Batter Angle Research Articles

Kinematic interaction factors of deep foundations with inclined piles

SUMMARYThe beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.

Laterally loaded rigid piles with rotational constraints

Elastic–plastic, closed-form solutions were developed recently by the author, to capture the nonlinear response of laterally loaded rigid piles. Presented in compact form, the solutions are convenient to use, and sufficiently accurate despite using only two input parameters of the net limiting force per unit length pu along the pile, and a subgrade modulus k. Nevertheless, piles may be subjected to limited cap-restraints or loading below ground surface, which alter the response remarkably.This paper provides explicit expressions for estimating loading capacity of anchored piles and develops new solutions for lateral piles with cap-rotation by stipulating a constant pu or a linear increasing pu (Gibson pu) with depth. Lateral loading capacity Ho (at the tip-yield state and yield at rotation point state) and maximum bending moment Mm (at the tip-yield state) are presented against loading locations, and in form of the lateral capacity Ho−Mo (applied moment) locus. The capacity is consistent with available solutions for anchored piles, and caissons with either pu profile, allowing a united approach from lateral piles to anchored piles. The new solutions are also presented in charts to highlight the impact of rotational stiffness of pile-cap on nonlinear response, offering a united approach for free-head piles through fixed-head piles.Several advantages of the solutions are identified against the prevalent p–y curve based approach. To estimate the key parameter pu, values of the resistance factor Np (=ratio of pile–soil limiting resistance over the undrained shear strength su) are deduced using the current expressions against available normalised pile capacity involving the impact of gapping (between pile and soil), pile movement mode, pile slenderness ratio, inclined loading angle (anchored piles) and batter angles (lateral piles). The Np is characterised by: (i) An increase from 5.6–8.6 to 10.14–11.6, as gapping is eliminated around lateral piles and caissons, and from 1.0–6.1 to 2.8–9.8, as translation is converted into rotation mode of footings. (ii) Similar variations with slenderness ratio between anchors and caissons (without gapping), and among anchors, caissons and pipelines (with gapping). And (iii) A reduction with loading angles (anchors) resembling that with batter angles (piles).

Predictive modeling on seismic performances of geosynthetic-reinforced soil walls

This paper presents the results of numerical parametric study of free-standing simple geosynthetic-reinforced soil (GRS) walls under real multidirectional ground motion shaking. The predictions were made using a validated finite element computer program. Design parameters, such as (1) wall height, (2) wall batter angle, (3) soil friction angle, (4) reinforcement spacing, and (5) reinforcement stiffness, were evaluated in the study. Prior to the parametric study, the extent of finite element model (FEM) boundary was verified in order to minimize the boundary effect. Results of parametric study were compared against the values determined using the Federal Highway Administration (FHWA) allowable stress design methodology. It was found that the FHWA methodology overestimates the reinforcement tensile load as compared to the FEM results. Multivariate regression equations were developed using FEM results for the various seismic performances based on multiple design parameters that are essential in the design of GRS walls. In particular, the prediction equations for wall facing horizontal displacement, wall crest settlement, and reinforcement tensile load are presented. The prediction equations can provide first-order estimates of the seismic performances of free-standing simple GRS walls.

Thin-layer Micro-element Method for Cohesive Soil Passive Earth Pressure Determination on Retaining Walls

AbstractA thin-layer micro-element method that is based on the thought of horizontal slice method was developed to deduce the passive earth pressure of cohesive soil by considering the retaining wall height, wall back batter angle, filler elevation angle, equispaced overload, bulk density, internal friction angle, cohesion, and the external friction angle between the soil and the wall back. An explicit solution of the critical rupture angle was obtained using the graphic method. The effects of the aforementioned parameters on the critical rupture angle, the passive earth pressure distribution, and the resultant force of this pressure as well as its application position were analyzed. The results show that (1) the distribution of the passive earth pressure along the wall back is non-linear; (2) Coulomb and Rankine’s theories on passive earth pressure are special cases of the passive earth pressure formula under the corresponding simplified assumptions; and (3) the passive earth pressure and its distributio...

