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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 IS-

2911 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.

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 four-

pile 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)

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

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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-and-

tie 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 three-

dimensional 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

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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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

.

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

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.

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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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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.

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

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.

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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 -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 -6: shear failure at the corner of cap

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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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.

REFERENCES

1. ACI Committee 318, “Building Code Requirements

for Reinforced Concrete (ACI 318-02) and

Commentary (ACI 318R-05)”.

2. ADEBAR, P.; KUCHMA, D.; COLLINS, M. P.

“Strut-and-Tie Models for the Design of Pile Caps:

An Experimental Study”. ACI Structural Journal,

v.87, n.1, pp.81-92, 1990.

3. ADEBAR, P.; ZHOU, Z. “Design of Deep Pile Caps

by Strut-and-Tie Models”. In: ACI Structural Journal,

v. 93, no. 4, July-August, pp. 1-12, 1996.

4. AMERICAN ASSOCIATION OF STATE

HIGHWAY AND TRANSPORTATIONOFFICIALS

(AASHTO). “AASHTO LRFD Bridge Design

Specifications”, 1st ed. Washington, D. C., 1994.

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7. Canadian Standards Association (CSA). “CSA

A23.3-M84. Code for the Design

8. CRSI Handbook, Concrete Reinforcing Steel

Institute, Chicago, 1992.

9. Marti, Peter, “Basic Tools of Reinforced Concrete

Beam Design” ACI JOURNAL, Proceedings V. 82,

No. 1, Jan.-Feb. 1985, pp. 46-56.

10. Collins, Michael P., and Mitchell, Denis, “Rational

Approach to Shear Design—the 1984 Canadian Code

Provisions,” ACI JOURNAL, Proceedings V. 83, No.

6, Nov.-Dec. 1986, pp. 925-933.

11. Schlaich, Jörg; Schäfer, Kurt and Jennewein, Mattias,

“Toward a Consistent Design of Reinforced

Structural Concrete” Journal of Prestressed Concrete

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12. “Code of Practice For Design and Construction of

Pile Foundation”, Is-2911-1984, Bureau Of Indian

Standards, New Delhi.