Pseudo-static Method Research Articles

Research on the Dynamic Response of a Bedding Rock Slope Reinforced by Pile–Anchor Structures Under Earthquakes: A Case Study of a Section of the Duyun-Shangri-La Expressway Project in Ludian County, Yunnan Province, China

Pile and anchor structures are extensively employed for slope stabilization. However, their dynamic response under seismic loading remains unclear and current seismic designs primarily use the pseudo-static method. Here, a three-dimensional numerical simulation of the dynamic behavior of a bedding rock slope supported by pile–anchor systems under earthquakes is conducted. The dynamic calculation for the slope subjected to seismic forces with varying excitation directions and acceleration amplitudes is performed. The dynamic behavior of both the slope and the pile–anchor system is investigated with respect to the slope’s failure mode, the dynamic soil pressure behind the pile, the anchor axial force, the bending moment, and the lateral displacement of the pile. The results indicate that the anti-slide piles cause a reflective and superposition effect on seismic waves within weak rock layers. As the input seismic intensity increases, the axial force in the anchor cables also increases, with the peak axial force occurring during the main energy phase of the seismic waves. The dynamic soil pressure acting behind the piles varies with the stratification of the slope rock layers, with lower peak dynamic earth pressure observed in weak layers. The weak layers on the slope surface experience through-shear failure. Under strong seismic loading, the structural element state undergoes significant changes.

Component and System Reliability Assessment of Landfill Cover Systems Using Pseudostatic and Pseudodynamic Methods

Component and System Reliability Assessment of Landfill Cover Systems Using Pseudostatic and Pseudodynamic Methods

3D seismic bearing capacity of rectangular foundations near rock slopes using upper bound method

The analysis of foundation's bearing capacity is generally conducted under the assumption of plane strain. However, the damage of rectangular foundation usually presents obvious three-dimensional (3D) effect. This article considers this 3D effect, which, for the first time, provides a theoretical framework for assessing the bearing capacity of rectangular foundations placed on rock slopes under seismic condition. In order to apply the kinematic method of limit analysis, a new 3D kinematically admissible collapse mechanism is first constructed. Owing to the point-to-point discretized technique, this 3D mechanism can avoid complex surface integration and effectively reduce spatial coordinate iterative calculations while maintaining high accuracy. The pseudo-static method is adopted to simulate the effects of earthquakes. Generalized multi‑tangential technique is employed to derive the Mohr-Coulomb constants from Hoek-Brown criterion. The comparison between the present results and results of previous literatures proves the validity of the theoretical framework in this paper. Shape factor and reduction factor are introduced in the parametric study, showing that the 3D effect is more obvious when the rectangular foundation aspect ratio is reduced. As the rectangular foundation location moves away from the slope, its bearing capacity gradually converges towards that of the horizontal foundation. The critical collapse mechanism is also explored, demonstrating that the collapse extent expands with increasing internal friction angle of the rock.

Seismic stability charts for three-dimensional rock slopes using Hoek–Brown criterion

Seismic excitation serves as a crucial trigger for slope collapse in seismically active regions. This study employs the non-linear shear strength reduction (SSR) technique in conjunction with the pseudo-static method to analyse the seismic stability of three-dimensional (3D) rock slopes following the generalised Hoek–Brown (GHB) criterion. Considering the non-linear characteristics of the GHB envelope, the instantaneous Mohr–Coulomb (MC) parameters for rock masses are identified by locating the tangent at the intersection of the GHB envelope with the shear and normal stress planes. These parameters are subsequently incorporated into the non-linear SSR analysis for seismic stability based on the MC criterion. The non-linear SSR technique is then validated by comparing the calculated factor of safety (FOS) with those from other methods and used to assess the impact of geometric and GHB parameters on the FOS of 3D rock slopes. Finally, a set of seismic stability charts for 3D rock slopes in GHB media has been developed and applied to evaluate the seismic stability of two practical rock slope cases following the GHB failure envelope.

Seismic analysis of geosynthetic-reinforced soil walls in tiered configuration

Research on geosynthetic-reinforced soil (GRS) walls in tiered configurations is increasing gaining attention, with numerical methods being predominantly used in the past. In recent years, there has been a growing trend in conducting shaking table tests to further explore this area. However, traditional limit equilibrium (LE) methods are more preferred for design purposes. This study utilized a modified top-down approach, which is based on LE and pseudo-static methods to investigate the horizontal seismic force on the distribution of required tension along each reinforcement layer. The approach is initially extended from static analysis to seismic analysis for multitiered GRS walls. Parametric analyses are conducted to study the impacts that horizontal seismic coefficient, reinforcement length and spacing, internal friction angle of soil, height ratio of upper/lower tier, offset distance have on the internal stability of two-tiered GRS walls. Meanwhile, influences of wall batter and number of tiers on the critical offset distance for different seismic coefficients are assessed. Results indicate that the internal stability differs between the upper and lower tiers under seismic conditions, particularly with higher seismic forces, where the lower tier requires greater reinforcement tension to enhance its stability. Additionally, the critical offset distance grows with the increase in seismic coefficient, and it is sensitive to the internal friction angle of soil and the height ratio.

