ANALYSIS OF LATERAL REACTION MODULUS FOR PILES IN SAND FROM CPT TEST

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1 Paramètres de calcul géotechnique. Magnan (ed.) 22, Presses de l ENPC/LCPC, Paris ANALYSIS OF LATERAL REACTION MODULUS FOR PILES IN SAND FROM CPT TEST ANALYSE DU MODULE DE RÉACTION LATÉRALE DES PIEUX DANS LE SABLE À PARTIR DE L ESSAI CPT A. Bouafia Université de Blida, Département de Génie Civil, Blida, Algérie ABSTRACT - This paper presents the results of analysis of lateral reaction modulus in correlation with the cone penetration resistance, the slenderness ratio and flexural soil/pile rigidity, on the basis of interpretation of full-scale lateral loading tests conducted by the LCPC in homogeneous sandy soils. Moreover, correlation between CPT and PMT tests is analysed in order to suggest a simple relationship between the lateral reaction modulus and the cone resistance. RÉSUMÉ - Cette communication présente les résultats de l analyse du module de réaction latérale en corrélation avec la résistance pénétrométrique, l élancement du pieu et la rigidité relative sol/pieu, sur la base de l interprétation d essais de chargement latéral en vraie grandeur menés par le LCPC dans des massifs sableux homogènes. En outre, la corrélation entre essai de pénétration statique (CPT) et essai pressiométrique Ménard (PMT) a été analysée en vue de proposer une relation simple entre le module de réaction et la résistance de cône. 1. Background Piles were initially designed to transmit vertical loads from a structure to the soil. When these foundations were besides loaded horizontally, inclined piles, often difficult to achieve were to be added. Due to the progress done in the knowledge of the behaviour of deep foundations, it is nowadays admitted that vertical piles can sustain horizontal loads. The earth pressure on a bridge abutment piles, the lateral displacement of a layer of soft clay under an access embankment to a motorway, and the effects of the wind on slender structures built on piles are usual examples of horizontal loading. Behaviour of piles under horizontal loads is a complex soil/pile interaction problem because of the 3D nature of the phenomenon and the dependence on a variety of governing parameters. Significant progress was done these two last decades in the understanding of the response of a pile to bending forces by means of several experimental studies in full-scale as well as in centrifuge. It should be however mentioned that the numerous current pile design methods existing in pile literature are insufficient to take into consideration many interaction parameters (Bouafia,199). Numerous design approaches exist in pile foundations literature, notably the methods based on p-y load-transfer curves, which are widely used in practice. Although the cone penetration test CPT is often carried out in sandy soils, it is however less used than the pressuremeter for defining the parameters of p-y curves. An intensive experimental programme of full-scale pile loading tests as well as in centrifuge was undertaken by the LCPC during the last three decades. The first part of this paper briefly presents the methodology of construction of p-y curves and focuses on the initial lateral reaction modulus E ti. The second part deals with the correlation of this latter with cone penetration resistance q c and relative soil/pile flexural rigidity K r. 2. Construction of p-y curves 2.1. Methodology A few full-scale tests on instrumented piles in sand were reported in the literature with successful derivation of p-y curves from double differentiation and integration of the bending moment profile. 59

