Prediction Model for Skin Friction and Tip Bearing Capacity of Bored Piles by FEM

Transcription

1 International Journal of Advanced Structures and Geotechnical Engineering ISSN , Vol. 02, No. 04, October 2013 Prediction Model for Skin Friction and Tip Bearing Capacity of Bored Piles by FEM GURDEEPAK SINGH 1, B. S. WALIA 2 1 Punjab Technical University, Kapurthala, India 2 Guru Nanak Dev Engineering College, Ludhiana, India klergs@yahoo.com, bswalia@gndec.ac.in Abstract: When pile foundation is designed from soil exploration data, if unit skin friction and unit tip bearing capacity are predicted accurately using cone penetration test (CPT) results, it becomes very convenient to select diameter and length of pile foundation. The unit skin friction and unit end bearing has been expressed in the form of set of equations involving cone penetration resistance and depth by the use of FEM (Finite Element Method). These equations are corrected by the analysis of 50 pile load test data with complete information of soil profile and cone penetration resistance values. This research work has six main components: (I) Compiling bored piles dataset containing pile loading test data, soil profile and continuous record of cone penetration resistance obtained from the published literature; (II) Calculation of soil parameters from soil type and cone penetration resistance; (III) Calculation of unit skin friction and unit end bearing by the use of FEM (IV) Relating unit skin friction and unit end bearing capacity to soil type, cone penetration resistance and depth; (V) Calculation of correction factors for unit skin friction and unit end bearing from pile load test data by the use of multiple regression analysis; (VI) Assessment of the performance of the presented model by comparing with conventional direct CPT methods. These equations can be used by engineers to predict ultimate pile load capacity in axial compression from cone penetration data. It has been observed that the presented model gives better accuracy than conventional methods. Keywords: Pile load capacity, Bored piles, Cone penetration resistance, FEM Introduction: A pile is most commonly used foundation for difficult soil conditions. The accurate prediction of load settlement behavior of piles is a complicated load transfer mechanism, involving the inter-related displacement of pile and surrounding soil. To predict a pile s load capacity precisely has always been a challenge for design engineers (Pooya Nejad et al. 2009).The cone penetration test (CPT) is simple, fast, and relatively economical, gives continuous records with depth, hence preferred penetration test for pile analysis and design. The shape of cone penetrometer is similar to model pile, so it can be used as geotechnical investigation tool for the estimation of pile capacity (Campanella and Robertson 1988). In some direct CPT methods, unit skin friction and unit toe resistance are estimated from measured cone resistance; others calculate from cone sleeve friction (Eslami and Fellenius 1997). The stability of pile foundations can be reliably assessed by pile loading tests. But high cost of this test makes it infeasible at every project apart from important projects. If reliable correlations are developed between pile loading test and in situ test like CPT, it will provide most benefit to engineers to execute project economically, because it will provide a model which will give stability and serviceability analysis with simple test. In literature, analysis of piles is done by various methods such as elastic approximation (Vesic 1977; Poulos and Davis 1980; Randolph and Wroth 1978), Finite Element analysis (Desai 1974), hyperbolic models (Chin 1970; Fleming 1992) and artificial neural networks models (Jaksa et al. 2008). In the present study, the unit skin friction and unit tip bearing capacity are calculated from two input parameters i.e. soil type and cone resistance with help of FEM. Conventional direct CPT methods: The direct CPT methods which utilize cone tip resistance only are considered in present study: (i) de Ruiter and Beringen (commonly called the European method) (de Ruiter and Beringen 1979) (ii) Bustamante and Gianeselli Method (LCPC/LCP Method) (commonly called the French method) ( Bustamante and Gianeeselli 1982) (iii) Aoki and De Alencar Method (Aoki and Alencar 1975) de Ruiter and Beringen Method: This method is also called as the European method and uses different coefficients for clay and sand. In clay, the undrained shear strength (S u ) for each soil layer is first calculated from the cone tip resistance (q c ). Then, the unit tip bearing capacity and the unit skin friction are calculated by using suitable multiplying factors. The unit tip bearing capacity is given by: q t = N c S u (tip) S u (tip) = q c (tip)/ N k where N c is the bearing capacity factor and N c =9 is considered by this method. N k is the cone factor that ranges from 15 to 20, depending on the local IJASGE Copyright 2013 BASHA RESEARCH CENTRE. All rights reserved

