Nonlinear Finite Element Analysis of Four-Pile Caps Supporting Columns Subjected to Generic Loading

IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

Nonlinear Finite Element Analysis of Four-Pile Caps Supporting Columns Subjected to Generic Loading Ambareesh Kumar1, Ashish Singh2, Kanhaiya Lal Pandey3 and Rohit Rai4 ABSTRACT: Comparisons with results from three pile cap tests demonstrate that the one way shear design provisions of the present IS2911 Indian standard code are excessively conservative for deep pile caps, and the traditional flexural design procedures the two-way slabs are un-conservative for pile caps. Flexural design can best be accomplished using a simple strut-and-tie model, and test results of the pile cap is using various load design with bending theory and the longitudinal and transverse reinforcement provided of the equal distance of both side. A simple shear design is proposed in which maximum load and deflection is considered the best indicator of shear strength for deep pile caps. The influence of confinement is more gradual than suggested by the ACI Code bearing strength provisions. The paper presents the development of an adaptable strut-and-tie approach that can be applied to the design or analysis of four-pile caps with different load of pile cap that support steel piles a supported rectangular column. Three piles were designed of varying depth and were tested for deflection and comparison of results was done. The results indicate that the use of the proposed model would lead to safe and economical designs. The proposed model can be easily extended to any number of piles, providing a rational procedure for the design of wide range of pile caps.

KEYWORDS: Pile Cap, Bearing Strength, Flexure, Compression, Deflection.

INTRODUCTION In traditional design practice, pile caps are assumed to acts as beams spanning between piles. The design of pile cap with different load and depth of a cap is then selected to provide adequate shear capacity and the required amount of longitudinal reinforcement is calculated using engineering beam theory. The methods for the design of pile cap have been developed that are based on the finite element analysis approach. These methods assume that an internal load resisting truss, so-called strut-and-tie model, carries the forces through the pile cap in which concrete compressive strut’s act between the column and piles and steel ties (reinforcement) act between piles.

This is highly undesirable behaviour as there is neither warning cracks nor pronounced deformations before these types of brittle shear failures occur.

These unexpected shear failures can be explained in two ways. Firstly, engineering beam theory was originally developed for structural elements with significant deformation capacity. As a consequence, if this theory is applied to elements with limited deformation capacity such as pile caps, the calculated effective depth will tend to overestimate the concrete contribution from shear.

Ambareesh Kumar1 and Rohit Rai 4 Department of Civil Engineering M.M.M. Engineering College Gorakhpur 273010 (UP) India Email: ambar006@gmail.com1 and rohit.rai2609@gmail.cm4

Secondly, engineering beam theory usually leads to more longitudinal reinforcement than would be calculated by using a strut-and-tie approach, and for the specific situation of fourpile caps, pile caps designed using engineering beam theory have a tendency to be over reinforced and as consequence, shear failures may occur as a result of longitudinal splitting of compression struts before yielding of the longitudinal reinforcement.

Although the strut-and-tie approach provides a more rational basis for the design of pile caps, it is only commonly applied for the design of simple pile caps such as pile caps supporting square columns subjected to axial load. This is believed to be due to the complexity and uncertainties as to the appropriate strut-and-tie model to use for more complex loading conditions. Thus, designers have chosen to rely on the use of engineering beam theory for the design of even slightly more complex pile caps, including four-pile caps that support four circular steel piles.

To address the situation of pile caps supporting columns under general situation (comparison on to different load design pile cap failure), an adaptable strut-and-tie model for four-pile caps is proposed in this paper. Unfortunately there is experimental test data on the performance of this type of four-pile caps.

Thus, non-linear finite element analysis (NLFEA) has been applied to make the best possible prediction of the behaviour of these pile caps. A NLFEA program was selected for use that was specifically written for predicting the behaviour of a three-dimensional continuum of structural concrete subjected to a complex state of stress. This program will be validated herein by available test data. The result of the analyses of four-pile caps design of different load and depth will illustrate the appropriateness and experimental check the behaviour of pile cap of the proposed model. They are design of three model of pile cap with different load (50KN, 75KN, 100KN)

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013 and check deflection of pile cap. This model can be further extended for the design of more complex pile caps.