Seismic Stability Study of Bedding Slope Based on a Pseudo-Dynamic Method and Its Numerical Validation

Earthquakes are one of the main causes of bedding slope instability, and scientifically and quantitively evaluating seismic stability is of great significance for preventing landslide disasters. This study aims to assess the bedding slope stability under seismic loading and the influences of various parameters on stability using a pseudo-dynamic method. Based on the limit equilibrium theory, a general solution for the dynamic safety factor of bedding slope is proposed. The effects of parameters such as slope height, slope angle, cohesion, internal friction angle, vibration time, shear wave velocity, seismic acceleration coefficient, and amplification factor on stability are discussed in detail. To evaluate the validity of the pseudo-dynamic solution, the safety factors are compared with those given by early cases, and the results show that the safety factors calculated by the present formulation coincide better with those of previous methods. Moreover, a two-dimensional numerical solution of bedding slope based on Mohr–Coulomb’s elastic–plastic failure criterion is also performed by using the finite element procedure, and the minimum safety factor is essentially consistent with the result of the pseudo-dynamic method. It is proved that the pseudo-dynamic method is effective for bedding slope stability analyses during earthquakes, and it can overcome the limitations of the pseudo-static method.

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek–Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis.

Seismic Performance Assessment for Serviceability of Geosynthetic Reinforced Embankments

Embankments in the field of civil engineering were historically not given much attention in terms of their ability to withstand seismic activity, as they were considered to be non-critical structures. However, in recent years, the seismic stability of embankments has gained increasing importance in the field of geotechnical engineering. This increased significance is due to the need to quickly restore functional infrastructure after earthquakes. The occurrence of lateral spreading, resulting from foundation liquefaction, is the primary factor leading to embankment distress in geotechnical engineering during seismic events. To address this issue, this study presents a novel approach that employs geosynthetic basal reinforcement. The research paper presents a technique that uses geosynthetic basal reinforcement to manage the lateral spreading of embankments both pre- and post-earthquakes, guaranteeing their ongoing effectiveness. The proposed approach utilizes a pseudo-static limit equilibrium method for determining the tensile load produced in the basal reinforcement. The serviceability criteria establish the maximum strain permitted in the basal reinforcement by imposing a restriction on the horizontal movement of the embankment toe. By taking into account the tensile load of the reinforcement and the maximum allowable strain, it is feasible to establish an appropriate geosynthetic reinforcement that considers various factors including tensile strength, strain, design life, installation, and durability impacts.

Critical Face Pressure of a Tunnel Driven by a Shield Machine Considering Seismic Forces and Tunnel Shape Influence

Evaluating critical face pressure with high accuracy is an important topic for shield tunneling. The existing research focuses more on the influence of complex geological conditions or environmental factors, and there are few reports on the influence of tunnel shape on critical face pressure. In reality, the tunnel shape has a significant impact on the deformation zone in front of the tunnel face, which may lead to non-negligible differences in shield pressure. To fill this gap, an efficient analytical approach is proposed to estimate the critical face pressure considering different tunnel shapes in the framework of limit analysis. As earthquakes are potential threats to the tunnel face stability in seismically active regions, the seismic effect is also taken into account with the help of the pseudo-static method. Several cases with the same area but different tunnel shapes are investigated using the limit analysis method. A comparison with static analysis is given to highlight the influence of seismic forces on the tunnel face stability. The results show that the critical face pressures increase by 15.3% when the tunnel face shape changes from rectangular to circular, and by 23.5% when the horizontal seismic coefficient varies from 0 to 0.1. A further validation with a 3D finite difference method is performed with respect to four typical tunnel shapes considered in this study. Lastly, several stability charts are provided for a quick estimation of the critical tunnel face pressure subjected to seismic forces. It is concluded that the proposed method can be applied to a tunnel stability assessment of various cross-sections and is highly efficient compared with numerical simulations.

