Soil stiffness degradation in the design of passive piles

Transcription

1 Soil stiffness degradation in the design of passive piles M. Kubilay Kelesoglu Assistant Professor, Civil Engineering Department, Istanbul University, Istanbul, Turkey S. Feyza Cinicioglu Professor, Civil Engineering Department, Istanbul University, Istanbul, Turkey KEYWORDS: Piles; Embankments; Soil-pile interaction; Soft soils; Lateral loads ABSTRACT: Design of laterally loaded soil-pile systems subjected to embankment induced movements is among the main concerns of geotechnical engineers. Despite surging interest and numerous researches, soil-pile interaction remains to be one of the most ambiguous aspects of the problem. There is a need for the methods that are capable to represent real field behavior and in this respect displacement-based methods are appraised the most. The method proposed in this paper is based on the measurements provided by field instrumentation and therefore is a displacement-based method, but with a distinctive capability of producing its own soil stiffness degradation curves from field measurements. As the calculations of the proposed method are made in accordance with the instrumentation records, the method enables the computation of resultant stress effects on the pile cross-section and the accompanying deflections, for any time considered. The method was applied on an example problem. The same problem was also analyzed with well-known commercial finite element software, thus comparisons of the results of the two methods were used to discuss the capability of the proposed method. 1 INTRODUCTION The loading mechanism of passive piles was distinguished by Stewart et al. (1994) as the soil moves past the piles. Passive piles are extensively used next to the embankments and in moving slopes. In these systems passive lateral pressure exerted to the pile by the moving soil causes displacements, moments and shear forces. Correct prediction of these values is a key element in the design, construction and serviceability of the piles. In the design of these structures, a number of ambiguities may arise due to the difficulty of determining the load transfer mechanism developed between the soil and the structure. In the analysis of the load transfer mechanism, knowledge of (i) the pressure acting on the pile from the moving soil and (ii) the lateral resistance that is developed in the pile and the responding soil is the main issue that requires considerable attention. In the literature, to analyze passively loaded pile problems, numerous methods have emerged. The methods in use can be categorized as empirical, pressure-based, displacement-based and numerical methods (Stewart et al. 1994). Despite different merits of each category, displacement-based method emerged to fulfil the need for better representation of field behaviour. Appropriately, displacement-based methods are described as the methods where the distribution of free-field lateral soil movements is input and the resulting pile deflection and bending moment distribution are calculated. Poulos (1973), 188

2 Springman (1989), Stewart et al. (1994) can be considered in the scope of the early examples of displacement-based methods. The methods by Chow (1996) and Goh et al. (1997) are among those that use free-field displacements directly to solve soil-pile load transfer mechanism. Although the method proposed in this paper is a displacement-based method, it uses not only the displacements but the whole response measured in the field, and transfers this knowledge as a prediction tool which can be defined as the soil stiffness degradation curve. Fig.1 demonstrates the zones of response in the problem of piles subjected to embankment induced lateral loads. Fig 1a shows the free-field case in which embankment induced loads resisted only by the response developed in the passively loaded zone. The free-field response in the zone ABCD can be measured in terms of lateral and vertical deformations, excess pore water pressures and vertical effective stresses. As can be noticed with this feature the proposed method is an improved version compared to the other displacement-based methods, which consider only lateral displacements. In the application of the proposed procedure, if there are piles in the system, the mechanism shown in Fig.1b holds true. In this case, soil in the passive zone, ABCD together with piles constitutes a composite system to resist the loads induced by the embankment loading which is transferred by the squeezed soil beneath it. Figure 1. Soil movement beneath an embankment (a) free-field (without piles) (b) with piles The proposed method calculates soil stiffness degradation curves by using the measured freefield response and employs these curves in the prediction of soil-pile interaction that will develop when piles are constructed. The details of the application of the procedure are given in the following sections. The proposed method was described by applying the procedure on Cubzac-les-Ponts test embankment case at which free-field response and soil investigation data was available. The same problem was also solved with Plaxis 3D to provide comparisons with the results of the application of the method. The proposed method is applicable for passively loaded single piles or passively loaded piles at a spacing that would not cause interaction or arching effects. The determination of soil response and obtaining them through laboratory testing is subject to difficulties (Reese and Van Impe 2001). Even with great care the differences between laboratory and in-situ strain rates result in the alteration of the pre-consolidation pressures and processes (Oztoprak and Cinicioglu, 2005). The variation of soil stiffness degradation found with the proposed method is exempt from these limitations and emerges as a fundamental soil behavior. 2 FIELD RESPONSES IN TERMS OF SOIL STIFFNESS DEGRADATION The Cubzac-les-Ponts case belongs to a fully instrumented test embankment built on soft soils. The soil profile, dimensional properties and applied instrumentation layout in Cubzac-les-Ponts test embankment case corresponding to free-field conditions are shown in Fig.2. The area ABCD represents the zone of interest that covers all notable soil movements responding to the loads induced by the embankment. In order to be more precise and to take care of possible changes along the depth, the area of interest can be divided into smaller zones vertically as shown in Fig.2a. 189