2 The main difficulty in deriving these curves is due to the high sensitivity of the lateral soil reaction p to the experimental conditions as well as to the method of fitting and differentiation of bending moments (Bouafia and Garnier, 1991) Measurement of axial deformation by strain gauges along the pile allow the determination of bending moment curve for a given load at pile top. Two successive integrations of this curve lead to easily determine lateral displacement y along the pile. Moreover, two successive differentiation of this curve allow the determination of horizontal soil reaction p and then to define p-y curve at any depth. Since the soil reaction p geometrically represents the curvature of bending moment distribution, it is therefore very sensitive to any fluctuation of bending moment at a given depth and strongly depends on the choice of the fitting curve of bending moment (Bouafia, 199; King, 1994). Quintic spline functions were used to fit the bending moment distribution by means of the computer program SLIVALIC-5 developed in LCPC (Degny, 1985). Degree of smoothness of the fitting curve is governed by an adjustment parameter which may be chosen according to a criterion. This criterion was defined as the satisfaction of static equilibrium under lateral reaction profile p(z) and loading on pile head within a tolerance of 1% at any depth (Bouafia & Garnier, 1991). This criterion was subsequently adopted for other studies at LCPC (Mezazigh, 1995; Remaud, 1999). Figure 1 illustrates an example of p-y curves obtained according to the procedure mentioned above and related to a centrifuged model of a circular steel pipe instrumented by 12 pairs of strain gauges fixed on the external surface along two diametrically opposite axes and regularly spaced. The geometrical reduction scale was 1/4. The prototype pile is characterised by a diameter B of.32 m, flexural rigidity E p.i p of MPa, and an embedded length D of 5 m. The horizontal load H is applied at a distance e equal to 1 m above the ground surface. The model is installed at natural gravity by pluviation of sand around the pile in the container. The soil used is a red silica poorly graded sand taken from the site of Le Rheu (Rennes, France) characterised by a relative density of 83%. It can be seen from this figure that p-y curves at different depths are non linear shaped with an increase in soil stiffness with depth. It is to be noticed that deflections and soil reaction change in sign at almost the same depth, say 1 diameters. This fact is in accordance with Winkler s hypothesis regarding the soil reaction modulus (Bouafia, 1998). Furthermore, for large displacements, no horizontal asymptote characterising the failure in the classical theory, appears in p-y curves except for the vicinity of surface. Accordingly, at large displacements, failure may occur in local zones surrounding the pile unlike traditional schemes of classical theory which consider a limit equilibrium of soil along the whole pile (Bouafia, 1999). The procedure of construction of p-y curves was validated by back-computation of the pile prototype. p-y curves were input in a non linear subgrade reaction software. The computer program PILATE (PILe under LATEral loads) developed in LCPC was used in this regard. Computed values were found in very good agreement with experimental results (Bouafia, 22) Initial lateral reaction modulus E ti The initial lateral modulus E ti was obtained from P-Y curves by fitting them by an hyperbolic function as follows : y P = (1) 1 y + E ti P u Regression coefficient was found more than 95% for curves corresponding to depths above the zero displacement depth. Beyond this depth values of E ti seem to be inaccurate, since p and y get small and the ratio p/y has no significance regarding the uncertainties due to experiments as well as to the procedure used for interpreting the bending moment curves. 51

3 Lateral reaction P (kn/m) Lateral displacement Y (mm) Z/B= Figure 1. Example of p-p curves at different depths. For all the piles, the moduli E ti vary linearly with depth. This fact is in accordance with the distribution of soil modulus in granular soils called Gibson s soils. Figure 2 shows a typical profile which may be fitted by : E ti =N H.Z (2) Figure 2. Typical Lateral reaction modulus profile 511

4 3. Evidences from full-scale pile loading tests Five full-scale lateral loading tests carried out on instrumented piles in two sandy sites were interpreted according to the methodology described above. The first site, noted S1, is located in Châtenay-sur-Seine, 7 km south-east of Paris (France). A big pit with a volume of 424 m 3 was previously dug to a depth of 3.2 m in a chalky soil. It was waterproofed by plastic sheets, then filled in by Fontainebleau sand into two medium dense layers. The underlying layer is 1.4 m thick with a density index I D =37% whereas the upper layer has a thickness of 1.8 m and I D =57 % (Canepa et al., 1988). Fontainebleau sand is a poorly graded sand. In-situ tests, notably PMT (Ménard pre-bored pressuremeter test), CPT (static cone resistance test) and DPT (dynamic penetration test) were carried out within the sandy mass. Figure 3 shows typical profiles from these tests. The second site, noted S2, is located in Le-Rheu, 5 km south-west of Rennes (France). The soil is composed of reddish poorly graded clean sand of marine origin from the Pliocene era. Ground water table was found at 1 m depth. The sand above the water table has an average water content of 8% corresponding to a saturation degree of 31%. It was possible to recover some samples with a 15 mm diameter auger sampler as far as 4. m of depth. The density index I D is 66%. Figure 3 illustrates profiles of PMT, CPT and DPT tests (Jézéquel, 1988). The piles used are steel pipes instrumented by strain gauges distributed by pairs along two diametrically opposite axes. The main geometrical and mechanical characteristics of the test piles are summarised in Table I. Figure 3. Typical in-situ profiles of sites S 1 and S 2 Table I. Summary of test piles characteristics Site Pile B (m) D/B E p I p (kpa) T S1 T T S2 P P