Numerical Investigation of Seismic Behaviour for a Flexible Cantilever Retaining Wall with Cohesive Backfill

In the seismic design of flexible cantilever walls retaining cohesive backfill soil, the common practice is to neglect the cohesion effect. Dynamic lateral earth pressure is typically evaluated based on approaches primarily intended for cohesionless soils or through analytical pseudo-static methods. Nevertheless, both experimental and theoretical evidence has demonstrated significant effects due to soil cohesion that are not accounted for by these methods. This study involved finite element modeling (FE) of a flexible cantilever wall with a height of 5.4m, supporting homogeneous cohesive backfill under initial static and seismic loadings. The calculated active earth thrust was then compared with values obtained experimentally and through conventional analytical methods. The obtained results indicate that the presence of soil cohesion significantly reduces seismic demands on flexible cantilever retaining walls, resulting in a substantial reduction of seismic active earth pressures and total seismic thrust by up to 50% and 52%, respectively. It enhances also the overall stability of the system by shifting the point of application of seismic thrust toward the base of the wall, thereby increasing the safety margin. In addition, it significantly decreases the wall displacement at the stem top, with reductions of up to 104% compared with the case involving cohesionless backfill. It was observed that the conventional methods recommended by some seismic regulations largely underestimate seismic active pressure.

Comparison and study of different seismic calculation methods for underground stations in Shanghai

In terms of seismic design methods for subway stations in the Shanghai area, both national and local standards have presented several pseudo-static methods, including response displacement, response acceleration, equivalent earthquake acceleration, and equivalent inertial force methods. However, certain issues are encountered when these methods are applied to the seismic design of real subway projects. The load input and results obtained from different calculation methods differ from each other. To address such discrepancies and compare the diversity of different methods, this study performs a comparative analysis based on the project case of a ground station in Shanghai. The seismic design is conducted using five different calculation methods. By referring to the results of the dynamic time history analysis, the causes of errors in the calculation results of the displacement and internal force are analyzed. The applicability of the methods is comprehensively explored in terms of a calculation model, determination of the equivalent load, error in the results, and project application. The results show that the response acceleration method exhibits the least error compared to the dynamic time history method. Therefore, the response acceleration method is recommended as the preferred method for the seismic design of underground stations in Shanghai.

Seismic performance and skeleton curve model of prefabricated coral aggregate concrete-filled aluminum tube joint

Corrosion-resistant and high load-carrying capacity coral aggregate concrete-filled aluminum tube (CCFAT) structures show promising applications in island construction. However, research on CCFAT joints related to structural safety remains scarce. To advance the engineering application of this structure, a novel prefabricated CCFAT beam-column semi-rigid joint with bolt connections is designed in this study. The seismic performance of the joint is investigated through a pseudo-static method, analyzing the effects of each parameter on failure mode, hysteresis curve, deformation characteristics, and energy dissipation performance, considering the earthquake-prone nature of islands. The primary objective of this study is to explore the influence of different parameters on the seismic performance of the CCFAT joint and establish the moment-rotation relationship of this joint. It is observed that the ultimate moment relationship between the beam and connector significantly impacts the failure mode of the joint, thus affecting its seismic performance. Hence, prioritizing the ultimate moment relationship between the beam and connector in the design phase is crucial to avoid undesirable joint failures. The skeleton curve of CCFAT joints differs significantly from that of steel and reinforced concrete structures, rendering existing joint theories inapplicable to CCFAT joints. Considering joint material, structure, and failure mode, this paper proposes a theoretical calculation method for the initial stiffness and ultimate moment of the CCFAT joints. This method is based on the component method and mechanical model, establishing an exponential three-parameter skeleton curve model for the joint. This model enables an accurate prediction of the moment-rotation relationship of the CCFAT joint, aiding in its seismic performance evaluation.

Analysing Slope Stability in Response to Blast-Induced Dynamic Loading by Pseudo-Static Approach

Regular blasting in opencast coal mines generates significant ground vibrations, impacting mine slope stability and posing risks to life and property. This study focuses on monitoring ground vibrations in an opencast coal mine through near-field monitoring and investigating the impact of blast-induced seismic loading on slope stability. The approach involves a pseudostatic method utilising Strength Reduction Factor (SRF), based on Finite Element (FE) numerical modelling software. The study examines a pit slope with a tension crack under seismic loading, varying the intensity of seismic coefficients (Ks) from 0 to 0.5. These coefficients are determined through field vibration monitoring during production blasts. In numerical modelling, seismic loading is considered in both horizontal (outward of slope face) and vertically downward (in-line with gravity). Numerical modelling incorporates dimensionless horizontal seismic coefficient (Kh) and vertical seismic coefficient (Kv), and both directions which is expressed as Seismic Coefficient Ratio (SCR) which is the ratio of Kv and Kh for interpretation of results. Although SCR induces changes in the Factor of Safety (FoS), its impact is minimal compared to seismic loading solely in the horizontal direction. Consequently, increasing SCR leads to a decrease in FoS. The study observes that Peak Ground acceleration (PGA) in the longitudinal direction has greater dominance than in the transverse direction. Additionally, the seismic wave in the horizontal direction destabilises the slope more than the corresponding vertical seismic wave. These findings are elucidated in the context of the Critical Slip Surface (CSS).

