Shear Strength Equation Research Articles

Shear strength equation of soils in a wide suction range under various initial void ratios

AbstractShear strength equation is a basic theory for solving many geotechnical engineering problems. Although the shear strength equation has received widespread attention, shear strength of clay under wide suction range and different initial void ratio conditions cannot be well predicted. This study aims to establish a new strength equation applicable to soils within a wide suction range. Considering the capillary and adsorptive parts of soil–water interactions, a cohesion expression related to the degree of adsorbed water saturation Sra and the effective stress related to the degree of capillary water saturation Src are proposed. After that, based on the Mohr–Coulomb theory, a shear strength equation of unsaturated soils in a wide range of suction under various is proposed. Five parameters are included in the equation. It is easy to calibrate them through shear tests on saturated and the fully dried soils. It is verified that not only the sandy clay till and clayed silt but also the expansive soil's shear strength in wide ranges of suction under various can be well predicted.

Shear Strength Equation and Database for High-Strength High-Performance Fiber-Reinforced Concrete and Ultra- High-Performance Concrete Beams without Stirrups

Shear Strength Equation and Database for High-Strength High-Performance Fiber-Reinforced Concrete and Ultra- High-Performance Concrete Beams without Stirrups

A modified truss-arch model for shear strength evaluation of corroded reinforced concrete columns

Under seismic loading, corroded reinforced concrete (RC) columns are prone to brittle shear failure, which poses a significant threat to existing structures. However, due to the mechanical defects and insufficient parameters included in the equations available in codes, the literature exhibits a lack of precision in predicting the shear strength of such columns. In this paper, a shear strength equation for the RC column was established based on the truss-arch model theory. On this basis, the effect of corrosion on key parameters such as the cross-sectional area of rebar, yield strength, compressive strength of concrete, and displacement ductility was fully considered to establish the shear strength equation of corroded RC columns. To assess the accuracy and applicability of the proposed equation, a database consisting of 215 specimen parameters was compiled. Comparative analyses were conducted with existing equations from the literature. The results indicate that the mean values and coefficient of variation for the ratio of calculated values to the tested values of the equation were 1.098 and 0.601, respectively, which proves the equation’s high computational accuracy and low dispersion. Consequently, the proposed equation offers a more effective calculation method for predicting and assessing the shear strength of corroded RC columns. This method holds significant potential for enhancing the resilience of structures in seismic-prone regions.

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules

The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used criterion in rock slope stability analysis and is still the base for the shear strength reduction method applied in finite element modelling. Different proposals for estimating the equivalent strength parameters based on confining stress level are evaluated. The limitation of stress-dependent linear Mohr–Coulomb parameters is emphasized by analysing the vertical cut problem, for which, depending on the chosen stress level, different critical heights are obtained for the same material. Sensitivity analysis of geotechnical parameters used as input for failure criterion is performed to determine their influence on slope stability. Probabilistic analysis is conducted to determine the probability of failure when different flow rules are applied. If slope stability analysis is performed with an assumption of associative flow rule, the probability of failure is within the acceptable limits for the considered case study, while employing non-associative flow rule, the probability of failure is rather high. The chart is presented that could be readily used to estimate the combination of σci, GSI, and mi values that produce failure for the analysed case study.

Undrained shear strength of soft clay reinforced with encapsulated stone dust columns