5 The influence of soil/pile rigidity on the initial lateral reaction modulus was rarely investigated and many practical methods simply correlate E ti to usual geotechnical parameters and pile diameter. Experimental studies of full scale pile loading tests as well as in centrifuge are the most appropriate to investigate this topic. Flexural soil/pile rigidity K r is usually defined in case of soils having linear modulus profiles by: EpIp Kr = (3) 5 N. D H Figure 3 shows that cone penetration resistance q c profiles are linear with a regression coefficient more than 92%. The slope N H was correlated to that of q c, noted λ. As shown in Figure 4, the ratio N H /λ decreases with the rigidity K r. For piles with slenderness ratio equal or larger than 1, the N H /λ- K r relationship in a bi-logarithmic scale, is linear. 1 P1 P2 (D/B=5.5) NH / λ R=96.4 % 1 T15 K r = E p.ip/ (N H.D 5 ) N H : initial slope of the E ti profile λ : initial slope of the q c profile T1 T Stiffness K r Figure 4. Variation of N H /λ versus K r Furthermore, this ratio linearly decreases with the slenderness ratio D/B as shown in Figure 5. It is obvious the limited number of piles studied here does not allow for generalisation of these findings. However, effects of soil/pile rigidity and slenderness ratio are not taken into account by the Ménard s pressuremeter method in which the ratio E ti /E M depend only on pile diameter B and coefficient of soil structure α (Baguelin et Al, 1978) as follows: E E M 18 = for B B = 6m (4) α α ti. ( 2. 65) Eti 18. B = else. (5) α EM B 4. B B. α B In order to assess the quality of the proposed correlation N H /λ, the deflections of the piles mentioned in Table I were computed by using the classical subgrade reaction formula of Reese & Matlock (196) for soils exhibiting a linear increasing of lateral reaction modulus with depth. 513

6 Figure 4 was used for estimating the slope N H. Inherent non linearity of lateral load-deflection curve led to compare initial slopes α of the curves rather than deflections. Small deflection pile behaviour may then be described by: Figure 6 shows a good accordance except for pile P 1. H= α.y (6) P1 K r = E p.ip/ (N H.D 5 ) N H : initial slope of the E ti profile λ : initial slope of the q c profile NH / λ R=97 % 2 1 T15 T D/B T5 Figure 5. Variation of N H /λ versus D/B 25 α: initial slope of lateral load-deflection curve 2 α pred. (kn/mm) 15 1 T15 α exp. = α pred. P1 5 T5 T α exp. (kn/mm) Figure 6. Comparison between predicted and experimental slopes 514

7 4. Analysis of the ratio N H /λ on the basis of E M /q c correlation Formulae 4 and 5 are prescribed in the French code (Fascicule 62) for p-y curves on the basis of PMT test. As alternative for estimating lateral reaction modulus from CPT test, the correlation E M /q c was combined with these formulae. Many authors have shown that the ratio E M /q c varies within the margin of 1 to 1.5 (Cassan, 1988). For both sites S 1 and S 2, this ratio was found varying between.77 and 2.5, with a mean value of 1.45 and a coefficient of variation of 28%. The correlation histogram presented in Figure 7, shows a main characteristic value of 1.4. Using formula 5 for piles studied in sites S 1 and S 2 leads to a rather wide range of 2.1 to 5.6 for the ratio N h /λ and a value of 4. for the mean value of E M /q c. On the basis of this value, initial slope of lateral load-deflection was computed, as done previously, according to Reese-Matlock method and found reasonably close to the experimental slopes as shown in Figure 8. Exception is made for pile P1, which exhibits a discrepancy with respect to the ideal line of accordance. No explanation was found for this. 1 Mean=1.45 Standard Deviation=.45 8 Normal distribution Counts 6 4 2,8 1, 1,2 1,4 1,6 1,8 2, 2,2 Ratio E M /q c Figure 7. Histogram of correlation between E M and q c 5. Analysis of the ratio N H /λ in the literature Elastic methods for analysis of small deflection behaviour of piles are usually used by correlating the elasticity modulus E to the cone resistance q c. In sandy soil, Gibson s medium where Young s modulus E varies linearly with depth is often used. Correlation E/q c is rather delicate since it relates a parameter for small deformation to another one dealing with failure. Moreover, a large number of factors are involved such a correlation. Table II summarises some usual correlations for sand. In some references, no precision was given about the type of CPT, the characteristics of the soil nor the margin of q c values. The ratio E/q c lies between 2.5 and 4.5 for bored piles, whereas it varies in a wider range for driven piles. Caution should be taken when using such correlations since they were established within the scope of a local geological context and should be considered as a rough estimation. 515

8 Many studies recommend to take a lateral reaction modulus in sand equal to the elasticity modulus (Bouafia, 199; Bouafia & Merouani, 1995). Therefore, in homogeneous sandy soils characterised by a linear cone resistance profile, for preliminary design purposes, the ratio N h /λ for bored piles may be taken approximately equal to α: initial slope of lateral load-deflection curve α pred. (kn/mm) Nh/λ=4. T15 α exp. = α pred. P1 T5 T α exp. (kn/mm) Figure 8. Comparison between predicted and experimental slopes Table II. Values of E/q c ratio for piles in sand Reference E/q c Observations Schmertmann (1978) 2.5 to 3.5 for bored piles Milovitch & Stefanovitch (1982) 2 to 4 for driven piles Poulos (1988) 5 normally consolidated sand for driven piles Verbrugge (1981) 2.5 to 4.5 Elson (1984) overconsolidated sand Van Impe (1986) 3 (q c <5MPa) norm. consolidated sand E= q c (5<q c <3 MPa) E, q c in MPa 6. Conclusions Correlation of the lateral reaction modulus with the cone penetration resistance for piles in dense homogeneous sand was investigated. Interpretation of five full-scale lateral pile loading tests 516