2 GURDEEPAK SINGH, B. S. WALIA experience. q c (tip) is the average of cone tip resistances around the pile tip computed similar to Schmertmann method. The unit skin friction is given by: f = βs u (side) where β is the adhesion factor, β =1 for normally consolidated (NC) clay, and β =0.5 for overconsolidated (OC) clay. S u (side), the undrained shear strength for each soil layer along the pile shaft, is determined by: S u (side) = q c (side)/n k In sand, the unit tip bearing capacity of the pile (q t ) is calculated similar to Schmertmann method. The unit skin friction (f) for each soil layer along the pile shaft is given by: f = q c (side)/300 de Ruiter and Beringen imposed limits on q t and f in which q t < 15 MPa and f< 120 kpa. Bustamante and Gianeselli Method (LCPC/LCP Method): It is also called as the French method and the LCPC/LCP method. In this method, both the unit tip bearing capacity (q t ) and the unit skin friction (f) of the pile are obtained from the cone tip resistance (q c ). The unit tip bearing capacity of the pile (q t ) is calculated from the following equation: q t = k b q eq (tip) where k b is an empirical bearing capacity factor that varies from 0.15 to 0.60 depending on the soil type and pile installation procedure and q eq (tip) is the equivalent average cone tip resistance around the pile tip. k b = for Clay-Silt (For bored piles) k b = 0.15 for Sand-Gravel (For bored piles) The pile unit skin friction (f) in each soil layer is estimated from the equivalent cone tip resistance (q eq (side)) of the soil layer, soil type, pile type, and installation procedure. Aoki and De Alencar Method: Aoki and De Alencar Velloso proposed the following method to estimate the ultimate load carrying capacity of the pile from CPT data. The unit tip bearing capacity (q t ) is obtained from: q t = q ca (tip)/f b where q ca (tip) is the average cone tip resistance around the pile tip, and F b is an empirical factor that depends on the pile type. The unit skin friction of the pile (f) is predicted by: f = q c (side).α s /F s where q c (side) is the average cone tip resistance for each soil layer along the pile shaft, F s is an empirical factor that depends on the pile type and α s is an empirical factor that depends on the soil type. F b =3.5 and F s =7.0 for bored piles. α s = 1.4 for sand, 2.0 for silty sand, 3.0 for silt, 6.0 for clay. Dataset: The dataset used in this study consists of 50 full scale field loading tests of bored piles. This database also includes diameter and length of the piles, type of soil, in situ CPT results and pile loading test results. The entire dataset is collected from the literature which are reported by (Alsamman 1995) and (Eslami 1996). The minimum embedded length of the piles is 5.6 m and the maximum length is 27 m in present study. The diameters of piles range from 320 mm to 1800 mm, and the shaft bearing capacity of piles varies from 356 kn to 9635 kn. The details are given in Table No.1. Table 1: Case record summary Sr.No. D (mm) L (m) Q u (kn) Soil Profile Location Silt, sand Hamburg, Germany Sand, clay Evanston, U.S.A Sand California, U.S.A Clay, sand Hamburg, Germany Sand California, U.S.A Clay, sand Houston, U.S.A Clay, sand Hamburg, Germany Sand, gravel Dusseldorf, Germeny Fine sand Not available Sand Berlin, Germany Silty sand, sand Berlin, Germany Sand, fine sand Berlin, Germany Sand Berlin, Germany Fine sand Not available Silt, sand, gravel California, U.S.A Clay, sand Berlin, Germany Sand, gravel Dusseldorf, Germeny Sand, fine sand Kallo, Belgium

3 Prediction Model for Skin Friction and Tip Bearing Capacity of Bored Piles by FEM Sand, fine sand Kallo, Belgium Sand, clay Shandong, China Clay, sand Hamburg, Germany Sand, clay Shandong, China Sand Berlin, Germany Silty sand California, U.S.A Silt, sand Not available Fine sand, silt Not available Sand Berlin, Germany Sand California, U.S.A Clay, sand Berlin, Germany Sand Not available Clay, sand Berlin, Germany Clay, sand Hamburg, Germany Silty sand Atlanta, U.S.A Gravel, sand Berlin, Germany Sand, gravel Dusseldorf, Germany Silt, clay, sand Berlin, Germany Sand California, U.S.A Silty clay, sand Hamburg, Germany Sand Not available Clay, sand Kuala Lumpur Clay, silty sand Guimaraes, Portugal Sand Not available Sand California, U.S.A Gravel, sand Berlin, Germany Sand Hamburg, Germany Sand Berlin, Germany Clay, silt, silt Sao Poulo, Brazil Sand Seattle, U.S.A Clay, sand Nertherland Sand Berlin, Germany Calculation of soil parameters from soil type and cone penetration resistance: The major soil types considered in the study are clay, silt, sand-silt, fine sand, coarse sand and gravel. The weight density, modulus of deformation, poisson ratio, angle of shearing resistance and unit cohesion are related to cone resistance as follows: Angle of shearing resistance and unit cohesion are calculated from relationship given by (Owuama 2000) in graphical form. The weight density is calculated from following relation given by (Mayne et.al. 2010). γ t (kn/m 3 ) = { log[z (m)] log[f s (kpa)] log[q t (kpa)]} The value of friction ratio varies from 0.5% to 1.2% depending upon the type of soil. The typical values used in the study are given in Table No. 2 by (Campanella 1995). Sleeve friction (f s ) = friction ratio (R f ) x cone penetration resistance (q u ) The modulus of deformation and poisson ratio are calculated from Table No. 3 (Olsen and Farr 1986) Table 2: Detail of friction ratio values for various types of soil Type of soil Clay Silt Sand-Silt Fine Sand Coarse Sand Gravel Friction Ratio (R f )