Pullout capacity of batter pile in sand

Many offshore structures are subjected to overturning moments due to wind load, wave pressure, and ship impacts. Also most of retaining walls are subjected to horizontal forces and bending moments, these forces are due to earth pressure. For foundations in such structures, usually a combination of vertical and batter piles is used. Little information is available in the literature about estimating the capacity of piles under uplift. In cases where these supporting piles are not vertical, the behavior under axial pullout is not well established. In order to delineate the significant variables affecting the ultimate uplift shaft resistance of batter pile in dry sand, a testing program comprising 62 pullout tests was conducted. The tests are conducted on model steel pile installed in loose, medium, and dense sand to an embedded depth ratio, L/d, vary from 7.5 to 30 and with various batter angles of 0°, 10°, 20°, and 30°. Results indicate that the pullout capacity of a batter pile constructed in dense and/or medium density sand increases with the increase of batter angle attains maximum value and then decreases, the maximum value of Pα occurs at batter angle approximately equal to 20°, and it is about 21–31% more than the vertical pile capacity, while the pullout capacity for batter pile that constructed in loose sand decreases with the increase of pile inclination. The results also indicated that the circular pile is more resistant to pullout forces than the square and rectangular pile shape. The rough model piles tested is experienced 18–75% increase in capacity compared with the smooth model piles. The suggested relations for the pullout capacity of batter pile regarding the vertical pile capacity are well predicted.

Design Considerations for Pile Groups Supporting Marine Structures with Respect to Scour

Piles supporting marine structures such as jetties, relieving platforms, quay walls and fixed offshore structures are subjected to lateral loads due to berthing and mooring forces, wind, waves, storm surges and current forces. This paper presents some factors that affect the design of pile groups supporting marine structures founded in cohesionless soils. Some main aspects that should be considered in the pile group design are addressed such as pile batter angle, pile group arrangement, pile spacing, pile slenderness ratio and magnitude of lateral static loading. Numerical analyses were conducted to investigate these design aspects with and without impact of scour. Different scour depths were considered to cover the possible root causes of scour around pile groups such as waves, current and ship propeller jets. The study revealed that scour has greater impact on lateral loading of pile groups compared to its impact on single piles. Pile groups with side-by-side arrangement exposed to scour are more critical than single piles and piles groups with tandem arrangement due to the combined effect of scour and pile-soil-pile interaction. It is also concluded that scour protection is not always required. More attention and considerations should be given to scour protection around piles especially if the piles are closely spaced, arranged side-by-side and if slenderness ratio is less than 12.5.

Study on Proportioanl Relation-ship of Lateral Bearing Capacity of Batter Pile by Model Experiments

Some researches indicate that the bearing capacity of negative battle pile is less than that of positive batter pile under free pile head. But the head of the engineering pile is used under some constraints. So the lateral bearing capacity is studied under different batter and different constraints at pile head by model experiments made by ourselves. The analysis indicates that (1) the lateral capacity of the negative batter pile decreases as the batter angle decreases when the pile head is only translational, (2) the lateral capacity of the negative batter translational pile is more than that of the positive batter free pile and (3) the proportional coefficients of the bearing capacity are provided under the experiment conditions.