PurposeThe stone dust column was used to strengthen the sample and had a significant effect on improving the shear strength of the kaolin clay. The application of stone columns, which can improve the overall carrying capacity of soft clay as well as lessen the settlement of buildings built on it, is among the most widespread ground improvement techniques throughout the globe. The performance of foundation beds is enhanced by their stiffness values and higher strength, which could withstand more of the load applied. Stone dust is a wonderful source containing micronutrients for soil, particularly those derived from basalt, volcanic rock, granite and other related rocks. The aim of this paper is to evaluate the properties of soft clay reinforced with encapsulated stone dust columns to remediate problematic soil and obtain a more affordable and environmentally friendly way than using other materials.Design/methodology/approachIn this study, the treated kaolin sample's shear strength was measured using the unconfined compression test (UCT). 28 batches of soil samples total, 12 batches of single stone dust columns measuring 10 mm in diameter and 12 batches of single stone dust columns measuring 16 mm in diameter. Four batches of control samples are also included. At heights of 60 mm, 80 mm and 100 mm, respectively, various stone dust column diameters were assessed. The real soil sample has a diameter of 50 mm and a height of 100 mm.FindingsTest results show when kaolin is implanted with a single encased stone dust column that has an area replacement ratio of 10.24% and penetration ratios of 0.6, 0.8 and 1.0, the shear strength increase is 51.75%, 74.5% and 49.20%. The equivalent shear strength increases are 48.50%, 68.50% and 43.50% for soft soil treated with a 12.00% area replacement ratio and 0.6, 0.8 and 1.0 penetration ratios.Originality/valueThis study shows a comparison of how sample types affect shear strength. Also, this article provides argumentation behind the variation of soil strength obtained from different test types and gives recommendations for appropriate test methods for soft soil.

Shear strength of prestressed concrete beams with short shear span: Full‐scale experiments and evaluation of design methods

AbstractPrestressed concrete (PC) is increasingly used in civil engineering construction. Notably, research on shear resistance in PC beams with short shear span remains relatively limited, necessitating further comprehensive exploration. In the study, tests were conducted on bonded post‐tensioned PC T‐beams with short shear span (a/h = 1.0), subjecting them to monotonic loading destructive tests. These beams measured 24.9 m in length, 1.605 m in height, and had a top flange width of 2.0 m. They featured a uniform cross‐section with a 0.22 m web thickness. Given the size of the full‐scale test beams and space constraints for loading, an innovative loading scheme was devised to minimize the counterweight. Test results demonstrate the safety and feasibility of the loading scheme. The tests were conducted five times and the main test variables were the draped tendons and the quantity of horizontal web reinforcement. The tests revealed that horizontal web reinforcement significantly influenced crack propagation but had a minimal effect on shear strength. For the parameter values taken for the test beams, the prestressing level has less effect on the shear strength of the beam. Simultaneously, an investigation was conducted involving a total of 119 PC beams. This investigation aimed to evaluate the degree of conservatism and accuracy in shear design code provisions and shear strength equations derived from various standards, including the strut‐and‐tie model (STM) of ACI, AASHTO, and Tan, as well as the critical crack model of Yuan and the truss model of Laskar. Comparative analysis indicates that, the design method provided by Yuan exhibit relatively superior predictive capabilities.

Efficient numerical implementation of limit equilibrium method for stability analysis of unsaturated soil slopes using Gaussian integral

Unsaturated soil is widely distributed around the world but less considered in design due to the absence of a convenient analysis method in practice. The Morgenstern–Price (MP) method incorporating the extended Mohr–Coulomb shear strength equation provides a reliable approach to evaluate slope stability in such conditions. However, this method is time-consuming due to the need for a tedious trial-and-error process in determining the scaling factor, which involves complex iterations during each trial. Furthermore, since the relatively complicated nature of unsaturated soil, a dense slice division is necessary to obtain reliable results, making the analysis even more cumbersome. In this paper, an improved MP method for unsaturated soil slope stability analysis is presented, which eliminates the need for a dense slice mesh by employing only a few strategically placed Gauss points along the slip surface. Moreover, the trial-and-error process for determining the scaling factor with the corresponding complex iterations is replaced by an efficient search algorithm with a more concise iteration process, resulting in a more convenient implementation of the proposed method. Extensive examples are provided to validate the effectiveness of the proposed improved MP method, indicating its potential as an accurate and efficient analysis method for unsaturated soil slopes in practical application and relative study involving repetitive analyses.

