Pseudo-static Conditions Research Articles

SOIL SLOPE REINFORCEMENT USING CANTILEVER RETAINING WALL ON THE WEST RING ROAD OF SADAWARNA DAM, SUBANG DISTRICT

The research was conducted in the West Ring Road of Sadawarna Dam, Subang Regency. This research aims to provide recommendations for the design of cantilever retaining wall to increase the value of the slope safety factor in the research area. Calculation of the value of the slope safety factor uses the limit equilibrium method with the Janbu calculation method. In actual conditions, the value of the slope safety factor shows an unstable value referring to SNI 8460:2017, namely in static conditions with a vehicle load is 1.31 and in pseudostatic conditions with a vehicle load is 1.083. Slope strengthening was carried out using cantilever retaining wall. The retaining wall design that has been made meets the criteria for stability against overturning, stability against sliding, and stability for the bearing capacity of the soil. The safety factor value for slope with retaining wall shows a stable FS value referring to SNI 8460:2017, namely 1.53 in static conditions with vehicle loads and 1.11 in pseudostatic conditions with vehicle loads. Keyword: slope, safety factor, retaining wall, cantilever

GCL-LLDPE geomembrane interface friction angle evaluation and stability analysis of a valley fill leach pad project

The Los Chancas mining project, initiated in 1998, is a copper mine focused on extracting copper sulfides and oxides. In 2020, a mine plan update required a review of the constructability design and an evaluation of the Permanent Leach Pad and Filtered Waste/Rock Dump's physical stability. This paper presents results from an evaluation study regarding friction angles at the liner interface and stability analysis in the VLF pad. Previously, an internal friction angle of 23° was established for the basal liner interface (LLDPE-GCL) to meet stability requirements. However, due to the high required friction angle, the pad design was updated with lower slopes. The study evaluated various GCL materials from two suppliers using direct shear tests, revealing that the GCL from the second supplier achieved a high friction angle of 22.3° at the interface. Stability analysis considered two critical sections, examining three types of failure under both static and pseudo-static conditions. Results showed a need for a minimum friction angle of 16° in static conditions and 20.5° in pseudo-static conditions to ensure compliance. These results suggest the potential use of high strength geosynthetic materials in the studied areas, with a preference for the GCL material offering the highest friction angle.

Static and Pseudo Static Analysis of Embankment Slope Stability of Bener Dam, Purworejo Regency, Central Java

The Bener Dam is considered as one of the largest rock-fill dams in Indonesia. This dam will impact the inundation area of three main villages in the Wonosobo and Purworejo regency. Since this zoned embankment dam consists of rock-fill and the core material, the stability of the dam slope has to be done to ensure that the dam is stable against any failures including the seismic effects. Moreover, the seismic coefficient in the study area in the seismic analysis of the large dam slope is needed to be used in the analysis which is not yet done from the previous studies. This paper presents the analysis of the embankment slope stability of the Bener dam under static condition and pseudo static condition. The analysis takes into account the end stage of construction, the steady-state stage, and rapid drawdown stage. The results of utilizing the Finite Element Method to analyse the slope stability demonstrates that the dam embankment slopes are stable under static and seismic stress conditions in all the reservoir condition stages. After applying the seismic loading, the result of safety factor of slope stability is reduced while the rapid drawdown stage has the lowest safety factor.

The Effect of Geometrical Features of Release Surfaces on the Stability of Tectonically Disturbed Deep Rock Slopes in an Albite Open Pit Mine

