Buckling Behavior of Axially Loaded Partially Embedded Concrete Piles in Sand


P. Senthil Kumar

Senior Lecturer, Department. of Civil Engineering
PSG College of Technology, Coimbatore, India

R. Rathina Giridhar

Graduate Student, Department of Civil Engineering
PSG College of Technology, Coimbatore, India

P. Parameswaran

Professor, Department of Civil Engineering
PSG College of Technology, Coimbatore, India




This paper presents a simple approach to predict the buckling capacity of axially loaded partially embedded slender reinforced concrete pile using Davisson and Robinson method. The flexural stiffness (EI) equation of the slender concrete column permitted by ACI building code is adopted as such for concrete pile. Results of experimental investigations carried out on axially loaded slender concrete piles in sand medium for the various combinations of unsupported length and coefficient of subgrade modulus are compared with the proposed approach. The analyses indicate the nearness between the theoretical predictions and the experimental results.


Keywords: Partially Embedded Pile; Concrete Pile; Flexural Stiffness; Subgrade Modulus; Buckling Capacity.


Piles are structural elements that transfer the applied superstructure loads to the foundation medium. Normally, the lateral support given to a fully embedded pile, even by the softest foundation medium, is sufficient to prevent it from buckling (Cummings, 1938; Glick, 1948). But, with the increasing use of very slender piles and long piles extending a considerable distance above the ground surface for offshore structures or bridges, where the unsupported section of pile behaves as a structural column and is vulnerable to buckling (Klohn and Hughes, 1964; Lee, 1968; Ramsamooj, 1975; Senthil Kumar et al., 2006).

Several studies available on partially embedded piles concerns mainly on arriving the buckling capacity of the pile theoretically one or other way (Hetenyi, 1946; Francis, 1964; Davisson and Robinson, 1965; Gabr et al., 1994; Chen, 1997; Hellis et al., 1997; Lin and Chang, 2002; Baghery, 2004). On the other hand, extensive experimental investigations on concrete pile conducted earlier were to understand the structural aspects of actual long pile (Hromadik, 1961), without taking the effect of surrounding foundation medium. At the same time, detailed studies made on partially embedded timber piles was covering well, both the theory as well as with the desirable field experiments (Klohn and Hughes, 1964), but its application is limited to such members only. Similarly, numerous laboratory investigations on piles in partially embedded condition with consistent foundation medium was carried out on steel as well as aluminum piles (Lee, 1968) and also on, brass piles (Ramsamooj, 1975). Senthil Kumar et al., (2006) presented a comprehensive review of literature indicating the necessity for carrying out the experimental investigations on partially embedded pile, in which the experimental study is extended to concrete piles for a particular relative density. However, limited attempts were made to understand the effect of supporting foundation medium together with the structural properties of concrete pile and that too for partially embedded condition. Though the eccentricity of loading is inevitable in practice, even under the best of the conditions (Klohn and Hughes, 1964; Prakash and Sharma, 1990), the ideal case of axial loading, however, is essential for analyzing the maximum capacity of the pile.

Therefore, the present study aims to formulate an approach for predicting the buckling capacity of axially loaded partially embedded slender reinforced concrete pile considering both geotechnical as well as structural aspects of the soil-pile system.


It is well known that the importance of the current problem lies on the exact determination of equivalent length of the pile (Le), which is equal to the sum of unsupported length (Lu) and depth of fixity (Lf). Davisson and Robinson (1965) have proposed simplified formulas, to determine the depth of fixity (Lf), which is adopted by AASHTO LFRD (1994) as well as ACI committee 543 (2000). For the partially embedded piles in sand, Lf, measured from ground, is computed from



E = Modulus of elasticity of the pile material

I = Moment of inertia of the pile

nh = Coefficient of horizontal subgrade modulus.

Equation (1) was based on conventional beam-on-elastic-foundation theory, and is intended for partially embedded piles. The coefficient of 1.8 in equation was suggested for simplification and compromise such that the equation is applicable to both bending and buckling. This equation is also included in the FHWA report (1987).