Resultant Force of Lateral Earth Pressure in Unstable Slopes

Traditionally, resultant force of lateral earth pressure serves as the basis for design of nearly vertical walls. Conversely, slopes are designed to be internally stable using a factor of safety approach. However, with the availability of heavy facing elements such as gabions, steep slopes are increasingly being constructed. Steep slopes are considered to be unstable unless supported; that is, such slopes require facings to resist lateral earth pressure. Extending Coulomb's formulation to such slopes may not be conservative as a planar slip surface may not be critical. Presented are the results of a formulation to find the resultant lateral force which utilizes a log spiral failure mechanism. Unlike Caquot and Kerisel or Coulomb, the soil-facing interface friction is assumed to act on segments of vertical surface only, thus replicating the geometry of stacked rectangular facing units. Given the batter, the backslope, the height, the interface friction, and the unit weight and design friction angle of the backfill, one can quickly determine the corresponding lateral earth pressure coefficient. Formulation assuming the interface friction is acting on an imaginary surface inclined at the batter angle, essentially equivalent to Coulomb and Caquot and Kerisel, is also presented. Its results show that for batters up to 20°, the common approach of using the Coulomb method, including the assumed interface friction direction to coincide with the batter, yields results that are quite close to those stemming from the log spiral analysis. Hence, use of Coulomb's analysis for such small batters is reasonable as its formulation is simple. However, the lateral resultant is grossly underestimated for larger batters, especially when Coulomb analysis is used.

Vertical stress distributions around batter piles driven in cross‐anisotropic media

AbstractThis work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.

Surface displacements due to batter piles driven in cross‐anisotropic media

AbstractThis article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.

Seismic Passive Earth Pressures in Soils

Seismic passive earth pressure coefficients were computed by the method of limit equilibrium using a pseudostatic approach for seismic forces. Composite curved rupture surfaces were considered in the analysis. While earlier studies using this type of analysis were mainly for sands, seismic passive earth pressure coefficients were obtained in the present study considering the effects of cohesion, surcharge, and own weight. The minimum seismic passive force was obtained by adding the individual minimum values of these components and the validity of the principle of superposition was examined. Other parameters considered in the analysis were wall batter angle, ground surface slope, soil friction angle, wall friction angle, wall adhesion to soil cohesion ratio, and horizontal and vertical seismic accelerations. The seismic earth pressure coefficients were found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and vertical directions. Results of the study are presented in the form of figures and tables. Comparisons of the proposed method with available theories in the seismic case are also presented.

Seismic passive resistance in soils for negative wall friction

In the presence of pseudo-static seismic forces, passive earth pressure coefficients behind retaining walls were generated using the limit equilibrium method of analysis for the negative wall friction angle case (i.e., the wall moves upwards relative to the backfill) with logarithmic spirals as rupture surfaces. Individual density, surcharge, and cohesion components were computed to obtain the total minimum seismic passive resistance in soils by adding together the individual minimum components. The effect of variation in wall batter angle, ground slope, wall friction angle, soil friction angle, and horizontal and vertical seismic accelerations on seismic passive earth pressures are considered in the analysis. The seismic passive earth pressure coefficients are found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and the vertical directions. The results are presented in graphical and tabular formats.Key words: seismic passive resistance, limit equilibrium, pseudo-static.

Engineering Analysis of Dynamic Behavior of Micropile Systems

A series of centrifugal tests was conducted on micropile groups and network systems to investigate the system response to earthquake loading and the superstructure soil-micropile interaction behavior. Model tests on vertical and batter micropile systems embedded in loose to medium-dry sand under different levels of shaking are described. Group and network effects were investigated for different configurations and at different levels of loading. The experimental test results were analyzed parametrically to study the effect of the main controlling parameters. For the model testing conditions, the experimental and parametric results indicated a positive group effect increasing with the number of piles and the batter angle. Dynamic p-y curves were found to be nonlinear with low damping and to be much softer than the published data. For inclinations of 10° and 30°, a substantial improvement is observed in the superstructure response with acceleration reduction to 40 percent of the values obtained in the case of vertical piles. The computer programs LPILE and GROUP were used in a pseudostatic analysis approach to simulate the representative centrifugal model tests. Comparisons between the method predictions and the experimental results illustrate that these methods could be used as engineering tools to assess the seismic behavior of micropile groups and network systems.