An albite deposit formed in orthogneiss has been operated using open pit mining process since 1996. However, landslides have occurred following the excavation works and heavy rainfalls. In the current state, the slopes are still susceptible to mass movement. For this reason, this study aimed to determine the root causes that are influencing continuous movements. In this context, two geometric features of the strike-slip faults that form tectonic slices in the pit were proposed. The first one (α-angle) is the acute angle between the dip direction of the overall slope and the general trend of the strike-slip fault and it was used for the kinematic evaluation of the sliding potential of the tectonic slices. The validity of α-angle was confirmed by investigating its relationship with the factor of safety values. The second one (undulation angle, i) was used to determine the effective surface friction angle (ϕeff). Thereafter, ϕeff value was used in the deterministic finite element (FE) slope stability analyses as well as back analyses. Its effect on the stability of overall slopes was investigated for static and pseudo-static conditions with different water table levels. The FE results confirmed the monitored field displacement measurements. It was found that as α-angle decreases, the ability to resist sliding also decreases since the low α-angle promotes block formation. This study also demonstrated that using the undulation angles on mapped profiles of large-scale discontinuities (≥270 m) would be a promising approach for slope stability assessments of open pit excavations in tectonically disturbed metamorphic rocks.

The effect of geological characteristics and earthquakes on natural slope stability analysis in landslide modeling using static and pseudostatic methods in Cianjur Area, West Bandung, Indonesia

The earthquake in Cianjur occurred on Monday, November 21, 2022. The epicenter was in Cugenang Subdistrict, Cianjur District, West Java Province. Cianjur is an area that is susceptible to landslides, which can be triggered by high rainfall and earthquake shocks. The Cianjur earthquake caused collateral hazard landslides that occurred in several locations. Based on the static and pseudo-static analysis, the pseudo-static analysis will provide information on how much the slope safety number decreases when earthquake loads are applied. This study aims (1) to calculate the safety factor value (SF) of slopes under static and pseudo-static conditions to assess the stability of the natural slope and (2) to determine the influence of geological characteristics and the Cianjur earthquake on slope stability analysis in landslides in Cianjur and its surroundings. Slope stability analysis was carried out using static and pseudo-static methods. This research result shows that the condition of the slopes of the study area before the earthquake occurred was in safe condition. The condition of the slopes in the study area experienced a decrease in the safety value of the slope from natural conditions to increased loads or earthquake shaking.

El impacto de incluir el coeficiente sísmico vertical kv en el análisis de estabilidad pseudoestático de tranques de relaves construidos con arenas mediante el método constructivo aguas abajo

In Chile, the limit equilibrium analysis under pseudostatic conditions is compulsory according to the Supreme Decree 248 (DS248, 2007), which establishes a minimum factor of safety (FoS) of 1.2 for stability analysis. In Chilean geotechnical practice, it is usually considered just the horizontal seismic coefficient (kh) for the analyses. However, there is a constant discussion about the necessity of applying both horizontal and vertical seismic coefficient (kv) into the analyses. In addition, there is uncertainty about what kv/kh should be considered and the effect that the sense of application (upward or downward) could have on the FoS. This paper presents an analysis of the effect of considering different |kv|/kh from 0 to 1 on both analysis directions for generic downstream tailings sand dam. Based on this, different dam heights, beach lengths and seepage conditions are also analysed. The obtained results show that when both kh and kv are applied, the FoS increase if kv acts downward and decrease when it acts upward. In addition, the effect for |kv|/kh ≤ 0.5 is almost neglectable, especially for kh ≤ 0.15. Furthermore, although a short beach length significantly impacts the FoS, the influence of applying both kh and kv seems to be independent of the beach length

Hill Dam Design to Improve Water Use in Rural Areas—Case Study: Sacachún, Santa Elena

The Sacachún commune in Ecuador currently faces a lack of water for its agricultural development; this reduces its possibilities of socio-economic development and causes migration to urban areas. This research proposes a presa colinar (hill dam) design that uses ancestral knowledge and classic engineering techniques to promote water use during the dry season in semi-arid regions. The methodology consisted of: (i) a systematic compilation of the ancestral structures used for water planting and harvesting in Ibero-American; (ii) selecting an appropriate place to build the hill dam; (iii) the dam’s body design; (iv) and creating a proposal for agricultural water use. The results helped define a good location for the hill dam implementation. In addition, a 10 m high and 40 m wide earthen dam was designed, with a storage capacity of 114,341 m3, extending agriculture to 7.5 ha through a polyculture system of six different plants. The embankment has a cofferdam located downstream, which provides stability in static and pseudo-static conditions. In addition, the dam slopes have a 2:1 ratio, and a spillway channel and filter drain were dimensioned to protect the dam.

