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# Laterally loaded piles in dense sand: Group effects

David Remaud, Josselin Garnier, Roger Frank

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David Remaud, Josselin Garnier, Roger Frank. Laterally loaded piles in dense sand: Group effects. Int. Conf. Centrifuge 98, Sep 1998, Tokyo, Japan. pp.533-538. hal-00864913

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# Laterally Loaded Piles in dense sand : Group Effects

D. Remaud, J. Garnier

Laboratoire Central des Ponts et Chaussées, Nantes, France

R. Frank

CERMES (ENPC-LCPC), Paris, France

**ABSTRACT** : In this study, centrifuge tests were conducted on a group of two model piles at 40g, in order to investigate the lateral group effect. A method is established to get the *P*-y reaction curves from the experimental results and test conditions. These *P*-y curves are compared to common design codes (P.H.R.I.-Japan, A.P.I.-USA, Fascicule 62-France). Head displacements and bending moment profiles allow the determination of group effect on *P*-y curves. Coefficients of reduction on the lateral soil resistance are established.

## 1. INTRODUCTION

Offshore structures, quay-walls or bridge piers foundations have to support high lateral loads. Deep foundations of vertical piles are common solutions in practice for the design of these structures.

The behaviour of a single laterally loaded pile has been the topic of many theoretical as well as experimental researches. They include the subgrade reaction or *P*-y curves methods in which the soil is modelled as a series of non-linear springs (*P* is the soil reaction and *y* is the pile deflection). These methods are the base of several design codes (P.H.R.I., A.P.I., Fascicule 62).

In practice however, the piles are in groups. In this case, the pile-soil-pile interaction is difficult to assess because of the non-linear and complex response of the soil to lateral loads.

Because this complex interaction is three-dimensional and many parameters have to be investigated, theoretical studies as well as numerical studies require a lot of time and computational efforts and therefore are not appropriate. Given the number of tests needed, full scale in situ studies are not appropriate either.

Thus, centrifuge modelling is a convenient approach to investigate this type of problem.

## 2. CENTRIFUGE TESTING

Barton (1982), Mezazigh (1990, 1995) and Terashi et al. (1991) conducted lateral load tests on single piles or group of piles. The results showed that the modelling is self-consistent and obeys the

commonly accepted laws of centrifugal testing.

A lot of efforts have been carried out on the model pile installation procedure in order to simulate the prototype soil conditions.

Oldham (1985) an apparatus to drive a single pile in flight.

Bloomquist et al. (1991), for a group of five piles, and later McVay et al. (1995), for a group of nine piles at 3B and 5B spacing (B is the pile diameter), also developed an in flight driving process. They showed that there is a difference in the group capacity between 1g and in flight pile installation.

The piles were not instrumented with strain gauges along their shafts. Therefore *P*-y curves determination were not obtained from the bending moment profiles but from numerical validation.

In the present study, the piles are installed at 1g. Sand is rained around the piles suspended in the container. This procedure is an approximate simulation of an in situ installation of bored piles without soil displacement. Thus, the study is limited to bored piles for which the effect of 1g placement on the behaviour under lateral loading is limited.

## 3. EQUIPMENT AND TEST PROCEDURES

In the following sections, all results are presented at prototype scale, except where noted.

### 3.1 *Model pile*

The model piles are designed for a centrifugal acceleration of 40g. They are made from AU4G aluminium hollow pipes. At model scale, they have
an outside diameter B of 18 mm, a thickness of 1.5 mm and a total length of 380 mm. The penetration depth in the soil is D = 300 mm.

Therefore they simulate a prototype pile of 720 mm in diameter with an embedded length of 12 m and classified as a flexible pile (EI = 51.4 MN.m²).

The piles are equipped with 20 pairs of gauges, every 15 mm down the pile. The first pair is located at the soil surface, the last one at the depth of 285 mm (11.4 m in prototype scale). The wires are placed inside the pipe.

## 3.2 Soil sample

The material used is a fine white Fontainebleau sand. With the selected dimensions, the ratio between pile diameter and grain diameter is approximately 900, which is comfortably greater than the minimum value of 40 usually accepted.

The sand is placed in the containers (1200 mm x 800 mm) by raining, using an automatic hopper, developed by L.C.P.C. It produces a homogeneous sand mass, with density deviations less than 1%. The density achieved is 16.3 kN/m³ (ID = 0.89) for the present tests.