Numerical Simulation of Polymeric Strap Material Reinforced Walls Under Seismic Excitation

This paper presents a comparison between the two-dimensional finite element and experimental results of shaking table tests on six one-third-scale polymeric strap or polymeric geostrip reinforced walls performed under seismic excitation at given peak ground accelerations [Formula: see text]. The effects of initial tangent stiffness or the stiffness of polymeric strap material [Formula: see text] and the slope angle of the cohesionless backfill material [Formula: see text] on the maximum relative displacement, [Formula: see text], of the reinforced earth wall, the values of the horizontal incremental dynamic earth pressure [Formula: see text] with distributions, acceleration responses, horizontal dynamic active earth pressure coefficient [Formula: see text] and maximum dynamic tensile forces [Formula: see text] were assessed in this study. Moreover, the vertical dynamic active earth pressure coefficients [Formula: see text] and the angles of the resulting dynamic active force with horizontal [Formula: see text] were predicted from the numerical analysis. Closely matched responses between the experimental and numerical studies were attained. Data obtained from experimental and numerical studies illustrated that increasing the slope angle of the cohesionless backfill material resulted in an increase in the values of horizontal displacement in the walls, and in dynamic earth pressure and root mean square acceleration [Formula: see text]. Increasing the stiffness of the reinforcement material caused a decrease in horizontal reinforced earth wall displacement and increases in dynamic earth pressure. In addition, the conventional pseudostatic limit equilibrium methods overestimated [Formula: see text] values, whereas they underestimated [Formula: see text] values, and the recommended [Formula: see text] values by current design codes were not found to be compatible with the numerical and experimental results.

Experimental study on seismic performance of stainless steel full-scale frames: Global response

This paper presents an experimental study of the seismic performance of austenitic stainless steel full-scale frames using the pseudo-static test method. The bottom single-span, two-storey substructure of the designed prototype frame was chosen as the test frame. Two full-scale frames were tested, one with a bolt-welded joint and the other with an extended end-plate joint. This paper is the first of two accompanying papers to this experimental study and focuses on the specimen design, testing details and global response of the stainless steel frame under cyclic loading. The test results were utilized to analyse the global response of the frames, encompassing failure mode, bearing capacity, deformation capacity, energy dissipation capacity, the overstrength factor, ductility factor and seismic response modification factor. The experimental findings suggest that the stainless steel frames with two joint types demonstrate consistent ability to dissipate energy during cyclic loading. The structure also performs well in terms of deformation, with uniform inter-storey deformation and no soft-storey detected. The maximum storey drift ratio of the frame is 7%. Prior to reaching a storey drift ratio of 2%, the frames with both joint types exhibit similar cumulative plastic deformation, stiffness degradation, and cumulative energy dissipation.

Numerical and analytical studies on the coupling effects of unloading and cutterhead vibration on tunnel face in dry sandy ground

When tunnelling in difficult ground conditions, shield machine would inevitably produce significant ground loss and vibration, which may disturb the ground ahead of the tunnel face. In this paper, discrete element models calibrated by model tests were established to investigate the response of tunnel face under the coupling effects of unloading and cutterhead vibrations. The results show that the friction angle reduction under cyclic loading and vibration attenuation in the sandy ground are significant and can be estimated by the fitted exponential functions. Under cutterhead vibration, the tunnel face stability is undermined and the limit support pressure (LSP) increases to 1.4 times as that in the static case with the growth of frequency and amplitude. Meanwhile, the loosening zone becomes wider and the arching effect is weakened with the reduction of peak horizontal stress and the increase of vertical stress above the tunnel. Based on the numerical results, a pseudo-static method was introduced into the limit equilibrium analysis of the wedge-prism model for calculating the LSP under vibration. With an error rate less than 5.2%, the proposed analytical method is well validated. Further analytical calculation reveals that the LSP would increase with the growth of vibration amplitude, vibration frequency and covered depth but decrease with the increase of friction angle. This study can not only lay a solid foundation for the further investigation of ground loss, ground water and soft-hard heterogeneous ground under cutterhead vibration, but also provide meaningful references for the control of environmental disturbance in practice.