DISPLACEMENTS AND STABILITY ASSESSMENT IN THE PORTAL OF TUNNEL 3, "EL SILLAR", THROUGH THE FINITE ELEMENT METHOD

As an application of geotechnical engineering, an analysis of portal stability of the exit of Tunnel 3, in the construction of the double lane central section "El Sillar" Cochabamba - Santa Cruz highway is presented. This study is carried out by using the finite element method FEM with the PLAXIS 3D software to determine the areas where slope stabilization of the portal is needed and the definition of the excavation construction method along with the support system for the tunnel. Later, the tunnel structure is evaluated. Initially, data compilation from geotechnical studies is done (pits, geomechanical stations, geophysical survey, in situ and laboratory tests on drilled rock cores) contrasted with proper bibliographic referenced ranges to obtain initial geomechanical conditions. Subsequently, mechanical parameters of the rock are calibrated by means of real deformations caused by the excavation of the tunnel in the portal with a plastic-type calculation. The calibrated model achieves the average measured deformation on the tunnel: 5 mm. Then, the stability analysis is carried out by means of a safety-type calculation to obtain global safety factors where different stabilization alternatives are assessed. In this way, the modification of the slope geometry is revealed as the most optimal solution. Subsequently, the construction stages of the tunnel are simulated by adopting the Belgium method, the largest number of supports is required, because it is a very unstable area. Finally, principal effective stresses and deformations for static and pseudo-static conditions are calculated and reach admissible values (6, 12 mm maximum deformation in the vault) and minimum safety factors were above minimum factors required by NSR-10: 1,25 and 1,0; assessing most optimal geometry considering reinforced and non-reinforced conditions in the tunnel at three different depths and lateral covers for the tunnel.

Generalized Interaction Diagrams for Caisson Foundations in Layered Soil under Seismic Conditions

Caissons are rigid foundations most commonly used to support bridge piers. In this study, numerical analysis using the finite-element method based computer program ABAQUS was carried out to study the response of caissons under static and pseudostatic conditions. The caisson was embedded in layered soil comprising a saturated clay layer sandwiched between two sand layers. Sand was modeled using an elastic, Mohr-Coulomb plastic model and clay was modeled using a porous elastic and clay plasticity model to account for soil consolidation. The wall friction angle (δ) and seismic acceleration coefficients (kh and kv) were varied in this study. Calculations were made by executing a mathematical code in MATLAB to obtain the lateral soil pressure, maximum and minimum base pressures, tilt, shift, and point of rotation of the caisson. The analysis was further extended to develop three-dimensional (3D) interaction diagrams relating the combination of applied vertical load (V), lateral load (Q), and moment (M) in nondimensional form required to cause caisson failure for different wall friction angles and seismic acceleration coefficients. These diagrams can be used for the safe design of caissons under different seismic conditions and ground conditions for a variety of design loads.

Numerical Stability Analysis of Undercut Slopes Evaluated by Response Surface Methodology

One of the most important tasks in designing the undercut slopes is to determine the maximum stable undercut span to which various parameters such as the shear strength of the soil and the geometrical properties of the slope are related. Based on the arching phenomenon, by undercutting a slope, the weight load of the slope is transferred to the adjacent parts, leading to an increase in the stability of the slope. However, it may also lead to a ploughing failure on the adjacent parts. The application of counterweight on the adjacent parts of an undercut slope is a useful technique to prevent the ploughing failure. In other words, the slopes become stronger as an additional weight is put to the legs; hence, the excavated area can be increased to a wider span before the failure of the slope. This technique could be applied in order to stabilize the temporary slopes. In this work, determination of the maximum width of an undercut span is evaluated under both the static and pseudo-static conditions using numerical analyses. A series of tests are conducted with 120 numerical models using various values for the slope angles, the pseudo-static seismic loads, and the counterweight widths. The numerical results obtained are examined with a statistical method using the response surface methodology. An analysis of variance is carried out in order to investigate the influence of each input variable on the response parameter, and a new equation is derived for computation of the maximum stable undercut span in terms of the input parameters.

