Batter Angle Research Articles

Response of Batter Piles Subjected to Static and Seismic Loading: Review Study

Battered piles are beneficial when used as foundations where significant lateral resistance is required, which could result from extreme water waves, winds, soil pressures, massive hits of explosions, or earthquakes. Experimental and numerical research must focus on that direction to reveal how these foundations behave under different loading conditions. The present study reviews the investigations conducted on the performance of batter pile foundations and attempts to understand and cover various aspects related to this issue; after conducting the review, the results indicate that the negative battered piles provide an efficient lateral stiffness corresponding to positive battered piles and a vertical one. Also, lateral bearing capacity improved with the inclusion of battered piles. Moreover, batter piles respond better than vertical piles in liquefiable soil under seismic excitation. The current study also showed that the pullout capacity of batter piles increased with the batter angle.

Upper bound stability analysis of tiered geosynthetic-reinforced soil wall

The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in practice. This study is aimed at proposing an upper-bound stability analysis method of a tiered GRS wall. The proposed method was firstly validated by the existing results from the centrifuge test and the numerical method, and then a parametric study was performed to investigate the effects of the cohesionless backfill friction angle ϕ1 and the wall geometric parameters including the offset distance, the total wall height, the batter angle δ, the number of tiers n, and wall height ratio of adjacent tiers on the dimensionless equivalent earth pressure coefficient KT. The analysis results demonstrated that as the ϕ1 increases, the shear strength of backfill is enhanced and thus the KT or the total reinforcement tensile force decreases, and the KT decreases with the increase of the offset distance at the initial stage and then becomes stable when it reaches a certain critical value. For a fixed offset distance, the KT or the total reinforcement tensile force decreases with the increase of the δ. For the two-tiered GRS walls having the offset distance less than the critical value, the wall with the smaller wall height ratio has a larger KT. Further, the variation of the location of the critical failure surfaces of tiered GRS walls was presented in this study with the variation of the ϕ1 and the wall geometry.

Lateral load-carrying mechanism of driven battered minipiles

The lateral load-carrying mechanism of vertically installed and battered minipiles is evaluated using 1g-physical and numerical modelling. Single minipiles with batter angles of 0°, ± 25° and ± 45° are tested under lateral load in medium dense and dense sand. The minipiles are instrumented with fibre Bragg grated optic fibres to obtain a strain profile (two-dimensional) along the minipile shaft. A calibrated numerical model is further adopted to produce p–y curves for battered minipiles at various node deflections. The ratio of soil reaction of battered minipiles to vertically installed minipiles is observed to change with both deflection and depth of the minipile. An analytical solution is developed based on the decomposition of lateral load into skin friction and passive pressure for battered minipiles. A reduction factor is proposed that considers a decrease in passive pressure when the minipile is loaded in the opposite direction of the batter. The analytical solution is capable of accounting for soil properties, pile rigidity and the angle of inclination of battered minipiles. The analytical method is subsequently verified for cohesive soils using full-scale field results. The ratio of the ultimate lateral load of battered minipiles to vertical minipiles presented in the literature corroborated the findings of this study.

Laboratory study on bearing capacity of batter rock-socketed pile group under combined loads

The batter rock-socketed pile (BRSP) groups have been gradually introduced in practice to support not only the vertical load caused by overlying infrastructures but also the horizontal loads caused by waves and wind. A series of laboratory model tests were conducted to investigate the bearing capacities of the BRSP groups installed with their batter piles ranging from 0° to 20° under combined vertical and horizontal loads. It is found that the vertical ultimate bearing capacities nonlinearly increase with the increase of the batter angle with its optimum batter angle of 10°. The normalized vertical loads and horizontal ultimate loads are nonlinearly related to their relationship in an ellipse function. The plumb rock-socketed pile groups develop primarily a pair of shear forces and secondary bending moments due to the clockwise rotation under the pure horizontal loads. The BRSP group may fail due to the pile fracture near the pile cap in the form of the plastic hinge or compression failure at the base of the front pile. The corresponding load-displacement curves mostly have no peak or sudden downward trend.