Strut-and-tie model to the design of fourpile caps The proposed model is an adaptable 3-dimensional strut-andtie model, which can be used for the design or analysis of four-pile caps supporting square or rectangular columns subjected to the vertical loading of pile cap and check the deflection. In the proposed model, vertical force applying on the centre column of pile cap check the behaviour of pile cap at centre and supporting of steel pile on the pile cap, and the net axial load acting from the column on the pile cap is always compressive.

Fig-1: Proposed strut-and-tie model for four-pile caps STRUT-AND-TIE MODEL The influence of a concentrated load with d from the column face support of a member subjected to one-way shears summarized in Fig. The pile cap shear force such a member is very different and depend the side of the concentrated vertical load with critical section is located. The truss model indicates that the vertical load is transmitted directly to the support of pile by a compression strut of the cap. No stirrups are required to resist the shear created by the vertical load. The vertical load does, increase the diagonal compression stresses of pile in the concrete immediately above the support, as well as the required tension force in the longitudinal reinforcement of the pile from the face of the support depicts simple threedimensional strut-and-tie model of the four-pile cap. The vertical column load is transmitted directly to the support of pile in inclined compression struts. The horizontal tension ties baris required to prevent the piles from being spread apart.

The shear design of pile cap using a strut-and-tie model

ISSN 2320 – 6020 involves limiting the concrete stresses of compression struts and nodal zones at the tension tie yields prior to any significant diagonal cracking in the plain concrete compression struts. That the concrete stresses are entire disturbed region can be considered in safe the maximum bearing stress in all nodal zones is the compression and tension below a certain limit. The analytical and experimental study of pile cap in deferent loading by plain concrete, it is proposed that the maximum deflection in nodal zones of deep pile caps be limited to the lower bearing stress.

The proposed strut-and-tie model is intended of the design of deep pile caps, it use steel pile. The concrete caps may be a general shear design procedure for pile caps can be accomplished by the following. The initial pile cap depth using in three model of the design at one-way and two-way shear design procedures from IS code. In the case of one-way shear, the critical section should be taken at d from the column face, and any pile force within the critical section should be ignored. The nodal zone bearing stresses should be checked.

The pile cap depth may be changed at the design of three model of cap, the pile cap dimensions may be constant at the every model confinement of the nodal zones, or the bearing stresses may need to be reduced by increasing the column or pile dimensions and the deflection of cap is increase to applying load. Thus, the shear strength of pile caps will be limited by the traditional sectional shear design procedures, while the shear strength of pile caps will be limited by the design load and the failure at the maximum load of nodal zone of the cap.

EXPERIMENTAL DATA OF PILE CAP The results on pile caps are tested of the deflection of four-pile caps. In all cases, the simulated rectangular column (250mm×250mm) and steel piles were the same depth as the “pile cap,” so the models were really wide deep beams. The models had various amounts of either straight deformed reinforcing bar that were anchored by a number of different methods. Shear failure occurred of a diagonal crack of the pile cap. The objective of the tests was to investigate the behaviour of cap at design from deferent loading of four pile cap depth and the amount of reinforcing steel. The specimens were stronger than anticipated. All pile caps behaved similarly with one main vertical (flexural) crack forming at midspan. They are tested of three series of pile caps. The first series consisted of three models at about the same load (50 KN) and depth (130mm), while the second series consisted of three approximately specimens. The main objective of the tests was to determine the load and deflection of pile cap at deferent loading of pile cap and check the behaviour of cap failure in transverse and longitudinal reinforcement layout. There enforcement of cap are resulted in higher capacities (for a given quantity of steel Fe 500 N/mm2), even though some parts of the specimens had poor crack control. Distributing an equal amount of reinforcement in a uniform grid resulted in the four-pile caps. The cap reinforcement in placed transverse and longitudinal at deferent spacing in deferent sample of cap.

The capacities were not significantly influenced by whether

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013 the bunched reinforcement was provided around the perimeter of the pile cap or diagonally across the pile cap; however, the best crack control under service loads occurred when a combination of the two was used. The longitudinal reinforcement layout and anchorage were the parameters studied.

The behaviour of all pile caps was similar of the all tested sample. The shear and vertical cracks formed near at centre of the pile cap sides, extending to near the top of the pile caps.

The pile cap fail at the steel pile from the corner at the support of cap. The testing at the cap at design vertical loading to find the deflection at the cap is middle at higher at the support pile.