3 Soil stiffness degradation in the design of passive piles Kelesoglu, M.K. & Cinicioglu, S.F. Figure 2. (a)the soil profile, dimensional properties and applied instrumentation layout in Cubzac-les-Ponts embankment (Magnan et al. 1983; Oztoprak and Cinicioglu 2005) (b) Initial and deformed states of a soil zone The proposed method can make calculations for any time or state that can be considered, because it has the property of following the behavior as stress-strain state changes with respect to loading and time. During mobilization of the responses, deformations develop and stress redistribution takes place at every point. The dissipation of the applied energy in the responding zone gives an indication of the applied action on it. This is a continuous process which should be measured both in the short and long terms. Measured responses change depending on many factors such as soil properties, drainage conditions, rate of loading, time-dependent behavior, degree of confinement etc. If the initial deformation states at the corners of a considered zone are defined, the average deformation and corresponding stress state in that element at any instant can be evaluated. The deformation state at any time t i is shown on a sample element in Fig.2b. The initial time is denoted as t = t0 condition and the coordinates of the nodes of the deformed mesh at any instant t = ti are found by shifting the initial coordinates by the measured amount of lateral and vertical deformations. The average lateral and vertical strains of a considered zone at any deformation state are found by (1) and (2). ε ε lateral vertical [( xb - xb) + ( xc - xc)] [( xa - xa) + ( xd - xd)] = εh = 2dx. [( zb - zb) + ( za - za)] [( zc - zc) + ( zd - zd)] = εv = 2dz. In order to find the relevant stresses corresponding to any strain state, vertical effective stresses are calculated. Then, for lateral effective stresses current values of coefficient of lateral earth pressure, K relevant for the considered strain state are used. The methodology proposed by Zhang et al. (1998) provides this opportunity. Zhang et al. (1998) methodology gives the relationship that enables the evaluation of lateral earth pressures for any non-failing stress state that falls between the states of at rest K 0, active Ka and passive K p. According to the methodology by Zhang et al. the earth pressure coefficient K varies continuously over a range of values extending from an active towards a passive state of stress depending only on the change in deformation ratio, R ε =Δεlateral Δ εvertical =Δε3 Δε1 where Δ ε 3 and Δ ε1 are the increments in minor and major principal strains, respectively. Zhang et al. (1998) generated a smooth curve that relates R ε to K. At (1) (2) 190