Experimental and Analytical Investigations on Shear Performance of Ambient-Cured Reinforced Geopolymer Concrete Beams

Geopolymer concrete (GPC) has emerged as a sustainable alternative to ordinary Portland cement concrete (OPCC) as GPC significantly reduces embodied carbon dioxide emissions. This study compared the shear behavior of reinforced OPCC beams and GPC beams of the same cross-section and compressive strength. The study tested nine beams under three-point bending to evaluate the effects of concrete type and shear span on the shear strength. The results showed that OPCC and GPC beams exhibited relatively similar reduction rates in the shear strength with increasing a/d ratios, while the failure mode shifted from shear in OPCC beams to shear-flexure in GPC beams. The maximum deflection of GPC beams significantly increased with increasing a/d ratios. Moreover, empirical shear strength equations, intended for OPCC beams in various design codes, underestimated the shear strength of GPC beams by about 11.0-26.9% at the a/d ratio of 4.3 but significantly underestimated the shear strengths of GPC beams by 77% at lower a/d ratios of 1.6 and 2.9. Therefore, modifications are proposed to the existing design OPCC shear strength equations to significantly improve the prediction accuracy for the shear strength of GPC beams.

Effect of Grain Size Distribution on Shear Strength Characteristic of Random Fill Material at Keureuto Dam, Indonesia

Earth-fill dams are commonly constructed by composing different geomaterials to optimally utilize local natural resources. In Indonesia, random fill materials are frequently used as a major composition in dam construction. The term random fill material originated from its broad range of grain size. Grain size distribution influences shear strength characteristics of geomaterials. There are 2 shear strength equations to model the behavior of fill material, i.e., linear Mohr-Coulomb and non-linear power curve. Two series of large scale in situ direct shear tests were performed at Keureuto Dam, Indonesia. Sieve analysis tests were performed accordingly. The random fill material was composed of cobbles, gravel, and less than 25% of sand. The stress-displacement characteristics of random fill material indicated that plastic deformation occurred at shear strain of 1% to 4%. The shear failure was reached in shear displacements of 60 – 90 mm, equivalent to shear strain of 8% – 12 %. Stress-strain relationships showed a dilative behavior indicating the random fill was in a relatively dense form. The dilatancy tends to decrease as the normal stress increases. The linear Mohr-Coulomb failure criteria and non-linear power curve equation are suggested to characterize the shear strength of the random fill material. To obtain a realistic value of the non-cohesive strength parameter of granular material, the Mohr-Coulomb approach should be intercepted at zero. A relationship between secant friction angles for different normal stresses is presented. This angle tends to decrease at higher normal stresses.

Reconsideration of shear strength expressions for CFSTs: Rectangular tubes

Concrete filled steel tubes (CFSTs) are typically circular or rectangular. Circular CFSTs are mostly used as vertical components of deep foundation systems; rectangular sections are more commonly used in building construction such as square CFSTs for columns. Prior work has focused on circular CFSTs with far fewer studies on square or rectangular sections. In addition to being more limited, prior research on square CFST sections has focused on flexural and axial response; there have been far fewerstudies on the shear response. As such, the accuracy of shear-strength equations is uncertain. A research study was undertaken to understand and improve design expressions for the shear design of rectangular CFSTs. First, the research team collectedexperimental data on shear resistance of rectangularCFSTs. Selected experimental data was used to develop and validate an advanced nonlinear finite element model (FEM) to predict the measured response and observed damage of rectangular CFSTs controlled by shear behavior. The validated model was then used to conduct parameter studies to investigate important design parameters of rectangular CFSTs responding primarily in shear including: 1) concrete and steel material properties, 2) cross-sectional aspect ratio, and 3) impact of enhanced bond capacity/composite action through the introduction of a single shear key at each end of the member. The results were used to better understand the importance of each parameter on the shear response and strength. A database was assembled, combining the experimental data with the strength predicted by each FEM, to evaluate existing design equations. The shortcomings of the existing equations included (1) only accounting for the steel or the concrete fill contribution, and (2) overestimating the total shear strength because the behavior of the CFST in shear is not well understood. This paper provides a new approach to assessing the shear strength as the individual contributions of the steel tube and the concrete fill are computed for each model to better understand their interaction. This also permits the development of a new design equation to remedy the shortcomings of existing codified models. In particular, the proposed model accurately estimates the individual contributions of steel tube and concrete fill to the shear resistance for salient design parameters.

Study on the control effect of local basement replacement on the stability of dump.

