Indian Geotechnical Conference (December 18-20, 2003) s9

Analysing the Optimum Length of Tie Rod Anchor for a Berthing Structure

analysing the optimum length of tie rod
anchor for a berthing structure

P.V. Premalatha

Ph.D. Research Scholar, Department of Civil Engineering, National Institute of Technology, Tiruchirappalli–620 015, India.

E-mail:

K. Muthukumaran

Assistant Professor, Department of Civil Engineering, National Institute of Technology, Tiruchirappalli–620 015, India.

E-mail:

P. Jeyabalan

Professor, Department of Civil Engineering, National Institute of Technology, Tiruchirappalli–620 015, India.

E-mail:

ABSTRACT: Berthing structures are constructed for berthing and mooring of vessels, to enable loading and unloading of cargo and for embarking and disembarking of passengers and vehicles. The soil found in the coastal areas is generally soft marine clay or a loose sandy soil deposit. Such kind of soil has a very low shear strength value. Hence pile foundations are adopted in these areas in order to by-pass the weak shear layers and transfer the loads to a deeper stable soil stratum. Piles of a berthing structure are subjected to both axial and lateral loads. Tie rod anchors are provided to support such structures in order to strengthen them and also to reduce the deflection of the structure caused by the lateral loads. The main objective of the present investigation is to study the behaviour of the piles in a berthing structure with anchor rod in a layered non-homogeneous soil.

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Analysing the Optimum Length of Tie Rod Anchor for a Berthing Structure

1. INTRODUCTION

The soil found in the coastal areas is generally soft marine clay or a loose sandy soil deposit or a mix of layered non- homogeneous soil. Such kind of soil has a very low shear strength values. Pile foundations are adopted in these areas in order to by-pass the weak shear layers of soil and transfer the load to a stable soil stratum.

Pile foundations are generally subjected to axial loads as well as lateral loads. The axial load is due to the self weight of the structure and the live load moving upon them. The lateral loads and moments, come up due to wind loads, seismic forces in buildings, earth pressure in retaining walls/abutments and water pressure in case of water front structure. The simplest method of restraining these piles against such force is to employ a pile shaft that is sufficiently long to take the whole of the lateral load in skin friction. As a result of which sufficient amount of reinforcement is required to maintain the stability.

In a berthing structure, lateral forces are caused by impact of berthing of ships, pull from mooring ropes and pressure of winds, currents, waves and floating ice. The deflection of the berthing structure due to mooring force is considerable when compared to other forces acting on the structure. Tie rod anchors may be provided in order to strengthen the structure and to resist these lateral loads and reduce the deflection to a large extent. The use of tie rod anchors in berthing structures will reduce the cross sectional area of the pile used and also the amount of reinforcement used in them resulting in an economical design of the structure.

The governing criterion in designing pile foundation to resist lateral loads in most cases is the maximum deflection of the foundation rather than its ultimate capacity. The maximum deflection at the pile head and the distribution of bending moment along the pile are important information for the successful design of piles that supports lateral loads. Knowing the maximum deflection at the pile head is important to satisfy the serviceability requirements of the super structure while the bending moment is required to structural sizing of pile.

Hence an analysis is essential in arriving at an optimum length of tie rod that will effectively reduce the deflection of the structure to a great extent. An analysis is carried out in evaluating the deflection of a pile with the effect of tie rod anchors in non-homogeneous soil.

The present investigation describes the typical modelling and analysis of a berthing structure using finite element approach. An analysis is done for various lengths of tie rod anchors in an existing berthing structure. The determination of suitable length of tie rod anchor is then examined briefly.

2. FINITE ELEMENT ANALYSIS

A two dimensional finite element program PLAXIS 2D has been used to model a single frame of a berthing structure using the concept of plain strain condition.

2.1 Plane Strain as Two-Dimensional Modelling

In PLAXIS 2D, selection of plane strain conditions results in a two dimensional finite element model with only two translational degrees of freedom per node. The 15-noded triangle provides a fourth order interpolation for displacements and the numerical integration involves twelve Gauss points.

2.2 Piles and Beam Elements

Plates elements in the two-dimensional finite element model are composed of beam elements (line elements) with three degrees of freedom per node: two translational degrees of freedom and one rotational degree of freedom. When using 15 noded soil elements, 5-noded beam-column elements are used. The beam column elements are based on Mindlin’s beam theory. This theory allows for beam’s deflection due to shearing as well as bending. Hence when the maximum bending moment or axial force reaches, the beam becomes plastic and starts yielding.

2.3 Mohr-Coulomb as Soil’s Model

Mohr Coulomb’s model can be considered as a first order approximation of real soil behaviour. This elastic perfectly plastic model requires 5 basic input parameters, namely Young’s Modulus (E), Poisson’s ratio (µ), cohesion (c), friction angle (φ) and dilatancy angle (y). This is a well known and a basic soil model. The soil nodes and pile nodes are connected by bilinear Mohr-Coulomb interface elements. This allows an approximate representation of the development of lateral resistance with relative soil-pile movement and ultimately the full limiting soil pressure acting on the piles.

2.4 Properties of Sand and Model Pile

A finite element program PLAXIS 2D Version 8 has been used to model the frame. The analyses are carried out in total stresses by generating initial stresses using the undrained parameters of soil. The analysis is carried out for various loads viz. 250 kN, 500 kN, 750 kN, 1000 kN and for the following cases:

Case 1: Berthing Structure Subjected to lateral load without tie rod anchor.

Case 2: Berthing Structure Subjected to lateral load with tie rod anchor of length 6 m, 8 m, 10 m, 14.5 m, 18 m, 20 m and 22 m in non-homogeneous layer of soil.