Nonlinear earthquake response of integral abutment bridges on vertical and batter piles: A practical approach

AbstractThis paper presents a new finite element framework for seismic analysis of IABs (and other similar structures) on vertical and batter piles that takes into account nonlinear soil‐structure interaction. A previously developed macro‐element and linear impedance matrix are implemented in a time and modal domain solution, respectively. Detailed pseudo‐codes describing the implementation strategy for the macro‐element are provided. The solutions are validated using rigorous numerical models constructed in OpenSees MP. The software is further demonstrated by performing an extensive set of incremental dynamic analyses, where the effect of linear and nonlinear SSI, batter angle, pile spacing and asymmetric configuration is addressed and discussed.

Bearing behaviors and design method of laterally loaded batter pile groups (BPGs) in sand

In recent years, the batter pile groups (BPGs) are increasingly used in offshore engineering; however, the optimal and economic design of BPGs is still poorly understood. Therefore, in this study, the lateral bearing behaviors of a typical 2 × 2 BPG in sand are comprehensively investigated by experimental and numerical methods. Firstly, a 1-g scale model test was carried out to study the effect of pile inclination on the responses of BPGs under lateral loads. Secondly, a total of 44 finite element (FE) models considering various conditions are utilized to reveal the lateral load bearing mechanism of BPGs, and the influence of design indicators on the lateral bearing capacity (Hu) of BPGs is thoroughly studied through a parametric study. Finally, an empirical design method is proposed based on 32 numerical model results to predict the bearing ratio (γ) as well as the lateral bearing capacity of BPGs in sand. The results show that, as the batter angle (θ) becomes larger, the lateral bearing capacity increases, and the maximum bending moments of both front-row piles (FRPs) and rear-row piles (RRPs) decrease, which means the shadowing effect on the RRPs is also reduced. With the increasing of batter angle (θ), the improvement effect of the pile length on the lateral bearing capacity becomes more significant, and the enhancement effects of the pile diameter and the relative density of sand on the lateral bearing capacity are decreased. The conclusions derived from this study can provide guidance for the design of BGPs in practice.

Theoretical and Numerical Analysis of Cohesive-Frictional Backfill against Battered Retaining Wall under Active Translation Mode

The appropriate prediction of horizontal earth pressure against retaining walls can lead to a safer and more efficient design of such structures. Retaining walls are among the structures in which the arching phenomenon plays an essential role in distributing horizontal earth pressure. In this research, based on the limit equilibrium condition and considering the arching effect, a new theoretical method is proposed to estimate the earth pressure against a battered wall under translation movement with a cohesive-frictional backfill soil. A parametric study is conducted for assessing the effect of the surcharge pressure, cohesion, internal friction angle, wall–soil friction angle, and wall inclination on lateral earth pressure. In addition, a series of numerical models is employed to implement the finite difference method. The development of shear bands inside the backfill and the changes in earth pressure behind the wall are studied. The outcomes of the suggested analytical solution are compared with the numerical data as well as with some other theories. It is concluded that the proposed method is applicable to a wide range of cohesive-frictional soils retained with walls, covering a variety of batter angles and face frictional conditions.

A Numerical Analysis on Pullout Capacity of Batter Pile Groups in Sandy Soil

Batter piles or raker piles are the piles driven in the soil at an inclination with the vertical to resist inclined forces or large lateral loads. Battered piles are widely utilized to support offshore buildings, towers, and bridges since these structures are risky due to the exposure to overturning moments resulting from winds, waves, and ship impact. This paper used a three-dimensional finite element analysis using PLAXIS 3D software to study the effect of several variables that affect the behavior of batter piles in a group under pullout loads. The study is conducted on a steel pipe pile model embedded in a dry sandy soil with three different relative densities (loose, medium, and dense sand) at different inclination angles and three embedment ratios L/D of 25, 37.5, and 50, respectively. The finite element model was carried out on a pile group of 2×1 with different configurations. The numerical results indicated that for all pile configurations, the pullout capacity of the batter pile group increased when the embedded ratio and relative density increased, and the maximum value was attained at a 20° batter angle. Furthermore, batter pile groups with BB (group with two battered piles) configuration of (-20°, +20°) gave a high resistance to the pullout load compared to other configurations of the pile group. In addition, pile Groups with battered piles marked the resistance to the pullout load more than pile groups that contain only the vertical piles.