Hence, the critical buckling capacity (Pcr) for an axially loaded partially embedded slender reinforced concrete pile is,


Equation (2) is applicable for the end conditions of the present study that is fixed at the base and pinned at the top. However, it can be solved for other top end conditions also.

For the estimation of flexural stiffness (EI) of the pile to be used in equation (2), the simplified equation (ACI 318-89 Eq.(10-11)) permitted by ACI building code (1989) for a slender reinforced concrete column subjected to short-time loads, is taken, as,



Ec = Modulus of elasticity of concrete

Ig = Moment of inertia of the gross concrete cross section.

It is known that the flexural stiffness of a slender member depends on various factors. However, considering the convenience, ACI building code continues to allow the equation (3) for practical applications.


Experimental Set up

An experimental investigation was planned to study the behavior of the axially loaded partially embedded slender reinforced concrete piles using the method outlined by Senthil Kumar et al., (2006). Totally three tests were carried out by varying unsupported length (Lu) and coefficient of horizontal subgrade modulus (nh), as detailed in Table 1. Figure 1 show the experimental set up used for the present study.


Figure 1. Experimental setup


Test Specimens

The pile specimens of size 40mmx50mmx2200mm were cast with OPC 53grade cement, river sand and crushed aggregates of maximum size 6mm, as per IS 10262 (1982) standards. Mild steel rod of four numbers of 4mm diameter were used as main reinforcement with 3mm diameter as lateral ties spaced at 40mm center to centre. Additional reinforcement with suitable arrangement was provided at the ends of the pile for better distribution of load and to avoid anchorage failure. Deflection rods were fixed during casting, to measure the lateral deflection in the embedded region. Control specimens were cast along with each pile specimen and cured under similar conditions as that of parent specimen. The values of concrete compressive strength (fcc) are given in Table 1.

Foundation Medium

Dry river sand was used as a foundation medium. The specific gravity and uniformity coefficient of the sand were 2.62 and 1.4 respectively. The limiting void ratios were emax = 0.63, emin = 0.47 corresponding minimum dry densities were 1.599g/cc and 1.782g/cc respectively. The placement density for various relative densities was obtained by calculation.

Experimental determination of the coefficient of subgrade modulus for the foundation sand at a particular relative density (R.D) was carried out separately, by the procedure outlined by Lee (1968), using a very rigid concrete pile with square cross-section as recommended by Terzaghi (1955). The values of nh for various relative densities are presented in Table 1, which is based on the average of three test values.


Table 1. Details of Partially Embedded Piles


Test Procedure

Amsler universal testing machine (UTM) of 1000kN capacity, suitably modified to allow a maximum specimen length of 2200mm, was used to test the pile specimen. UTM keeps the assembly set up intact until failure, even under large deformations of the specimen.

A specifically designed wooden box (figure 1) of size 0.6mx0.6mx1.5m, to meet the testing requirement, was placed in position to fill the sand after securing the position of the specimen between the ball-socket arrangements at both ends. Weighed mass of sand obtained for 150mm thickness, based on the placement density, was poured and uniformly compacted till achieving 150mm graduated level mark for each and every layer.

The deflection of the pile was measured along the full length using Linear Variable Displacement Transducers (LVDT) at five locations that is 410mm (LVDT-1), 1140mm (LVDT-2), 1460mm (LVDT-3), 1750mm (LVDT-4) and 2180mm (LVDT-5) distances from top, where three (namely, LVDT-3, 4 and 5) among that were attached with deflection rods extending through the foundation medium.

The loads were applied axially using the load control system. In all the tests, an initial set load of 2kN was applied and then initial readings were observed. At every loading increment, the deflections were recorded carefully besides observation of failure and marking cracks simultaneously.


Load-Deflection Diagrams

From the experimental results, the basic observations obtained such as applied load and lateral deflections are plotted in various forms, as shown in figures 2 to 8.