<table><caption>Table 1. Properties of the Fontainebleau sand</caption><thead><tr><th>γs<br>(kN/m³)</th><th>γd min<br>(kN/m³)</th><th>e<sub>max</sub><br>(kN/m³)</th><th>γd max<br>(kN/m³)</th><th>e<sub>min</sub></th></tr></thead><tbody><tr><td>26.44</td><td>13.64</td><td>0.940</td><td>16.83</td><td>0.616</td></tr></tbody></table>

## 3.3 Tests procedures

Several tests were performed to investigate different experimental configurations : single pile or pair of piles with 2B, 4B and 6B spacing. The pile head is free.

Lateral loading of the pile is performed by an hydraulic servo-actuator. The lateral force is applied by a metallic cable connected to the pile at the height of 40 mm above the soil surface. The same displacement is applied to both piles at load level.

Two displacement transducers at the heights of 20 mm and 65 mm measure the pile head deflections and thus give the rotation.

The load is applied in about 20 steps of 80 N each. To prevent the piles from failure, the loading is stopped when the maximum bending moment generated in the piles reaches 3 MN.m.

# 4. INTERPRETATION

## 4.1 Method

The strain gauges fixed on the piles give the bending moment profiles during lateral loading. The study is

based on the analysis of these experimental data.

For a given lateral load, the measured distribution of bending moment M, with depth z, is used to derive the reaction profile of the soil P, by double derivation, and the displacement profile y, by double integration, according to:

$$P = \frac{d^2 M}{dz^2} \quad (1) \quad \text{and} \quad y = \iint \frac{M}{EI} dz \quad (2)$$

The main difficulty is the interpolation of the bending moments and the definition of the boundary conditions.

Barton (1982) used cubic spline functions and imposed the shear force at the ground surface and the soil reaction at great depth (set to zero).

The software SLIVALIC5, developed at L.C.P.C., fits the data with quintic spline functions and differentiates twice the interpolated profile. Each function is based on six consecutive experimental data. The only input parameter ρ enforces the spline function to fit more or less accurately the experimental data. The method used to choose the best ρ value consists in checking the static equilibrium of the pile under the derived soil reaction profile and applied lateral load.

This procedure has been developed in previous studies. Bouafia (1990) used 12 pairs of gauges and showed that the number of strain gauges should be large enough to ensure a good precision in the soil reaction profiles. Mezazigh (1995) carried out series of tests on laterally loaded piles near slopes with the same model piles. In his analysis, he postulated the following conditions:

- the static equilibrium of each pile must be satisfied within ± 5%,

- the depths of zero displacement point and zero soil reaction point coincide.

In the present study, attention was first focused on the boundary conditions. As the pile is a flexible one, the displacement, bending moment and soil reaction values at the tip should be zero.

The experimental moment data are in good agreement with this hypothesis. Hence, we added a value M=0 at the pile tip (z= 300 mm) where no bending moment is directly measured. This additional condition improves the double derivation results close to the tip.

Furthermore two centrifuge tests on isolated piles (Test 1 and Test 2) were performed in order to determine the displacement at the tip. A horizontal displacement transducer was installed at the tip of a single pile. The tests confirm the zero displacement condition at the tip. Therefore the only conditions for the double integration process are the displacements at the head and at the tip of the pile. For this double integration, polynomial functions are used.

Figure 1 shows good agreement between results of the two tests with horizontal displacement transducer at the pile tip (Tests 1 & 2) and results of Test 3 (without tip displacement measurement).
<figure><img src="image_3.png" /><figcaption>Figure 1 - Validation of the boundary conditions.</figcaption></figure>

## 4.2 Validation of the P-y curves

As the study is based on the obtaining of P-y reaction curves, it is important to validate the previous defined process, by checking the consistency of the results.

For this purpose the software PILATE-LCPC (Frank, 1990) is used, which is devised to calculate the response of a single pile to lateral loading under any given set of P-y curves. The experimental P-y curves obtained from the present analysis are input in the software where the soil is modelled by 20 layers. Four load increments $F_H$ are applied to the pile head (163 kN, 322 kN, 489 kN and 652 kN).

The results are presented in terms of deflections (Figure 2), bending moments (Figure 3) and soil reactions (Figure 4). The calculated deflections and soil reactions agree well with the data directly derived from the loading tests.