Stability Charts for Pseudostatic Stability Analysis of Rock Slopes Using the Nonlinear Hoek–Brown Strength Reduction Technique

This paper presents a set of stability charts for the stability assessment of rock slopes that satisfy the Hoek–Brown (HB) criterion under various seismic loading conditions. The nonlinear Hoek–Brown strength reduction technique is used to conduct pseudostatic stability analysis of rock slopes subjected to horizontal seismic excitation. Based on an extensive parametric study, first, a set of stability charts with a slope angle of β = 45° under static and pseudostatic conditions are proposed by using ABAQUS 6.10 software. Second, the slope angle weighting factor (fβ) and the seismic weighting factor (fkh) are adopted to characterize the influence of slope angle (β) and horizontal seismic acceleration coefficient (kh) on the rock slope stability. Finally, the reliability of the proposed charts was validated by three typical examples and two case studies, and the results show that the values of the factor of safety (FOS) obtained from the proposed charts are consistent with the values from other methods. The proposed charts provide an efficient and convenient way to determine the FOS of rock slopes directly from the rock mass properties (γ and σci), the HB parameters (mi and GSI), the slope geometry (H and β), and the horizontal seismic coefficients (kh).

Pseudo-static bearing capacity of strip footing with vertical skirts resting on cohesionless slopes by finite element limit analysis

ABSTRACT Using vertical skirts as soil reinforcement in conjunction with strip footing can increase the bearing capacity of a footing located near a cohesionless slope. This paper adopted lower and upper bounds of finite element limit analysis (FELA) to compute the bearing capacity of a strip footing with vertical skirts resting on the cohesionless slope under pseudo-static condition. A wide range of efficient factors on the bearing capacity and the failure pattern are investigated. Design tables are presented to obtain the bearing capacity of a strip footing with vertical skirts resting on cohesionless slopes in terms of bearing capacity ratio (BCR). The results showed that the BCR is improved notably, by using vertical skirts in conjunction with a strip footing in all cases. Furthermore, the BCR is affected markedly by increasing kh . Also, the results of this study are compared with available solutions in the literature.

Comparative analyses of finite element and limit-equilibrium methods for heavily fractured rock slopes

Limit-equilibrium method (LEM) and finite element method (FEM) with shear strength reduction (SSR) technique are the most widely used analysis tools in slope stability assessment. Recently, researchers have reported that both factor of safety (FOS) values and failure surfaces obtained from LEM and FEM are generally in good agreement except in some particular cases. On the other hand, the consistency between two methods has not been adequately discussed for heavily fractured rock mass models by employing Generalized Hoek–Brown Criterion (GHBC). In this study, the FOS values and failure surfaces derived from LEM and FE-SSR based on GHBC were compared concerning static and pseudo-static conditions, various overall slope angles, geological strength index (GSI) values, and various water table levels. In this context, three homogeneous, highly fractured rock slope models with irregular geometry and different slope heights were generated by two-dimensional Slide and Phase2 software. Limit-equilibrium (LE) analyses were performed by Bishop, Fellenius, Morgenstern–Price, and Spencer techniques. The comparisons of global minimum FOS values for 431 cases and the effects of variables on two methods were investigated by statistical analyses. Consequently, it was determined that the difference between the FOS values are statistically significant. However, if the seismic coefficient is higher than 0.1 g, slope angle is higher than 34°, and the slope is assumed to be fully saturated, Morgenstern–Price is the most well-matched technique with FE-SSR than the others. For the same cases, the failure surfaces detected by Fellenius is more similar to the ones detected by FE-SSR.