Investigation of the vertical responses of 2 × 2 square flexible batter pile groups in sand

The vertical bearing behaviors of the flexible batter pile groups in sand are investigated in this study. A series of model tests are carried out to study the effects of the batter angle (θ) on the vertical bearing capacities (V g) and distributions of internal forces of the pile groups. In addition, finite-element (FE) analysis is performed to explore the vertical bearing behaviors of the pile groups with various configurations, and the vertical bearing mechanism of the batter pile groups is analyzed. Moreover, a design method is proposed for predicting the bearing ratios (β) of the batter pile groups. The results show that the batter pile groups generally can provide higher vertical bearing capacities than the vertical pile groups with the same configuration. The batter angles for providing the greatest vertical stiffness are decreased with the increase of length–diameter ratio (R) and are not affected by the variation of relative density (D r). The predicting results obtained from the design method match well with the model test and FEM results. Some suggestions are proposed for guiding the application of the batter pile groups in practice engineering.

Kinematic response of vertical and batter pile groups in non‐linear soft soil

AbstractThis paper presents a comprehensive numerical study on kinematic response of vertical and batter pile groups in soft soil, where soil non‐linearity, batter angle, pile spacing and excitation frequency are related to pile‐cap displacements, rotations, maximum pile moments, shear forces and axial forces. The finite element model is constructed in OpenSees MP, and parallel computing is utilized for a better (faster) performance. Results reveal that soil non‐linearity has a profound impact on the kinematic interaction. Increasing batter angle decreases horizontal displacements but increases rotations. Batter pile groups yield lower spectral accelerations compared to vertical pile groups. For high , the spectral accelerations of the pile‐cap may be lower compared to the spectral acceleration of the seismic input motion. Estimation using non‐linear interaction factors conservatively estimates pile‐cap displacements and rotations, while roughly captures the effects with respect to batter angle and frequency content within the specified framework.

Consideration of batter angle in pseudo-static analyses of pile foundations

Inclined piles have been widely used in geotechnical practices due to the enhanced lateral stiffness of the foundations as a consequence of the lateral load transfer along the axial direction. However, the simplified analysis approach for this type of foundation is still not well-developed. Based on the conventional simplified seismic assessment of pile foundations, this paper proposes the pseudo-static analysis of inclined piles. Firstly, a series of three-dimensional (3D) numerical analyses was conducted using the OpenSees finite-element platform. The axial and shear capacities of single inclined piles embedded in a uniform soil continuum were investigated and compared with the capacities of vertical piles. Based on the results of the 3D numerical analyses, explicit relationships have been proposed to estimate the capacity ratios of inclined and vertical piles from the pile inclination, relative density of the soil, and the ratio of the stiffnesses of the pile and the soil. The properties of the soil springs, which were initially proposed for vertical piles, were then modified and adapted to the inclined condition. Finally, the modified springs were implemented in the pseudo-static method to evaluate the pile responses of four case studies from which a desirable agreement with the observations was achieved.

Battered minipiles in fine-grained soils: Soil-structure interaction

The ultimate lateral load capacity of battered minipiles is investigated in fine-grained soil via field testing equipped with optic fibre sensing and consequently complemented with finite element modelling. The numerical model developed in COMSOL Multiphysics was validated against (i) field-obtained force-displacement data of minipiles battered at 25° and (ii) strain profile along a vertical minipile shaft. The numerical model was then further used to predict force-displacement curves for minipiles with batter angles of 15°, 30° and 45° using the full-scale pile and field soil parameters. The model helps in understanding how the combination of normal and shear stresses along the minipile shaft leads to the optimum batter angle of 30° when subjected to lateral loading. Furthermore, a parametric study was performed to comprehend the effect of apparent cohesion and minipile length on the optimum batter angle. When the apparent cohesion of the soil was reduced, the optimum angle changed from +30° to +45° in the case of positive battered minipiles. A change in optimum batter angle was observed when the minipile length was increased as well. These varying parameters influenced the optimum batter angle of laterally loaded minipiles, and the numerically obtained normal and shear stress profile justified this behaviour.