This study focuses on effectively controlling landslides at the boundary of a soft rock open-pit dump while ensuring safe increases in the dump's capacity and optimal utilization of external dump sites. To achieve this, the adoption of a local filling method for the dump base is proposed. By leveraging the concepts of limit equilibrium theory and equivalent shear strength parameters, the mathematical expression of the slope stability coefficient in the Morgenstern-Price method is derived and improved. This improved method is then applied to a real engineering example to determine the optimal basement replacement rate required to maintain slope stability. The findings reveal that the local filling of the base is well-suited for slopes susceptible to potential landslides associated with cutting layers, bedding layers, and swelling. For practical ease, it is advisable to choose the lowest step in the dump's slope for construction convenience. As the local replacement rate of the base increases, the slope's stability coefficient gradually improves, with the K-Fs ratio showing a prominent role in this process. Additionally, numerical simulation methods are employed to elucidate the mechanism of the dump's landslide following local basement replacement, thereby providing comprehensive evidence of the engineering applicability of this method. The research results demonstrate a promising practical application prospect for effectively controlling the stability of soft base dump slopes.

Development of the tied butterfly shape for structural fuses

Recently, there has been research and interest in structural fuses as a way to concentrate seismic damage in replaceable elements and protect the rest of the structure from inelastic actions. However, there is no consensus on structural fuse shape, particularly for structural fuses consisting of a steel plate subjected to shear deformations, because studies with different objectives arrive at different shapes. For example, studies seeking to optimize the structural fuse shape to maximize fracture resistance often result in something that looks like the butterfly-shaped link, whereas other studies that optimize the form to maximize buckling resistance result in a shape with links that are tied together. In this study, a new structural fuse shape, named the tied butterfly shape, was developed to integrate the advantages of both the buckling-resistant configuration and the butterfly-shaped link. First, the concepts for the tied butterfly shape are presented along with plastic mechanism analysis to derive an equation for shear strength. Then, an experimental program is described including three tied butterfly shape structural fuses and one straight link structural fuse for comparison. Finite element models are then validated against the experimental results and a parametric computational study is presented that evaluates the effect of key design variables on the structural behavior of this tied butterfly shape. The experimental study revealed that the tied butterfly shape structural fuse was capable of maintaining stable hysteretic behavior up to a shear angle of 23% before fracture or buckling and that multiple tied butterfly shapes can be connected together. Based on the plastic mechanism analysis and parametric study, design equations and recommendations for implementation in practice are provided.

Safety assessment of slope on in-service dump under severe dry–wet cycles at high-altitude

This study aimed to evaluate the safety of dump slopes in high-altitude areas subjected to severe dry–wet cycles. The slope of No. 1 and No. 2 in-service dumps in limestone mining areas for cement in high-altitude mining areas is taken as the research object. The unsaturated soil shear strength and matrix suction distribution equations were imported based on the unsaturated–saturated seepage theory. Therefore, the evolution characteristics of the unsaturated–saturated seepage field in the dump are analyzed by numerical calculation, and the safety state of the dump slope is evaluated. The results indicated the following rules: under the action of four dry–wet cycles, the surface soil of the dump slope changes from an unsaturated state to a saturated state. Furthermore, with the increase in the times of the dry–wet cycle, the maximum vertical displacement of the No. 1 and No. 2 dump slopes increased. The numerical calculations of the maximum cumulative vertical displacement of the slope were consistent with the actual monitoring data. The factor of safety of the dump slope decreased continuously with the increase in the times of dry–wet cycles. Nevertheless, it still met the safety and stability standards. It was concluded that the slope of the in-service dump remains stable after enduring four severe cycles of dry–wet.

A unified shear strength equation for slabs and beams longitudinally reinforced with FRP or steel bars based on simplified cracked elastic properties