The Generalized Coefficients of Earth Pressure: A Unified Approach

This paper offers an extension of Cauchy’s first law of motion to deformable bodies with internal resistance with application to earth pressures. In this respect, a unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed. Adopting Jaky’s (1944) sand heap hypothesis, modified suitably to accommodate the needs of the present research, the analysis led to generalized, yet remarkably simple in form, expressions for the “at rest”, active and passive earth pressure coefficients. The validity of the proposed coefficients is strongly supported by the fact that, under static conditions they are transformed into the well-known Rankine’s expressions for cohesive-frictional soils for the active and passive state. Comparisons with widely used solutions (e.g., Rankine’s and Mononobe–Okabe’s), design code practices (Eurocode 8-5; AASHTO), and results from centrifuge tests further support the validity of the proposed coefficients. In the framework of the present work, analytical expressions for the calculation of the depth of neutral zone in the state “at rest”, the depth of tension crack in the active state, the required wall movement for the mobilization of the active or passive state, as well as the mobilized shear strength of soil (for all states) are also given. Finally, following the proposed approach, the earth pressure can be calculated for any intermediate state between the state “at rest” and the active or passive state when the allowable wall movement is known.

A method for selection of optimum distance between twin tunnels under static and pseudo-static conditions, case study: Pooneh tunnel

Determination of optimum distance between twin tunnels is very important to reduce the construction’s costs in road or railway projects. When two tunnels are located close together, stress concentration in their space increases and it is possible that plastic zones would be merged. In mining engineering and especially underground mining applications, this zone (the distance between twin tunnels) is called pillar and there are some empirical models to estimate its width. However, these models are not completely suitable for all rock types and different tunnel geometries. In this study, an attempt was made to present a new criterion for the design of twin tunnels. It is based on ground reaction curve and takes width to height ratio (w/h) and shear strain of the pillar (obtained by numerical modeling) into consideration. Strain magnitude observed when normal stress (σ1) in the pillar reaches the value of compressive strength of the rock mass (σcm), denotes the allowable ratio of width to height (w/h) which shows the optimum distance between twin tunnels. Pooneh twin tunnels which located in Iran were selected as a case study. These are road twin tunnels excavated in layers of nine different zones (Arak–Khoramabad Expressway). Results of the suggested method show a good agreement between the pillar dimensions seen in the case study and the present method. Taking all aspects of geomechanical and geometrical characteristics of the tunnels into consideration, it is one of the main advantages of this method.

Strainburst phenomena and numerical simulation of self-initiated brittle rock failure

This paper focuses on ‘self-initiated’ strainbursts, and starts by providing an overview of these phenomena and their relevance to mining. This is used to set the framework for the numerical simulations presented in the second part of the paper. The numerical simulations examine and address challenges in modelling strainbursts related to the inherent difficulties in dynamic failure simulation. Existing methods either simulate dynamic failure under static or pseudo-static conditions while adopting some threshold factor (normally in terms of stress, strain, or energy) as an indicator of rockburst potential, or incorporate an assumed dynamic disturbance to cause rockburst damage. A distinct-element bonded block method is presented to simulate strainbursts. Instead of triggering failure by an assumed dynamic disturbance, the adopted method simulates the generation of a seismic event by self-initiated rock mass fracturing. This simulation of a self-initiated strainburst is interpreted using patterns of cracking, displacement and strain fields, ground velocities, and calculated kinetic and dissipated slip energies. The mechanisms of self-initiated strainbursting are successfully captured by the distinct-element bonded block method.

Integrated risk of rail buckling in ballasted tracks at transition zones and its countermeasures

Railway ballasted tracks at transition zones from embankment sections to bridge sections (or the reverse) suffer not only from seismic motions, but also from differential settlements during seismic motions. Therefore, an attempt is made in this study to evaluate the combined effects of hanging sleepers and seismic inertia force on the lateral resistance of ballast in the tracks at transition zones. A series of laboratory tests was conducted on 1/5 scale models to evaluate the lateral resistance characteristics under situations of hanging sleepers or under pseudostatic conditions. The results of the pullout tests revealed that the rail-buckling potential can be underestimated without the consideration of combined effects of hanging sleepers and the seismic inertia force on the lateral resistance. Based on the model test results, the combination of anti-buckling plates and ballast retaining walls is proposed as a new earthquake countermeasure.