Revisiting the face stability of rock tunnels in the Hoek–Brown strength criterion with tension cutoff

AbstractIn this work, the three‐dimensional stability of deep tunnel faces is evaluated in rock masses characterized by the generalized Hoek–Brown (H–B) criterion from the perspective of the limit analysis theorem. Considering that underground engineering is gradually developing towards larger burial depths and larger sizes, and the tensile strength of rocks is usually overestimated, the concept of tension cutoff (T‐C) is introduced to substitute the parabolic form of the H–B envelope in the tensile region with a circular arc. The multitangent technique is used to piecewise approximate the H–B envelope, instead of the conventional linear substitution, accounting for the nonlinear dependence of the shear strength on the pressure. Meanwhile, the earthquake loading is considered by the classic pseudostatic method. The tunnel face stability is measured by a stability number, which is calculated based on a newly developed multicone failure mechanism. Parameter studies indicate that the T‐C has almost no impact on the critical support pressure, while has a significant effect on the critical stability number, especially in the presence of earthquakes. Nearly all stress points back‐calculated from the rupture angles fall within the T‐C region, except for the first stress point associated with the first segment. Interestingly, the influence of the geological strength index (GSI) on the face stability is inverse to that of mi due to the brittleness of rocks. Moreover, the critical stability number is not sensitive to mi, but sensitive with the introduction of earthquake loadings.

Behavior of large SCFST column with different confinement effects under pseudo-static loading

In this study, tests of twenty-four square concrete filled steel tubular (SCFST) columns with different structural sizes by the pseudo-static method were conducted to investigate the influence of the confinement effects. In addition, the structural size and the confinement effect are respectively represented by column width and width-to-thickness ratio. The experimental results, including the failure mode, the lateral load-displacement curves and the indices of the seismic performance were recorded and analyzed. The mode of failure is typical compressive flexure pattern. As the structural size increases or the confinement effect decreases, the nominal flexure strength of SCFST column decreases. Compared of the nominal flexural strength of small column, the influence of confinement effect is more significant on that of large column. The displacement ductility coefficient, the mean energy dissipation factor and the relative stiffness decrease with the increasing column width. Then enhanced confinement effect has no obvious influence on the displacement ductility coefficient of the SCFST column. When the confinement effect increases, the energy dissipation capacity of the SCFST column increases. Finally, the modified calculated method considering size effect is established, and this method is applicable to predict the bending moment of the SCFST column with different confinement effects and structural sizes.

Investigating the Strength Characteristics of Reinforced Concrete Grouted Sleeve Connections in Seismic Zones

Four precast columns with vertical grouted splice anchor connection are simulated using the pseudo-static method while the cast-insitu columns are the control group to assess the performance of the precast concrete members having steel sleeve connections. The result showed that the cracking modes of the precast columns and the cast-in-place columns are identical, however, these variations come into play when considering the pattern distribution of fractures. The insitu columns are usually base cracked horizontally and much higher diagonally descending fractures at their sleeves while prefabricated columns experience higher sleeves horizontally cracked followed by descending diagonally high at their bases. Also, additional cracks progress into the beam within a high range of 300 mm that appear on the underside of the beam. The hysteresis curves for prefabricated columns are generally stably shaped, signalling the fact that such structures are prone to dissipate or absorb energy. In addition, the rate at which the stiffness of the prevailed prefabricated specimens reduces is lull compared to the rate at which the stiffness of the wet-cast specimens reduces. A base mold of columns with a minimum displacement angle of 0.55 degrees is used and it is an appropriate displacement ratio for the design of large earthquakes. At the very end this given paper recommends the best way to do the construction of the Earthquake Framework applying precast concrete constituents with the grouted secured joinages.

Response Displacement Method for Seismic Calculation of Subway Station Complex Structure of TOD Mode

The TOD mode with rail transit stations as the center has become an important direction of future central city construction. However, at present, there is still a lack of simplified calculation methods for the seismic design of a subway station complex structure of TOD mode. Based on the load-structure model of the classic response displacement method and the seismic deformation characteristics of the underground complex structure, an improved response displacement method for seismic calculation of the subway station complex structure considering the influence of the upper frame structure was proposed in this paper. Then, based on the actual engineering case, the applicability of the improved reaction displacement method was verified through investigating the influencing factors such as seismic wave type, ground motion intensity, building position, structure form, structure stiffness, and stratum stiffness. Furthermore, a series of numerical simulation experiments were conducted to verify the simplified method and further evaluate its computational accuracy. The result shows that the error in calculating the internal force and deformation response of a station complex structure by using the improved reaction displacement method can be controlled at about 10%. The improved response deformation method is proved to be a highly practical pseudo-static method.