At service load conditions, deflections and stresses in reinforced concrete (RC) slabs and beams are typically calculated using the properties of the transformed cracked cross section. For more than eighty years, the depth of compression zone factor k in cracked singly-reinforced rectangular RC sections has been calculated using k=2ρn+ρn2-ρn where ρ is the reinforcement ratio and (n) is the modular ratio. It is shown that in slabs and beams with a wide range of concrete compressive strength fc′ that are reinforced longitudinally with steel or FRP bars, ρn ranges from 0.005 to 0.16. Within this range, k can be accurately calculated using k=0.95ρn0.43 or simply k=ρn0.44. The error between the former equation and the exact equation ranges from –2% to + 3 %. This equation is used to show that the shear strength of concrete vc in the ACI–440.11-22 code for GFRP–reinforced members depends effectively on ρ, fc′ and d, just like the strength of steel–reinforced members in the ACI–318-19 code equation. It is proposed to apply to the factor Er/Esteel1/3 where Er and Esteel are the moduli of elasticity of the FRP and the steel bars respectively to the ACI–318 equation to make it suitable also for FRP–reinforced members. This unifies the equation for the two types of reinforcement and provides a better correlation with the experimental results from 233 FRP–reinforced members available in the literature than the current ACI–440.11 code equations. On the other hand, the transformed cracked moment of inertia Icr can be related solely to ρn and approximated using Icr=0.36ρn0.81bd3 where b and d are the sectional width and effective depth respectively. This equation is used to show that the cracked flexural stiffness is effectively related to the modulus of elasticity and the area of the reinforcing bars raised to the power 0.8, to d2.2 and to modulus of elasticity of the concrete raised to the power 0.2.

Shear damage repair of masonry walls using different materials

In this research, the effects of different repairing materials and techniques used on damaged Masonry walls under an in-plane lateral loading were investigated. Seven clay brick walls with dimensions of (1200 × 935 × 115) mm were tested. The walls were tested until a visible crack was observed, later repaired, and tested again up to failure. The repairing materials consisted of grid configured strip materials (metal, plastic, flat webbing ‘textile’ and wild cane ‘organic’ strips), near surface mounted (NSM) steel re-bars and steel wires in mortar joints. Based on the experimental results, the repairing materials/techniques restored the shear strength by about 48–103% of the original strength. The ductility factor of the repaired walls ranged from 4.5 to 48.3 (flat webbing ‘textile’ highest). The energy dissipation ratio of the repaired walls ranged from 4.3 to 12.7 (flat webbing ‘textile’ highest). Prediction equations for shear strength are presented giving reasonable results compared to the experimental results.

A new robust equation for shear strength of GFRP-RC deep beams using hybrid experimental and synthetic data based-FE quasi-static analysis procedure

The main objective of this article is to propose a new, more robust, and comprehensive design equation for Glass-Fiber-Reinforced-Polymer (GFRP) reinforced concrete (RC) Deep Beams (DBs). The investigation is based on a numerical model using Quasi-Static Two-Dimensional FE simulation of GFRP-RC DBs. The numerical model is validated by calibrating four parameters (concrete dilatation angle ψ, concrete tensile strength fct, fracture energy Gf, mesh size) against data from ten full-scale experiments on GFRP-RC DBs available in the literature. Additionally, a numerical parametric study based on a full factorial design with 5 factors (and between 2 and 5 modalities) is conducted using the validated quasi-static FE model, which includes 360 large-scale GFRP-RC DBs. The impacts of primary design variables on the concrete contribution Vc to the shear capacity of GFRP-RC DBs are assessed. The effects of various geometrical and mechanical variables, such as cross-sectional dimensions (width b × height H), concrete compressive strength grade (fc), GFRP properties (modulus Ef, and strength ffu), GFRP reinforcement ratio (ρf), and shear span to depth ratios (a/df), are examined to understand the shear behavior of GFRP-RC DBs.The numerical simulations demonstrate that the proposed FE model accurately captures the behavior of GFRP-RC DBs. Building upon these findings, a new shear design equation is proposed for DBs, and its accuracy and robustness are compared with five established international design codes (ACI-440.1R-15, ISIS-Canada, CAN/CSA-S806-12, JSCE-1997, and BS-8110). The existing design codes significantly underestimate the concrete contribution to shear capacity, leading to uneconomical designs. In contrast, the new design equation provides a fair prediction of Vc, with a standard error of 7.734 % and 20.84 % compared to the FE and experimental datasets, respectively. This represents a substantial improvement over the existing design guides.