Stability Evaluation of Slopes Using Kinematic and Limit Equilibrium Analyses in Seismically Active Balakot, KPK, Pakistan

The Northern segment of Pakistan, especially Balakot city is affected up to large extent by the landslides. Tectonically, it lies in the proximity of Hazara Kashmir Syntaxis and other two active regional faults: Main Boundary and Hazara Frontal Thrusts that traversing right through the Balakot town. This study focuses on the evaluation of slopes near Balakot town in static and pseudo-static condition. A geological map is produced at 1:24,000 scale to separate various rock and soil units. During reconnaissance study, two slopes were selected which seem prone to sliding. The procured data on condition of natural slope, properties of material entailed, structural setting, and vegetation cover distribution was gathered. Discontinuity Surveys of slopes were carried out to collect discontinuity parameters. Kinematic analyses were performed on DIPS v. 7.0 to assess mode of failures based on joints data. Limit equilibrium analyses were carried out at Slide v. 7.0 to check factor of safety at different conditions. The study concluded that the slopes were affected by the plane, wedge and toppling failures, while although in seismically active zone, circular failure is not likely.

Slope stability assessment and design of remedial measures for Tungnath Temple at Uttarakhand, India: a case study

The present paper assesses the slope stability of the Tungnath Temple at Rudraprayag District, in the Indian state of Uttarakhand, and suggests the remedial measures. The temple is made of stone masonry and is believed to be over 1000 years old. Recently, signs of distress such as the development and subsequent widening of the cracks were observed on the walls of the temple. The field investigation reveals that the inadequate stability of the site, stagnation of water at the foundation level of the temple and poor drainage of the rainwater from the upper hill are the primary causes of distress for the temple. The factor of safety (FoS) values computed using the limit equilibrium method indicate that the site is marginally stable (FoS—0.8 to 1.0) under static condition and unstable (FoS—0.6 to 0.9) under the pseudo-static condition for a particular section. Thus, suitable control measures have been proposed to ensure the long-term stability of the site. The proposed control measures include the construction of a geosynthetic lined drain at critical locations and geosynthetic lining in the periphery of the temple to prevent the ingress of water. Additionally, the construction of two levels of gabion wall (6 m to 8 m high) at the periphery of the site has been proposed to improve the stability. The paper discusses the possible causes of the cracks, slope stability analysis and subsequently present the design details of the remedial measures for the long-term stability of the temple.

Non-dimensional analysis for rock slope plane failure in seismic (pseudostatic) conditions

This study examines plane failure analysis of rock slopes and discusses its effect on seismic actions in a non-dimensional form, incorporating external loads transferred by anchors and stability indicators such as the depth of tension cracks and the failure plane dip. The results of limit equilibrium analyses, in terms of attained level of safety, are summarized in stability charts which can be used for design and assessment. Following guidelines established by Eurocode EC7, the stability is assessed through the R/E ratio, i.e. the ratio of the resisting shear forces (R) acting on the sliding surface and those promoting sliding (E). The proposed stability charts can be applied to various common practical situations, in order to provide a preliminary - but quantitative - assessment of the rock slope stability. As an example of an application, the paper focuses on the stability of a rock mass located at the bottom of the southern slope of the “Sasso di Pale” mountain (Central Italy), at the outskirts of the village of Pale. As many other historical towns in Central Italy, due to their location close to rock masses, this site is particularly exposed to instability phenomena such as plane failure and rock wedge failure. The structural-geological survey allowed us to identify the main joint sets affecting the behavior of the rock mass and, accordingly, we examined the plane failure mechanism involving sliding along a single plane. Stability verifications in pseudostatic conditions have been performed by adopting the proposed charts, consistent with Eurocodes prescriptions.