<figure><img src="image_4.png" /><figcaption>Figure 2 - Validation of the P-y curves - Pile deflections</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3 - Validation of the P-y curves - Bending moments</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4 - Validation of the P-y curves - Soil reactions</figcaption></figure>

## 4.3 Comparison with design codes

The validated experimental P-y curves may now be linked with those of standard codes :

- Fascicule 62 P-y curves are obtained from in flight CPT tests. The needed pressuremeter characteristics are deduced from CPT tip resistance

$q_c$ by : $p_1 = q_c/9$, $E_M = 10 \cdot p_1$ and $p_f = p_1/1.8$

where $E_M$ is the Menard's modulus, $p_1$ and $p_f$ are respectively the limit and creep pressure ;

- the A.P.I. curves are calculated from unit weight $\gamma = 16.3 \text{ kN/m}^3$ and friction angle $\phi = 40^\circ$ ;

- the P.H.R.I. curves are based on a subgrade modulus $k_S = \sqrt{0.8 / B}$ and $p = k_S \cdot z \cdot y^{0.5}$.

Figures 5 and 6 compare the P-y reaction curves obtained at two different depths : $z_1 = 0.6 \text{ m}$ near the surface and $z_2 = 2.4 \text{ m}$ where the maximum bending moments are located.
<figure><img src="image_7.png" /><figcaption>Figure 5 - Comparison to standard P-y curves at z=0.6 m</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 6 - Comparison to standard P-y curves at z=2.4 m</figcaption></figure>

Figure 5 shows some difference between shallow P-y curves derived from the three reference tests (±15%). In depth, P-y curves from the three reference tests are much closer (Figure 6). However starting data were quite close as seen in Figure 1. These results confirm that the determination of P-y curves from bending moment profiles is rather difficult (high sensitivity of the reaction P to the curvature of the bending moment profile). Differences on obtained soil reaction smaller than ±10-15% may be considered as not significant.

At both depths, the measured P-y curves agree well with the P.H.R.I. predictions.

For the two other codes, large differences are observed with the experimental results : they tend to underestimate the ultimate soil reaction near the surface and overestimate soil reactions at larger depth (close to the maximum bending moment depth).

## 5. GROUP EFFECT

Pile spacing is the main parameter for the group effect. It is usually postulated that the P-y stiffness on the trailing pile is less than on the leading pile (shadowing effect).

### 5.1 Loading curves and group efficiency

As the piles are free headed, they may not have exactly the same deflections at ground level. In order to investigate their response to lateral loads, the displacements are thus compared at load level.

Figure 7 shows the lateral load applied to each pile in the group and the load supported by a single pile (Test 2) for the same deflection.

The group efficiency is a good criterion to qualify the group effect. It is calculated in the different configurations for the same displacement at the load level as follows :

$$e = \frac{\text{total load on the group for a given displacement}}{n \times \text{load on single pile for the same displacement}} \quad (3)$$

We get 0.81, 0.87 and 0.95 respectively for a pile spacing of 2B, 4B and 6B. These results underscore the fact that the interactions between the piles bring higher displacement of the group.

<figure><img src="image_9.png" /><figcaption>Figure 7 - Loading curves at the load level</figcaption></figure>

The load distribution in the group is determined from the bending moment measured at the soil surface. The leading pile takes 59% of the lateral load applied at 2B, 56% at 4B and 51% at 6B spacing. This is in agreement with Barton (1982).

The pile-soil-pile interactions are small as soon as the pile spacing is greater than 6B.

### 5.2 Bending moment profiles

The bending moment profiles of the 4 tests configurations are plotted (Figures 8 and 9) for the
same head displacement of about 10% of the diameter.

The bending moments in the leading pile are very similar to the ones of the single pile. In the trailing pile, with pile spacing rising from 2B to 6B, they tend to be equal to those of the single pile.

The group effect is characterised by higher maximum bending moments (around 1.6 MN.m) in the leading pile than in the trailing pile (1.3 MN.m at 2B spacing).

<figure><img src="image_10.png" /><figcaption>Figure 9 - Bending moment profiles of the trailing piles</figcaption></figure>

These results also confirm the conclusion of the previous section : the group effect is small for a pile spacing equal to 6B.

## 5.3 P-y curves

The P-y curves are calculated with the procedure previously developed. Results are shown below for the two depths previously defined.

Taking into account the comment done in section 4.3 about the natural scatter of the obtained P-y curves, Figures 10 and 11 show that the leading pile P-y curves are not different from the single pile one. No significant group effect is observed on leading piles even at small spacing.

The P-y curves of the trailing piles are plotted in Figures 12 and 13. As seen before, the group effect is more significant on the trailing pile when compared to the single pile.