4 which the definition of K ranges from K a towards condition defined as K0 = 1 Sin φ by Jaky. K p. On this curve R ε = 0 corresponds to K0 Owing to the fact that field response is demonstrated in terms of deformations and excess pore water pressures the procedure proposed in this paper finds soil stiffness degradation by using freefield measurements and applying a conceptually different technique than the conventional methods used for this purpose. The strain-dependent behavior of soil affects its load reception capacity, which can be interpreted in terms of stiffness degradation properties. To find the K value with respect to strain ratio provides a unique opportunity to combine strain anisotropy and stress anisotropy in one parameter, that is K (Oztoprak and Cinicioglu, 2005). Provided that K is found in terms of strain anisotropy, the function of K can then be expressed as to carry the influence of strain anisotropy into stress anisotropy. As a result, stresses experienced by the responding soil at any instant can best be defined as σ v and σ h ( = Kσ v ) where K is found by applying Zhang et al. (1998) with the strain states ( ε v, ε h ) calculated from field measurements. In these calculations, principal stresses and strains are assumed coaxial with the imposed condition of no stress rotation. In the course of application of the method, each calculated horizontal stress state corresponds to a lateral deformation state in the considered zone (e.g. ABCD in Fig.2). In order to find a horizontal stress variation that would be applicable for any level of deformation, the values of lateral stress states, σ h were normalized with the corresponding lateral deformations and then plotted against lateral deformations, y. Lateral displacement, y values have been chosen as the free-field lateral displacement values measured along the vertical section beneath the toe. The soil stiffness parameter, khs found with this approach is defined as in (3). k hs K = v y σ The resulting variation found with this approach can be defined as the soil stiffness degradation curve, which reflects real-time field behavior under the action of embankment induced loads. Equations (4) and (5) can be written to express k hs in terms of fundamental soil parameters (Kelesoglu 2006, Cinicioglu and Kelesoglu, 2006). ( ) ( ) khs = 1-Sinφ 1- Sinφ. Rε. y. σv for ε1 =Δεvertical (4) ( ) ( ) k = 1- Sinφ. Rε 1- Sinφ. y. σ for ε =Δε hs v 1 lateral As seen in (4) and (5) k hs has now been defined as a function of φ, R ε, y and σ v. While maximum internal friction angle, φ stands as the strength parameter, R ε covers the implications of structural changes and σ v reflects the influence of depth. To apply the developed theory to Cubzac-les-Ponts test embankment case, equations (4) and (5) have been used to plot the degradation curves for each zone specified in Fig.2. Since field monitoring (Fig.2) gives a series of measurement readings, a series of k hs values can be obtained by the application of (4) and (5) starting from the commencement of construction ( t = 0 ) towards any state considered. Having obtained the whole set of data, k hs values are plotted against y values to find stiffness degradation curves of the soil. In this way, field degradation curves which have been calculated by using (4) and (5) for each zone (ABCD in Fig.2) in Cubzac-les-Ponts embankment case are demonstrated in Fig.3. Soil stiffness degradation curves presented in Fig.3 provide the resistance capacity of the soil against any kind of lateral loading. In Fig.1, where the deformation mechanisms of free-field and piled cases are given, the works done in the passively loaded zones should be the same since both mechanisms dissipate the same amount of energy imparted by the same construction work. Thus, if there are inclusions other than soil such as piles, the validity of the soil stiffness degradation curves (3) (5) 191