Vertical pullout capacity of model batter anchor piles in marine clays

Many offshore structures are subjected to overturning moments due to wind load, wave pressure, and ship impacts. For foundations in such structures, usually a combination of vertical and batter piles is used. Little information is available in the literature about estimating the capacity of piles under uplift. In cases where these supporting piles are not vertical, the behavior under vertical pullout is not well established. In this article the vertical pullout behavior of batter piles is examined through an experimental investigation carried out on model batter anchor piles. The tests are conducted on model aluminum pipe piles of 19 mm diameter with different embedment ratios in a soft marine clayey bed at different consistencies and with various batter angles of 0°, 10°, 20°, and 30°. Results indicate that the pullout capacity of a batter pile is less than that of a vertical pile. This reduction is explained in terms of reduced area available for skin friction. Based on this, pullout behavior of batter ...

Induced Bending Moments in Batter Piles in Settling Soils

In this paper the concept of load transfer onto a batter pile in settling cohesive soil has been brought out. A theoretical method is developed to estimate the axial and transverse forces on a batter pile embedded in settling cohesive soil and this method is verified with the results obtained from model tests. Testing is carried out on a model pile group with four piles, at a batter angle of 10° with the vertical. The tests were carried out in homogeneous clay layer of thickness 570 mm, the piles used were made of aluminium pipes 38.1mm in diameter and 1.5 mm in thickness. Due to the settlement of the surrounding soil, there can be soil separation below the pile surface, and in such cases the analysis of the pile as beam on elastic foundation is not appropriate and the pile can be treated as a beam with appropriate end conditions. The bending moments measured through instrumented pile are compared with theoretical expressions developed and they are in good agreement in the case of fixed beam end conditions assumed.

Behaviour of flexible batter piles under inclined loads in layered soil

The behaviour of single free-head model flexible vertical and batter piles under central inclined loads in two-layered soil is investigated. The bearing capacity of the piles is found to depend on the layered structure, load inclination, and pile batter. The theoretical estimates obtained from semiempirical relations agree well with the test results. Previous displacement equations for flexible batter piles in elastic isotropic soil are modified for piles in anisotropic layered soil using an effective embedment depth of equivalent rigid piles. Practical equations for horizontal and vertical displacements of flexible batter piles are presented on the basis of resultant influence factors that are related to the batter angle, load inclination, and distribution of soil modulus with depth. The observed horizontal and vertical displacements of the piles are in reasonable agreement with the theoretical estimates, which are also supported by the results of some field cases. Key words : bearing capacity, deformation, batter pile, inclination factor, inclined load, layered soil, model test, sand, clay.

A case history of pre-extraction site investigation and quarry design, Cliffe Hill Quarry, Leicestershire

Abstract A brief history of the reasons leading up to the initiation of this project is followed by a description of the geographical location and geological significance of the chosen site. An initial phase of test pitting produced evidence which warranted a follow-up phase of continuous flight auger drilling along existing tracks. This work in turn indicated that serious exploration at great expense was warranted and a relatively powerful, brand new, drilling rig, capable of both coring and drilling through substantial thicknesses of overburden, was purchased. Several years of drilling, much of it on a 50m grid, subsequently proved the existence of a viable quantity of resource beneath an acceptable depth of overburden. Simultaneous testing of the core samples for a range of physical properties (as per BS 812) indicated the materials to be of acceptable quality for the anticipated markets, including rail ballast for high speed tracks. The drilling information was supplemented by a limited amount of geophysical work, mainly employing a shallow seismic refraction technique. Initial quarry planning studies indicated that a viable reserve could be generated by stripping overburden to a depth of 40 m around the periphery, and a planning application for areas of quarrying and overburden disposal was submitted. After considerable discussion and some modification, permission was granted, subject to a large number of conditions. Phased overburden stripping will ultimately involve several million cubic metres. This site will be subject to a full investigation as required by Section 9 of the Mines & Quarries (Tips) Regulations and this will determine the angles of safety for both the cut slopes and the deposited overburden. Preliminary configurations for the quarry, in terms of face heights, batter angles and bench widths were determined from geotechnical logging of the cores, the results of which were subsequently augmented by detailed mapping of the early exposures created. Full site investigations were also carried out for the location of load bearing structures.