2.5 Bore Hole Data

Typical bore hole datas are collected from Chennai port trust for getting the layered soil profile. The depth vs. SPT N values are plotted in the Figure 1 shown below and the soil parameters arrived for the critical bore hole data is considered for the analysis.

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Analysing the Optimum Length of Tie Rod Anchor for a Berthing Structure

Table 1: Input Parameters Pile, Beam and Tie Rod

Table 2: Soil Property

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Analysing the Optimum Length of Tie Rod Anchor for a Berthing Structure

Fig. 1: Depth vs. SPT N Values

3. RESULTS AND COMMENTS

Figure 2 shows the generated 2D FE mesh of a single frame of berthing structure without tie rod anchor. The center to centre distance between the piles is 7.5 m and the pile is 35 m long. Total number of element is 433, node is 1102, node stress points 1299. The soil stratum is idealized by 15 noded triangular elements with elastic-plastic Mohr Coulomb model and the structural elements are idealized by beam element.

Fig. 2: 2D Mesh for a Single Frame of a Berthing
Structure Values

Figure 3 shows the load vs. deflection for the structure without tie rod anchor for various loads viz. 250 kN, 500 kN, 750 kN and 1000 kN. The max deflection corresponding to 1000kN load is observed to be 0.149 m.

Fig. 3: Load vs. Deflection Values

Figure 4 shows the bending moment variation along the length of the pile for the structure without tie rod anchor for various loads. The fixity depth is observed at a distance of 20 m below the top of the pile. The bending moment is zero at a depth of 14.5 m below the pile head.

Figure 5 shows the generated 2D FE mesh of a single frame of berthing structure with a tie rod length of 14.5 m. The center to centre distance between the piles is 7.5 m and 35 m long. The length of tie rod is 14.5 m with a diameter of 115 mm.

Total number of element is 464, node is 1208, node stress points 1392. The soil stratum is idealized by 15 noded triangular elements with elastic-plastic Mohr Coulomb model and the structural elements are idealized by beam element.

Fig. 4: Bending Moment Variation along
the Length of the Pile

Fig. 5: 2D Mesh for a Single Frame of a Berthing
Structure Values

Figure 6 shows the lateral load—deflection curve for a berthing structure with 14.5 m tie rod. From Figure 3 and Figure 7, it can be seen, that the deflection is reduced by 19.5% by providing a tie rod of length 14.5 m.

Figure 7 shows the bending moment variation along the pile depth for a 14.5 m tie rod anchor. The fixity depth is observed at a distance of 20 m below the top of the pile. The bending moment is zero at a depth of 14.5 m below the pile head. It is observed that there is no variation in the depth of fixity as compared to the case without tie rod anchor but the bending moment is reduced by 11.8%.

Fig. 6: Load vs. Deflection

Fig. 7: Bending Moment Variation along the Length of Pile

Figure 8 shows the max deflection for various length of tie rod anchor. It is observed that the deflection is reduced by 8.72% when a tie rod of 6 m length is provided. The displacement is reduced to 10.07%, 11.4%, 14.09%, and 15.43% when the length of tie rod provided is increased to 8 m, 10 m, 14.5 m, and 18 m correspondingly. Beyond 18 m, the further increase in length of tie rod to 20 m, 22 m and so on does not show any percentage reduction in the displacement. The deflection is stable at 0.126 m for 18 m, 20 m and 22 m length of tie rod anchor. Hence optimum length is arrived as 18 m for this particular case which reduces the deflection of the structure effectively.

Fig. 8: Length of Tie Rod vs. Deflection for Layered Soil

Figure 9 shows the Force vs. length of tie rod in a layered soil. It can be observed that the increase in force transferred to tie rod is 12.62%, 15.83%, 18.82% and 10.48% when the length is increased from 6 m to 8 m, 10 m, 14.5 m and 18 m. Beyond the optimum length of 18 m the increase in force transferred to tie rod increases only by 1.8% and 1.6%.

Fig. 9: Length of Tie Rod vs. Force in Tie Rod

4. CONCLUSIONS

The effect of tie rod anchors on the behaviour of laterally loaded piles in a berthing structure is studied. The following con-
clusions are observed from the analysis:

(a) The effect of tie rod plays a major role in reducing the deflection of the berthing structure thereby reducing the length of pile, material and reinforcement used for construction.

(b) The variation in location of these anchors through finite element modeling can be very helpful in analyzing the behavior of piles in such berthing structures and an economical design too

(c) It is observed that the deflection is reduced by 8.72%, 10.07%, 11.4%, 14.09%, and 15.43% when the length of tie rod is increased in sequence from 6 m, 8 m, 10 m, 14.5 m, and 18 m correspondingly. After 18 m, when the length is increased to 20 m, 22 m and so on there is no percentage reduction in the displacement and increasing the tie rod length beyond this will not reduce the deflection of the structure. Hence optimum length is arrived as 18 m for this particular case which reduces the deflection of the structure effectively.

REFERENCES

Broms (1964a). “The Lateral Resistance of Piles in Cohesive Soils”, Journal of the Soil Mechanics and Foundation Div., 90(2), 27–63.

Broms (1964b). “The Lateral Resistance of Piles in Cohesionless Soils”, Journal of the Soil Mechanics and Foundation Div., 90(3), 123–156.

Kok, S.T. and Bujang, B.K. Huat (2008). “Numerical Modelling of Laterally Loaded Piles”, American Journal of Applied Sciences, 5(10):1403–1408.

Martin, G.R. and Chen, C.Y. (2005). “Response of Piles Due to Lateral Slope Movement”, Computers and Structures, Vol. 83.

Matlock, H. and Reese, L.C. (1960). “Generalized Solution for the Laterally Loaded Piles”, Journal of the Soil Mechanics and Foundation Div., ASCE, 86(5), 63–91.