5 Soil stiffness degradation in the design of passive piles Kelesoglu, M.K. & Cinicioglu, S.F. equally holds true, and these curves act as envelopes under which soil-pile interaction mechanism can be solved. Figure 3. Field degradation curves and their best-fit equivalents for zones 1 and 4 3 SOIL-PILE INTERACTION If there are piles in the system, the relationship defining the proportioning of the applied load with respect to relative stiffness values of each component was used by several researchers (Chow 1996, Goh et al. 1997) and is given as { } [ ]{ } K K + Δ y = K Δy p s p s s where { Δ y P } and { Δ y S } are the incremental free-field soil movement and incremental deflection of the pile respectively. [ K P ] and [ K S ] are the pile and soil stiffness matrices. [ K P ] is made up of pile geometry and material properties, whereas, [ K S ] is constituted by the horizontal soil stiffness values, (k hs,1 k hs,n ) which have been found for each considered soil element from their respective response curves. Two of the response curves are exemplified in Fig.3, for the zones 1 and 4. In the application of the method, both the magnitude of exerted pressure (right-hand side of (6)) and the soil-pile interaction (left-hand side of (6)) can be deduced from the same response curve. The use of the response curves to solve interaction properties is demonstrated in Fig.4. Any incremental stage can be considered by the area under the curve extending from the deformation state corresponding to the start of that stage and the deformation state corresponding to the end of it. As deformations increase soil degrades more, thus stiffness values modeling the deformation capability get smaller. The response curves can be generated and applied for any number of soil elements in front of the pile and therefore they are suitable to be used within a FE formulation. Using this property, the individual pile is modeled with beam elements. Similarly, the soil next to the pile is divided into a number of layers and the soil response envelopes for each layer are found separately. The consideration of equilibrium and compatibility is essential for the computations. The proposed method is capable of analyzing the behavior for all possible cases: either when piles are constructed before (Case I), during or after embankment construction (Case II) as demonstrated in Fig.4. The application in Fig.4 can be explained as follows. As piles are already in place in Case I, the time that embankment construction has started can be denoted as t = 0. Considering a deformation state y s( t1) corresponding to the time, 0 t1, the calculations can be made by applying (6) in a suitable form as in (7). (6) 192

6 Figure 4. Solution for Pile Deflection and Load Sharing for Case I (a-b-c) and Case II (d-e) [ K ]{ app app P y pt1 ( )} [ K S]{ y pt1 ( )} [ K S]{ y s( t1) } app Δ + Δ = Δ (7) In (7), Δ y p ( t1 ) stands as the approximate pile deflection value because stiffness degradation has not been introduced yet. To include the effects of degradation, adjustments are necessary on both sides of (7). The right-hand side of the equation is corrected by calculating the area beneath the response envelope between the states of y s = 0 and ys = yst1 ( ) to find the total value of applied load, P y * y S St1 ( ) -B S s( t1) hs, i.. (8) 0 ys * app y p t1 [ ]{ } P = K Δ y = k dy + Ay dy Once the applied load P is calculated and inserted as the right-hand side of (7), Δ ( ) can be found by using (7). The part of the area that lies above the response envelope, shown in Fig.4c, should be real transferred below the response envelope to obtain the exact value of pile deflection, Δ y p ( t1 ). real Consequently, following the area transfer shown in Fig.4c, Δ y p ( t1 ) can be extracted from real y pt1 ( ) B, ( ). app * ( hs i ) ( pt1 s ) k y y = Ay dy (9) * ys The procedure is similar for Case II as shown in Fig.4d and 4e. In the application of the method, there is a need to find an initial stiffness, k hs,i value to specify the elastic part that will be used in the calculations. As a matter of fact, while applying the soil-pile interaction process the first movement of the pile is indicative of the commencement of the calculations. Carrying out a critical review of literature on the subject (Prakash and Kumar 1996, Poulos and Davis 1980) the ratio of yd= for the crust and over consolidated clay layer and the ratio of yd= for the soft layers were used with the simplified-best fit curve equations (Fig.3) of the field degradation curves. 193