The cap is fail in two-way shear and punching failure at the centre of cap. The pile caps had usually split into four separate pieces hinged supported below the column base. According to the code, most specimens failed in shear and bending after the longitudinal reinforcement yielded. The code also classified the failure modes as either one-way (beam) shear or two-way (punching) shear, depending on the appearance of the failed specimen. Bunching the reinforcement over the steel piles resulted in a 100 percent increase in capacity compared to spreading the reinforcement uniformly. The so-called of the full anchorage resulted in approximately a 75 percent increase in capacity. The reference at the research Sabnis and Gogate tested in the six very small (1/10) scale models of four-pile caps to study. The quantity of uniformly distributed longitudinal reinforcement is influences the shear capacity of pile caps. They are Similar to the design of Clarke, the longitudinal reinforcement are hooked and extended from the top surface. The tests showed that varying the load and deflection ratio between 0.0014 and 0.012 had little influence on the shear capacities of the models. All pile caps were statically indeterminate (steel piles in four-pile caps were arranged in a rectangular shape), and the actual pile reaction loads were measured throughout the test. Sliding bearings were used under the pseudo-piles to simulate the lateral flexibility of piles.

External and internal dial gauge measurements the deflection during the tests demonstrated that the behaviour of pile caps is very different from two-way slabs. The third pile caps deform very little before failure and thus, have virtually no ability to redistribute pile loads. Dial gages in five of the specimens indicated that the middle point and every corner of cap had definitely yielded prior to failure. The failure mode still a very much like shear failure because the plain concrete in the pile caps had very little ductility. They believed that true shear failures were a result of compression struts and deflection of the pile cap at the deferent dial gauge. Depending on the geometry of the pile cap, the final failure mechanism resembled either a one-way or two-way (punching failure) shear failure. The maximum bearing stress of the specimens that failed in shear varied from 1.13 to 1.27 (fc)1/2.

ISSN 2320 – 6020 from four-pile caps tested. Present data of different load and depth of pile cap as well as the measured cracking, yielding, deflection and failure of pile cap.

Prior to the use of a NLFEA program for evaluating this adaptable strut-and-tie model, it is first necessary to evaluate the ability of this program to predict the behaviour of tested pile caps. This was completed using the experimental data

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

Reinforcements were modelled using an embedded formulation and the Newton-Raphson solution method was applied for the solution scheme. Boundary conditions and material properties were defined in order to accurately represent the described experimental setup and the overall response was recorded using monitoring points for loading (at the top of the column) and displacements (at the centre bottom of the pile caps)The predicted load-displacement behaviour for the simulated four-pile caps using Staad pro.

COMPARATIVE STUDY The properties of four pile cap of 130mm depth to the load and deflection curve are used in the study of the experiment.

The specimens are considered the small wide-beam cap models tested.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013 In the case of one-way shear, the three different predictions is given the ACI Building Code:1) the 1977 edition of the ACI Building Code (critical section at d from the column face); 2) the 1983 ACI Building Code (critical section at the column face); and 3) the special provisions for deep flexural members.

The table four in the ratio of measured pile cap capacity to predicted capacity for the three ACI Code predictions, as well as the CRSI Handbook prediction. The interesting to note that three pile caps predicted to fail in flexure and punching shear at the centre were reported to have failed in shear of the deflection of cap. The testing of the pile cap applying the load from universal testing machine at the 25KN to check the deflection of the cap to find the cracking load and the failure load of cap. They are design the pile cap at IS 2911 at load and deflection compression of three deferent model at 28 days curing. As previously mentioned, the likely reason for the pile caps is large blocks of plain concrete that do not have the ductility to undergo significant flexural deformations a shear failure.

The strut-and-tie model and compares the predictions with the experimental results. The “shear” capacity is the maximum rectangular column load limited by the nodal zone bearing stresses, while the flexural capacity is the maximum column load at the various interval of the limited by yielding of the longitudinal transverse reinforcement of cap. The flexural capacity is depends strongly at the inclination of the compression strut in the pile cap is defined by the location of the nodal zones. The lower nodal zones of the pile cap were located at the centre of steel piles at the level of the longitudinal reinforcement, while the upper nodal zones were assumed to the top surface of pile cap at the column quarter points. It is obvious from, the one-way shear design provisions of the 1984 and subsequent editions of the IS Code are excessively conservative for pile foundation. They also demonstrate the traditional flexural strength of cap predictions are un-conservative for pile caps. These flexural strength procedures in the meant for lightly reinforced beams they are able to undergo extensive flexural deformations after the reinforcement yields. As the curvature increases, this flexural compression stresses concentrate at the near compression face of pile cap. As mentioned previously, the pile caps are brittle and undergo such deformations; therefore, assuming that the flexural compression is concentrated near the compression face is inappropriate.