Study on Vertical Piles Batter Piles and Pile Groups Under Uplift Load Conditions in Non-Cohesive Sub-soil

Model study was carried out in the laboratory to know the effect of uplift loads on vertical piles, batter piles and pile groups. Mild steel piles having 22 mm outer diameter and 1 mm thickness were considered for the study. Different slenderness ratios of 18, 28, and 38 and various angles such as 0°, 15°, 25°, 35°, and 45° were considered for the study. Sand was poured at a fixed relative density in the mild steel tank. The experimental study shows that the pile and pile group attain a maximum value of uplift load capacity when the batter angle reaches to 35°. Further, increase in batter angle causes a reduction in the uplift capacity of the pile. It is also noticed from the experiment that the uplift capacity increases with the slenderness ratio of the pile but its variation is not linear. Pile group of four piles with two vertical piles having L/D ratio 38 and two batter piles of L/D ratio 28 offers same resistance as of the same pile group with all the piles having L/D ratio 38. Numerical modeling was performed using Plaxis-3D to analyse the behavior of vertical piles, batter piles and pile groups under uplift loads. A good correlation between Plaxis-3D results and experimental results was observed.

Battered minipile response to low-frequency cyclic lateral loading in very dense sand

This experimental study investigates the response of vertical and battered minipiles to two-way symmetrical low-frequency (0.1 Hz) cyclic lateral loading. Laboratory (1-g) tests were performed on scaled-down minipiles in very dense cohesionless soil, for batter angles of 0°, 25° and 45°. The cyclic loading is classified into two categories: multi-amplitude and long-term single amplitude, where force-controlled load was applied at a constant frequency. The minipiles were instrumented with optic fibres, and strain profiles were obtained at each loading stage, in both compression and tension stroke. The results are presented in terms of hysteresis loops, variation of normalised stiffness, minipile strain and bending moments under cyclic loading. In the multi-amplitude loading category, backbone curves show a stiffer force–displacement response in tension stroke than in compression stroke. For the single-amplitude category, the area of the hysteresis loop is largest for 45° battered minipiles with the lowest accumulated deformation. The normalised stiffness at the end of 50 cycles is highest for 25° minipiles with a value slightly greater than one. The strain profiles along the minipiles show stabilisation of measured strain before the number of cycle reaches 50, for all three battered conditions. A multi-surface hardening constitutive model is used to explain the effect of shearing and cyclic loading, with increasing loading amplitude on 25° battered minipiles. These test results are indicative of better performance capability of 25° battered minipiles, in terms of secant stiffness, compared to the vertical and 45° battered cases.

Dynamic response of underreamed batter piles subjected to vertical vibration

ABSTRACT This paper presents the dynamic vertical response of a vertical and two batter piles with an underreamed bulb. Batter angles (i.e. inclination to the vertical) of 10 and 20 degrees have been considered. The dynamic vertical tests were conducted using a mechanical oscillator-motor assembly by varying the intensity of exciting force level with a change in eccentricity setting of the oscillator. The dynamic response was recorded in terms of operating frequency and acceleration response. The test data were analysed to estimate the dynamic vertical responses of the piles in terms of resonant frequency, f y ꞌ; peak vertical displacement amplitude, dyꞌ and axial strain εy , and they were compared. For all three piles, with an increase in intensity of exciting force level, the resonant frequency decreased, whereas the peak vertical displacement and axial strain increased.

1-g Shaking table tests to determine the behavior of geosynthetic reinforced soil walls under seismic loads

Geosynthetic reinforced soil structures are widely used to support and enable transportation infrastructure. Given the importance of the transportation infrastructure within the context of disaster resilience, it is crucial to fully understand the response of the elements which constitute and support the infrastructure assets. This study presents and discusses the results of four heavily instrumented large scale geosynthetic reinforced soil walls which were subjected to seismic loading under 1-g conditions. The walls were constructed with different reinforcement arrangements, backfill materials, and batter angles to study the effects of these parameters on the behaviour and seismic performance of model walls. The test results indicate an interplay with the wall response and Arias Intensity which is an earthquake intensity measure.