7 Soil stiffness degradation in the design of passive piles Kelesoglu, M.K. & Cinicioglu, S.F. 4 SOLUTION OF THE OVERALL SOIL-PILE SYSTEM The procedure outlined so far corresponds to the behavior of a segment of the pile and the soil in front of it. Applying the rules of compatibility and equilibrium, FE solution for the overall pile and the responding soil system is conducted for all the stages during and after load application and afterwards. Summation of moments and displacements calculated in each loading increment gives the total values up to any desired stage. In order to apply the method to the specific case of Cubzacles-Ponts, the reference days were chosen as; 1, 4, 5, 6, 7, 8, 13, 15, 63, 174, 741, 817 at which the field measurements were taken. Figure 5. The schematic representation and the idealization of the problem The test embankment was constructed in five steps and six days. At the end of the each step, the embankment height was 0.70 meters (1 st day)-1.20 meters (5 th day) meters (6 th day). For Case 2, it is assumed that the piles are constructed at the end of embankment construction, on the 7 th day. The schematic representation of the loading created by soil movements and the lateral response developed against it by the composite soil-pile system for Cubzac-les-Ponts case is given in Fig.5. As the interaction mechanism is solved by using the eq. (6) the geometry and material properties of the pile constitute the pile stiffness matrix, [ K p ]. Therefore elements of [ K p ] have been kept constant during the application of the method for different loading stages. In addition to considering the degradation in the soft clay layers which is the main concern of this paper, the degradation in the underlying stiff layers was also taken into account. 5 ANALYSES WITH OTHER FINITE ELEMENT SOFTWARES Case 1 and 2 has also been solved by using Plaxis 3D Foundation v2.1. The purpose is to provide comparisons between the outcomes of the proposed method and a method that have gained general acceptance as an advanced prediction method which is capable of considering three dimensional nature of the problem. Soft soil layers of the Cubzac-les-Ponts test site are modeled using Soft Soil Creep (SSC) model. Creep parameters of these layers are defined with the equation proposed by Mesri and Choi (1985) as Cα / C C The stiff substratums were modeled with Hardening Soil (HS) model to consider the soil nonlinearity and hardening. 194

8 Figure 6. Finite element model and stiff substratum-embankment-pile parameters Table 1. Soil parameters used in the FEM analyses: the soft soil layers (Magnan et al. 1983, Wood 1990, Oztoprak and Cinicioglu 2005) Material Depth φ σ / vc γ κ λ e CS M G k X k Y Crust x x10-9 Over cons.cl x x10-9 Very soft cl x x10-10 Very soft cl x x10-9 Soft cl x x10-9 φ : friction angle [ 0 ], σ / vc : precons. press. [kn/m 2 ], γ : unit weight [kn/m 3 ], κ : swelling index, λ : comp. index, e cs : crit. void ratio, M : slope of the crit. state line, G : shear mod. [kn/m 2 ], k X, k Y : coef. of vertical and horizontal perm.[m/s] Piles are modeled as embedded piles in 3D analyses. In 3D analyses, a single pile was modeled due to the symmetry of the problem as given in Fig.6. Parameters of soft soil layers were obtained as a result of an extensive research as provided in Magnan et al. (1983) and Wood (1990). The parameters defining these soft and stiff layers are listed in the Table 1 and Fig.6, respectively. 6 RESULTS The results of these applications have been displayed as bending moment-depth, pile head displacement-time graphs. The graphs of bending moment-depth relations found with the application of the aforementioned methods for the Case I for the reference days 15 and 817 are presented in Fig.7a and 7b. These figures indicates that Plaxis 3D gives bending moments comparable to the curves provided by the proposed method. This approximation is better towards the late stages. The reasoning behind the differences in the calculations can be interpreted by comparing the measured free-field lateral soil displacements with those predicted by Plaxis 3D given in Fig.8a. The differences of calculated displacements compared to the measured ones in Fig.8a were reflected in the bending moments calculated by Plaxis (Figs.7a and 7b). This finding gives a clear indication of the dependability of the proposed method. The graphs of pile head displacement against time have been demonstrated in Fig.8b. The proposed method gives considerably higher pile head displacements especially at construction and early consolidation stages compared to Plaxis 3D, complying with the trend seen for the free-field displacements displayed in Fig.8a. 195

9 Soil stiffness degradation in the design of passive piles Kelesoglu, M.K. & Cinicioglu, S.F. Figure 7. Bending moment depth (a) Case I 15 th day, (b) Case I 817 th day, (c) Case II 817 th day Figure 8. Lateral Movement time (a) in-situ and Plaxis 3D free-field lateral soil displacement, (b) Case I pile head displacement, (b) Case II pile head displacement In the application of Case II, piles were considered to be installed on day 7, which corresponds to the end of fill placement. Fig.7c demonstrates the bending moment-depth relationships for the day 817. The latest day was chosen to cover all the effects of construction and consolidation stages. Differing from Case I, Plaxis 3D gave higher positive bending moment values compared to the proposed 196