A Deep Learning-Informed Design Scheme for Shear Friction at Concrete-to-Concrete Interface: Recommendations for Inclusion in AASHTO LRFD Guidelines

Recent advancements in construction technology have led to high-strength concrete and steel. However, these developments have depreciated the accuracy of the design equations in current provisions, which were based on normal-grade materials. To fill such a research gap, this study presents a novel deep learning-based computation scheme that can replace the current design provisions by virtue of its superior accuracy and reliability. The proposed approach exploits Neural Additive Models (NAMs) in which geometric and material properties associated with a normalweight concrete-to-concrete shear interface are inputted to individual neural network blocks. The outputs of the individual blocks are linearly combined to produce the prediction for interfacial shear strength. This model provides a way to identify and quantify the individual contributions of the input parameters, thus enhancing the interpretability of the model predictions for shear strength at the normalweight concrete-to-concrete interface. The deep learning-informed design (LID) scheme improves the prediction accuracy of the shear strength equation in the existing AASHTO LRFD Bridge Design Specifications by over 32%.

Anchor conditions for estimated unsaturated shear strength functions

Since the mid-1990s, several empirical unsaturated shear strength equations have been proposed for use in geotechnical engineering practice. Most of the equations have been based on information associated with the measured drying soil-water characteristic curve (SWCC) in combination with the effective shear strength parameters of the saturated soil. There have been few studies, however, undertaken on verifying and comparing the suitability of the proposed unsaturated shear strength equations. This study involves consideration of a wide range of possible drying SWCCs plotted as a relationship between the degree of saturation and suction (saturation soil-water characteristic curve ( S-SWCC)). The study forms the basis for comparing five methodologies that have been proposed for the estimation of the shear strength of unsaturated soils. The SWCCs are defined by the fitting parameters for the Fredlund and Xing (1994) sigmoidal equation. This study supports the use of unsaturated soil shear strength empirical estimation methods using the S-SWCC anchor points of air-entry value and residual suction of the soil.

Improved Shear Strength Equation for Reinforced Concrete Columns Retrofitted with Hybrid Concrete Jackets.

The adequacy of retrofitting with concrete jacketing is influenced by the bonding between the old section and jacketing section. In this study, five specimens were fabricated, and cyclic loading tests were performed to investigate the integration behavior of the hybrid concrete jacketing method under combined loads. The experimental results showed that the strength of the proposed retrofitting method increased approximately three times compared to the old column, and bonding capacity was also improved. This paper proposed a shear strength equation that considers the slip between the jacketed section and the old section. Moreover, a factor was proposed for considering the reduction in the shear capacity of the stirrup resulting from the slippage between the mortar and stirrup utilized on the jacketing section. The accuracy and validity of the proposed equations were examined through a comparison with the ACI 318-19 design criteria and test results.

Block shear and tear-out in bolted connections as limited by curling

In the literature, the block shear and tear-out phenomena and strengths of cold-formed steel bolted connections have been well understood and thoroughly investigated. However, the strength of these failure modes in the bolted connections between thin and thick plates may be governed by the effect of out of plane curling of the thin plate, and this phenomenon has not been studied in detail yet. It is apparent that the curling not only affects the shear strength but also changes the behaviour of the bolted connections. In particular, the design shear strength of the bolted connections remains unchanged with high ductility even though the end distance between the bolt holes and the free edge is becoming larger. An experimental program on the block shear and tear-out behaviour of bolted connections was performed at the University of Sydney in order to provide a better understanding on the effect of the curling. A total of 48 tests including thicknesses of thin plates (1.0 mm, 1.2 mm and 1.9 mm) and 10 mm thick plates was conducted at the University of Sydney with three configurations of bolted connections in conjunction with two different hole diameters (9 mm and 14 mm) and various end distances as the main variables. Three different failure modes being block shear, tear-out and curling were observed in the tests. In addition, different material properties of the cold-formed sheet steels (i.e., G300, G450, G500 and G550) were also considered in this program to create a large database for the investigation. Consequently, a design equation for block shear and tear-out strength accounting for the curling effect is proposed in this paper. It provides a better correlation with the experimental results than those predicted in the current Australian and New Zealand Standard (AS/NZS 4600) and the North American Specification for cold-formed steel structures (AISI S100). In addition, a calibrated Finite Element Model (FEM) was subsequently developed using the commercial finite element program ABAQUS to verify against the test results. The reliable data set of the FEM models is further utilised to extend the data range in a parametric study and is finally used for the verification procedure of the proposed formula over a wider range of data.