Behavior Characteristics of Single Batter Pile under Vertical Load

The purpose of this study is to grasp the behavior characteristics of a single batter pile under vertical load by performing a model test. The changes in the resistance of the pile, the bending moment, etc. by the slope of the pile and the relative density of the ground were analyzed. According to the results of the test, when the relative density of the ground was medium and high, the bearing capacity kept increasing when the angle of the pile moved from a vertical position to 20°, and then decreased gradually after 20°. The bending moment of the pile increased as the relative density of the ground and the batter angle of the pile increased. The position of the maximum bending moment came closer to the ground surface as the batter angle of the pile further increased, and it occurred at a point of 5.2~6.7 times the diameter of the pile from the ground surface.

Experimental investigation on pullout capacity of model pile in Cohesionless Deposits

In this project, an experimental study is made on pile pullout capacity, varying the diameter of the pile (d), Length to diameter ratio (L/d), the effect of pile inclination or batter angle (α), nature of the pile surface by placing the pile in cohesionless soils. The experimental values are determined and are compared with case studies in literature. In this project, various literatures on pullout capacity of piles were studied and experiment procedure was derived. Poorly graded river sand was used for cohesionless deposit. The sand is tested for engineering and index properties. Two types of piles, rough and smooth with different lengths were tested at different batter angles. The results are plotted in the graph. These graphs are used for comparative studies of various outcomes of the experiment and results were established.

A Numerical Analysis on the Behavior of Single Battered Pile under Pullout Loading

Batter or raker piles are piles driven at an inclination with a vertical to resist large inclined or lateral forces. Many structures like offshore structures and towers are subjected to overturning moments due to wave pressure, wind load, and ship impacts. Therefore in such structures, a combination of the vertical and batter piles is used to transfer overturning moments in compression and tension forces to the foundation. This paper presents a three-dimensional finite element analysis using PLAXIS 3D software to study the battered pile's behavior under the effect of pullout load. Several variables that influence the pile tension capacity embedded in sandy soil are investigated. The pile models are steel piles embedded in the dense sand at different batter angles (0, 10, 20, and 30) degrees with two embedment ratios, L/d (15 and 20). To clarify the pile shape's influence on a pullout capacity, two shapes are used, a circular pile with a diameter equal to 20 mm and a square pile with a section of 15.7×15.7 mm. These dimensions are chosen to achieve an equal perimeter for both shapes. The numerical results pointed that the pile pullout capacity increases with the increasing of the batter angle and embedment ratio, and the maximum values are marked at a batter angle of 20o. The shape of the bending moment profile is a single curvature, and the peak values are located approximately at the midpoint of the battered pile, while a zero value is located at the pile tip and pile head.

A three-dimensional investigation on performance of batter pile groups in laterally spreading ground

The performance of batter pile groups in laterally spreading ground has rarely been investigated. The present study evaluates the performance of 2 × 1 batter pile groups with four different configurations subjected to lateral spreading displacement through three-dimensional, fully coupled numerical investigations. Pressure dependent multi-yield model for the soil medium complemented with variation in permeability of liquefiable soil for excess pore pressure generation is considered. The nonlinear behaviour of the reinforced concrete pile is also incorporated. The behaviour of batter pile groups is evaluated for various earthquake time histories. The study indicates that the bending moment developed in the pile sections of both upstream and downstream sides of the ground displacement is observed to reduce under combined (kinematic + inertial) loading conditions for batter pile group configurations considered. However, shear and axial forces show increasing trends for batter pile groups, especially with higher batter angles for both kinematic and combined loading conditions. It is also observed that the presence of batter piles reduces both pile cap and superstructure displacements. However, significant pile cap rotations are recorded for pile groups with higher batter angles. The performances of the pile groups are confirmed for earthquake motions with a wide range of peak ground accelerations.