10 method, which is consistent with the differences in free-field lateral displacements in Fig.8a. In accordance with the results related to bending moments Fig.8c shows that pile head displacements found by the proposed method are in good agreement with those of Plaxis 3D. It is also noteworthy to compare the results found for Case I and Case II against each other. It is seen that the proposed method gives much bigger bending moments for Case I (Fig.7b) compared to the Case II (Fig.7c). The proposed method can be applied as an integrated part of an observational method especially for the cases where the embankment is constructed prior to piles. 7 CONCLUSIONS The problem of laterally loaded piles in soft soils beneath embankments has been investigated in this paper by applying a new theoretical approach to find soil stiffness degradation from free-field instrumentation data. Since the proposed approach is a displacement-based method, field deformations and pore water pressure measurements are used as input. As the stresses are calculated by the direct use of free-field deformations, the proposed method is capable of reflecting the real field behavior. Therefore, all the challenging aspects of the field behavior such as nonlinearity, inhomogeneity, time dependency, unpredictable interactions and others can automatically be accounted for with the proposed method. REFERENCES Brinkgreve, R. B. J., Broere, W., and Waterman, D. (2006). Plaxis 2D Version 8 Plaxis bv, Delft Chow, Y. K. (1996). Analysis of piles used for slope stabilization. International Journal for Numerical and Analytical Methods in Geomechanics, 20(9), Cinicioglu S. F. and Kelesoglu, M. K. (2006). Strain dependent lateral reaction mechanism of piles beneath embankments. Proceeding of Int. Conf. on Physical Modelling in Geotechnics, Hong Kong, Goh, A. T. C., Teh, C. I. and Wong K. S. (1997). Analysis of piles subjected to embankment induced lateral soil movements. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(9), Kelesoglu, M. K. (2006). Piles subjected to displacement induced lateral loads in soft soils. PhD thesis, Istanbul University, Istanbul (In Turkish.) Magnan, J. P, Mieussens, C. and Queyroi, D. (1983). Etude d un remblai sur sols compressibles: Le remblai B du site experimental de Cubzac-lesPonts, Laboratoire Central Des Ponts Et Chaussees Rapport de recherche, LPC No.127. Mesri, G. and Choi, Y. K. (1985). Settlement analysis of embankments on soft clays. Journal of Geotechnical Engineering, ASCE, 111(4), Oztoprak, S. and Cinicioglu, S. F. (2005) Soil behaviour through field instrumentation. Canadian Geotechnical Journal, 42(2), Poulos, H. G. (1973). Analysis of piles undergoing lateral soil movement. Journal of Soil Mechanics and Foundation Engineering, ASCE, 99(5), Poulos, H. G. and Davis, E. H. (1980). Pile foundation analysis and design, John Wiley&SonsInc,New York. Prakash, S. and Kumar, S. (1996). Nonlinear lateral pile deflection prediction in sands. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 122(2), Reese, L. C. and Van Impe W. F. (2001). Single piles and pile groups under lateral loading, A.A.Balkema, Rotterdam, Brookfield. Springman, S. M. (1989). Lateral loading of piles due to simulated embankment construction. PhD thesis, University of Cambridge, Cambridge. Stewart, D. P., Jewell, R. J. and Randolph, M.F. (1994). Design of piled bridge abutments on soft clay for loading from lateral soil movements. Geotechnique, 44(2), Wood, D. M. (1990). Soil behaviour and critical state soil mechanics. Cambridge Uni. Press, Cambridge. Zhang, J., Shamoto, Y. and Tokimatsu, K. (1998). Evaluation of earth pressure under any lateral deformation. Soils and Foundations, 38(1),