ISSN 2320 – 6020 remains until at the failure step when at the central span suddenly increases and sample fail in the shear. If considering the practical serviceability of pile caps, all the models in the FEA can be treated as having experienced shear failures i.e. the shear cracks caused failure before bending failure occurred.

Assuming the flexural compression are uniform and across the entire pile cap failure at the top of cap, which deflection measurements have shown to be incorrect leads to a further over prediction of the flexural capacity. While the proposed strut-and-tie method in the least amount of scatter between experimental in pile cap results predictions. This can be explained, the fact that the shear failure of pile caps involves a tension failure of the concrete in the upper surface of cap. The most important issue is that the proposed design method is simple, rational, and conservative, and unlike the other design methods, it does not over predict any of the pile cap test results.

Crack propagation and distribution The cap has stated that for most in sample one, two and three, punching failure and shear failure were always very close at the failure step. This is also true in the FEA. Though many samples one failed by punching failures, wide shear cracks are also observed in showing that bending failure and shear failure are very close.

For all samples in failure crack at the compressive splitting shear crack linking the vertical loading to the pile head matured at the failure. For those caps observed to fail in bending in FEA, the bending crack supersedes the compressive splitting shear crack only at the failure steps. This

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

While calculated displacements were generally lower than experimental displacements, the cracking patterns and failure modes were quite well predicted. The typical radial crack pattern predicted for four-pile caps with bunched reinforcement.

Fig -3: Predicted crack pattern at failure for pile cap

Fig -6: shear failure at the corner of cap

Fig -4: Shear failure of the side in cap Typical failure cracks for the designed four-pile caps supporting a rectangular column subjected to the various depth are shown in Typical deformed shapes at maximum load, as well as, the principal stress acting in the ties are shown.

Fig -5: Crack pattern at maximum load for the Specimen.

Fig -7: Failure of pile cap at FEM

Fig -8: Deformed shape at maximum vertical load and deflection in the reinforcements ties for the Specimen.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013 In order to assess the concrete contribution on the capacity of the pile caps, additional analyses were conducted of unreinforced pile caps. As can be seen, for pile caps with heights over 50 cm, no longitudinal reinforcement would be necessary to support the design loads. These results show that concrete tensile strength, often neglected in structural codes, is a critically important factor in the design of stocky member such as pile caps. Taking into account that safety factors are additionally applied to the design, it is very clear that a large portion of some pile caps will be reinforced.

CONCLUDING REMARKS Due to the lack of a generic strut-and-tie model for the design of pile caps to support realistically complex loadings from columns, designers commonly use engineering beam theory or very simplified strut-and-tie models for the design of pile caps. In the latter approach, knowing the piles reactions due to the simultaneous action of comparison of deferent load and depth, the highest reaction is multiplied by the number of piles, in a manner that an equivalent compressive axial load is found.

To encourage the use of more appropriate design procedures for pile caps, an adaptable3-dimensional strut-and-tie model was presented in this paper. The main strength of the proposed model is that it provides a clear methodology for calculating the deflection of four-pile caps supporting steel piles subjected to various load and depth. The proposed methodology is shown by analyses to result in safe and economical design solutions.

The performance of the proposed model was evaluated using non-linear analyses. The results show that the predicted capacities are greater than those calculated from the adaptable strut-and-tie model. The lower the shear span-to-depth ratio, c/d, the higher was the failure load. However, as the same strut-and-tie model was applied for the same loading condition, the same capacity at reinforcement yielding and at failure would have been expected for all specimens. The differences in the predicted behaviour can be explained by the significant influence of the concrete tensile strength in the bottom region of the pile caps, which is not considered in the present formulation and in most codes of practice.

The proposed adaptable strut-and-tie model is considered to provide a more rational basis for the design and analysis of four-pile caps. Even so, it should be noted that the proposed model may lead to the use of more than necessary amounts of longitudinal tension reinforcement.

The numerical simulations illustrated the capacity provided by the concrete alone would support most service loads. This implies that field experience should not provide a good indication of the appropriateness of design practice.

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Reinforcing

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