<figure><img src="image_11.png" /><figcaption>Figure 10 - P-y reaction curves of the leading pile at z=0.6 m</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11 - P-y reaction curves of the leading pile at z=2.4 m</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12 - P-y reaction curves of the trailing pile at z=0.6 m</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 13 - P-y reaction curves of the trailing pile at z=2.4 m</figcaption></figure>

"P-multipliers" P<sub>m</sub> are commonly used for group effects (Brown et al. 1990) :

$$P_{\text{group pile}} = P_{\text{m}} \times P_{\text{single pile}} \quad (4)$$

Thus a first qualitative analysis was done on the trailing piles. The P<sub>m</sub> coefficient was calculated at four different depths ranging from z<sub>1</sub> = 0.6 m to z<sub>2</sub> = 2.4 m. The observed average values obtained at maximum displacements are then :

$$- S/B=2 : P_m = 0.52$$

$$- S/B=4 : P_m = 0.82$$

$$- S/B=6 : P_m = 0.93$$

## 6. CONCLUSIONS

Centrifuge lateral load tests on pairs of piles in sand were performed. The pile spacing effect on the group response was investigated.

P-y curves were derived from the bending moment profiles. For a single pile, the experimental P-y curves compare well with the curves proposed in the P.H.R.I. method. Large differences are observed with the A.P.I. and Fascicule 62 ones.

A clear group effect is shown for pile spacing less or equal to 6B :

- the total load for the group is reduced (by about 20% for 2B spacing and 5% for 6B spacing);

- the load and bending moments on the trailing pile are reduced. For 2B spacing the trailing pile supports 41% of the total load and the maximum moment is about 20% less than in the single pile ;

- the P-y curves are also affected by group effects. For 2B spacing the mobilised soil reaction on the trailing pile is 50% that of a single pile.

Furthermore, tests shown that bending moments and P-y curves on the leading pile are close to those of a single pile.

This study will be extended to tests on 3 piles groups with various geometrical arrangements (line, row and triangle) and pile spacing.

## REFERENCES

American Petroleum Institute (1993). *A.P.I. RP 2A-LRFD - Section G : Foundation Design*, A.P.I., pp. 64-77.

Barton, Y. O. (1982). *Laterally Loaded Piles in Sand : Centrifuge Tests and Finite Element Analysis*, PhD, University of Cambridge, 141 p.

Bloomquist, D., Feld, T., Townsend, F.C., Gravgaard, J., & Gill, J. (1991). Development of a Multiple Pile Driver/Load Test Device for Pile Group Studies, *Centrifuge 91*, Ed. by Ko, H-Y & McLean, F.G., A.A. Balkema Publishers, Rotterdam, Netherlands, pp. 335-359.

Bouafia A.,1990, *Modélisation des pieux chargés latéralement en centrifugeuse*, Thèse de Doctorat, Université de Nantes, 267 p.

Brown, D. A. & Shie, C.-F. (1990). Numerical Experiments into Group Effect on the Response of Piles to Lateral Loading, *Computers and Geotechnics*, N° 10, pp. 211-230.

Frank, R. & Romagny, J.C. (1990). PILATE-LCPC Version 10.4 - Notice d'utilisation, Ed. LCPC.

Ministère de l'Equipement, du Logement et des Transports (1993). *Règles Techniques de Conception et de Calcul des Fondations et des Ouvrages de Génie Civil, Fascicule 62 - Titre V*, Min. de l'Eq. du Log. et des Trans., France

McVay M., Casper, R. & Tchang T. (1995). Lateral Response of Three Row Groups in Loose to Dense Sands at 3D and 5D Spacing, *Journal of Geotechnical Engineering*, ASCE, Vol. 121, N°5, pp. 436-441.

Mezazigh, S., Levacher, D. & Garnier, J. (1990) Comportement d'un couple de pieux sollicité latéralement, *Premières Journées Génie Civil - Génie Côtier*, Le Havre, pp. 149-160.

Mezazigh, S. (1995). *Etude Expérimentale de Pieux Chargés Latéralement : Proximité d'un Talus et Effet de Groupe*, Thèse de Doctorat, Université de Nantes, 272 p.

Oldham, C. E. (1983). *Lateral Load Tests on Piles*, PhD, University of Manchester, 162 p.

Port and Harbour Research Institute (P.H.R.I.) (1980). *Technical Standards for Port and Harbour Facilities in Japan*, Japan Ministry of Transport, 317 p.

Terashi, M., Kitazume, M. & Kawabata, K. (1989). Centrifuge modelling of a laterally loaded pile, *Proc. of XIIth I.C.S.M.F.E.*, Rio de Janeiro, Vol. 2, pp. 991-994.