9 carried out by the LCPC in two sandy soils allowed for the analysis of pile behaviour within the scope of p-p curves method. The methodology of construction of p-y curves was presented and a compilation of the experimental results has shown a dependence of the lateral reaction modulus on the flexural soil/pile rigidity and the slenderness ratio. The limited number of piles studied here does not allow for generalisation of these findings. Further extension of the existing database may improve the quality of this correlation. 7. References Baguelin F., Jézéquel J.F., Shields D.H. (1978) The pressuremeter and foundation engineering. Series in Rock and Soil Mechanics, Vol.2 (1974/77), No.4, TransTech Publications, Germany, 68 pages. Bouafia A. (199) Modélisation des pieux chargés latéralement en centrifugeuse (in French). Thèse de Doctorat, Université de Nantes (France), 267 pages. Bouafia A., Garnier J. (1991) Experimental study of p-y curves for piles in sand. Proceedings, International Conference Centrifuge 91, Boulder, Colorado, June 1991, Bouafia A., Merouani Z. (1995) Analysis of horizontally loaded pile behaviour from cone penetration tests in centrifuge. Proceedings, 1 st International Symposium on Cone Penetration Testing, CPT 95, Linköping, 4-5 October 1995, Vol. 2, Bouafia A. (1997) Étude en centrifugeuse du comportement d un pieu chargé horizontalement. Proceedings, 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Bouafia A. (1998) Experimental analysis of large lateral displacements of piles in centrifuge, Proceedings, 4 th International Conference on Case Histories in Geotechnical Engineering, St- Louis, Missouri, paper N 1-12, 5 pages. Bouafia A. (1999) Large lateral displacements of piles in sand. Modelling in centrifuge, Proceedings, 12th European Conference on Soil Mechanics and Geotechnical Engineering, Amsterdam, The Netherlands, 7-1 june Bouafia A. (22) Response of flexible pile under lateral loads in dense sand in centrifuge, Proceedings of the International Conference on Physical Modelling ICPMG 2, July 1-12, 22, Newfoundland, Canada. Canepa Y. et al. (1988) Essais de sollicitation horizontale de tubes de différents diamètres fichés dans une fosse de sable de Fontainebleau. Report F.A.E.R /867, February 1988, LRPC Melun, France, 32 pages. Cassan M. (1988) In-situ tests in soil mechanics. Vol 1, Eyrolles editor, Paris, 574 pages. Degny E. (1985) SLIVALIC-5, Programme de lissage par splines quintiques. Notice d utilisation. LCPC, FAER , 25 pages. Elson W.K. (1984) Design of laterally loaded piles. Report N 13, CIRIA, U.K. Jézéquel J.F. (1988) Résistance latérale des pieux. Prévision du comportement des pieux. Report F.A.E.R GSC5, Mars 1988, LRPC St-Brieuc, France, 43 pages. King G.J.W. (1994) The interpretation of data from tests on laterally loaded piles, Proceedings, Intern. Conference: Centrifuge 94, Singapore, 31-2 september 1994, Mezazigh S. (1995) Étude expérimentale des pieux chargés latéralement : proximité d un talus et effet du groupe. Thèse de doctorat, Université of Nantes (France), 272 pages. Milovitch D., Stefanovitch S. (1982) Some soil parameters determined by CPT. Proceedings, Second European Conference on Penetration Testing ESOPT-2, Amsterdam, vol. 2, Ministère de l équipement, du logement et des transports (1993) CCTG - Fascicule 62, titre V : Règles techniques de conception et de calcul des fondations des ouvrages de génie civil. 182 pages. Poulos H.G., Davis E. (198) Load-deflection prediction for laterally loaded piles. In Pile Foundation Analysis and Design, chap. 8, Wiley and Sons Editors. Poulos H.G. (1988) Marine geotechnics. London, Unwin Hyman Editors. Reese L.C, Matlock H. (196) Generalized solutions for laterally loaded piles, Journal of the Soil Mechanics and Foundations Division, ASCE, vol. 86,SM5,

10 Remaud D. (1999) Pieux sous charge latérale. Étude expérimentale de l effet de groupe. Thèse de Doctorat, Université of Nantes, 28 pages. Schmertmann J.H. (1978) Guidelines for CPT. In Performance & Design, U.S. Dept. of Transportation, FHWA, Washington D.C. 518