In all the piles lateral deformation was observed indicating the buckling of the partially embedded piles. Flexural cracks were observed over the middle region of the unsupported length indicating the initiation of failure. Finally, the pile failed by crushing of concrete in compression with spalling of cover concrete. Further, in all the tested piles, the failure occurred above the foundation medium, as expected.


Figure 2. Trend in Pile Lateral Deformation at various stages of loading up to failure for Lu = 0.9 m and R.D = 30%


Figure 3. Trend in Pile Lateral Deformation at various stages of loading up to failure for Lu = 1.1 m and R.D = 50%

Figure 4. Trend in Pile Lateral Deformation at various stages of loading up to failure for Lu = 1.1 m and R.D = 70%

From figures 2 to 4, it is interesting to note that the deflection of the pile reverses direction during the test under continuous increasing loading. The change in the structural behavior may be due to the nonlinear relation between the deflections and the applied load (Timoshenko and Gere, 1961). This phenomenon of reversal of deflections is well noticed with increasing relative densities.

From figures 2 to 4, it is noticed that the general trend in the variation of deflection is more at the middle of unsupported length and it is less along the remaining portion of the pile. It is seen that the partially embedded concrete pile, while nearing the failure stage divides into two units clearly, one is the unsupported length slightly extending into ground with larger deflection, and behaves as like column and other is the embedded length with very small deflection laterally supported by surrounding foundation medium. All this confirms the column behavior of the pile in the unsupported length as well as its influence over the soil-pile system and ultimately its capacity.

Figure 5. Comparison of Load–Deflection Curve at various locations for ALR 1

Figure 6. Comparison of Load–Deflection Curve at various locations for ALR 2


Figure 7. Comparison of Load-Deflection Curve at various locations for ALR 3


From figures 5 to 7, it is clear to observe that the deflection measured using LVDT-2 (near the middle of the unsupported portion) is maximum than all other LVDTs, and reveals the actual representation of the load-deflection relation for the partially embedded piles. Based on this further analysis is carried out to determine the experimental critical loads. Moreover, a separate load-deflection curves specifically using LVDT-2 alone was plotted for the sake of comparison between the tested piles, as shown in figure 8.

From figures 5 to 7, based on the observations of LVDT- 4 and 5, it is observed that when the relative density increases then the deflection below the ground level is less pronounced.


Figure 8. Comparison of Load – Deflection Curve near middle of unsupported length for different piles


Figure 8 shows the typical axially loaded column behavior of the partially embedded pile under varying relative densities of the foundation medium. Based on the experimental results, the following general features were also observed.

The trend in the variation of deflection along the length of the pile is same.

The deflection of the pile is high near the middle of the unsupported length and reduces while approaching the foundation medium.

The behavior of the piles is almost similar in loose (R.D = 30%), medium (R.D = 50%) as well as dense (R.D = 70%) states of sand.

A summary of test results is given in Table 2, which gives the ultimate load (Pu) for the test specimen, the theoretically predicted critical load (Pt) and the experimental critical load (Pe).

Table 2. Summary and Comparison of Results


Finally, the theoretical critical loads were estimated based on the present approach and compared with the experimental critical loads. In which, the experimental critical loads were determined based on the procedure suggested by Kwon and Hancock (1992). Comparison between the theoretical and experimental critical loads shows that the present approach is highly conservative for axial loading, since the ACI equations for EI singly accounts many factors including the slenderness effects and the use of most conservative (i.e., greatest) value (Lee, 1968) for the coefficient of the depth of fixity.


Buckling capacity of the partially embedded slender concrete pile may be predicted reasonably using the flexural stiffness equation of the slender concrete column. The good agreement attained between predicted loads and the test results indicates the correctness in determining the effective length of the pile. The variation of pile lateral deformation and maximum deflection near the middle of unsupported length confirms the column behavior of the partially embedded pile in the unsupported region and its control over the soil-pile system.


The authors wish to thank PSG College of Technology, Coimbatore, Tamilnadu for providing testing facility. The authors thank the members of Civil Engineering Department for their help.


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