor, also known as the stability equations, for both 3D reinforced and unreinforced slopes. These equations are highly accurate and can provide a convenient means to assess slope stability in practical engineering. An example of a convex reinforced slope with a turning arc is illustrated in this study to investigate the effect of the 3D effects on the required reinforcement length for design. The results indicate that the 2D method underestimates the required reinforcement length when dealing with a 3D reinforced slope problem. Furthermore, a forensic analysis of the Yeager Airport reinforced slope is conducted within the framework of the variational LE method. The required strength for stability is found to be significantly less than the allowable strength of reinforcements without considering the decrease in soil shear strength. However, the required strength greatly exceeds the allowable strength when the decrease in soil shear strength is considered. The results verify that the decrease in shear strength of the weak layer is responsible for the collapse.