4 GURDEEPAK SINGH, B. S. WALIA Table 3: Detail of modulus of deformation (E) and poisson ratio (µ) values for various types of soil S. No. Soil parameter Clay Silt Silty Sand Sand 1 Modulus of Deformation. (E) 3 to 8q c 3 to 5q c 1 to 2q c 2 to 12q c 2 Poisson Ratio (µ) 0.4 to to to to 0.35 Calculation of unit skin friction and unit end bearing: The unit skin friction and unit end bearing for major soils types i.e. clay, silt, sand-silt, fine sand, coarse sand and gravel are calculated for normal range of cone penetration resistance values by FEM as a single pile under axial compressive load. The soil parameters required by FEM are calculated by the correlations given in the previous section. The variation of unit skin friction and unit end bearing for major soils types i.e. clay, silt, sand-silt, fine sand, coarse sand and gravel with cone penetration resistance are given in fig.(1) and (2). The FEM simulation of pile foundation is capable of calculating the full load-displacement curve of a vertically loaded pile, as well as the load transfer mechanism of the pile. The pile model is solved by Winker-Pasternak method (Bittar 1996) using Young modulus, Poisson s ratio of the soil and depth of the influence zone. Pile is modeled as number of onedimensional bar elements. The pile-soil interface is simulated in forms of nodes made up of nonlinear soil springs. The pile-soil interface behaves as elastic-plastic material which satisfies Mohr- Coulomb yield condition. The input parameters for this method are the angle of internal friction, cohesion, bulk weight, poisson ratio and modulus of deformation of soil. As a result, the method provides the load-displacement curve up to pre-specified limit deflection. Fig. (1) The variation of unit skin friction for major soils types i.e. clay, silt, sand-silt, fine sand, coarse sand and gravel with cone penetration resistance

5 Prediction Model for Skin Friction and Tip Bearing Capacity of Bored Piles by FEM Fig. (2) The variation of unit end bearing for major soils types i.e. clay, silt, sand-silt, fine sand, coarse sand and gravel with cone penetration resistance soil layer and unit end bearing is converted to end Relating unit skin friction and unit end bearing capacity to soil type, cone penetration resistance and depth: The trend lines are plotted between unit skin friction and cone penetration resistance (q c ), unit end bearing bearing for a particular soil in which pile rest. In this way, a total of 50 equations are developed, one equation for each pile. The multiple regression analysis is conducted to find corrections in skin friction and end bearing for various soil types. The and cone penetration resistance (q c ). These multiple regression analysis balances 50 equations polynomial equations of these trend lines give the relation between unit skin friction and cone penetration resistance and also between unit end bearing and cone penetration resistance. simultaneously by giving due weight to each soil type in the form of regression coefficient. The following equations are developed for each pile strata as input equations for multiple regression analysis: Q ui = a.(sf ci +eb ci )+b.(sf mi +eb mi )+c.(sf smi +eb smi ) Calculation of correction factors for unit skin friction and unit end bearing from pile load test data by the use of multiple regression analysis: A dataset of 50 pile loading test with complete detail of soil profile and continuous record of cone penetration resistance are analysed by set of equations given by curves shown in fig. 1 and 2. The unit skin friction is converted to skin friction for each +d.(sf fsi +eb fsi ) +e.(sf csi +eb csi )+f.(sf gi +eb gi ) (i=1,2,3,..50) where a,b,c,d,e,f are regression coefficients, sf ci, sf mi, sf smi, sf fsi, sf csi, sf gi are skin frictions for clay, silt, sand-silt, fine sand, coarse sand and gravel layer for i th pile, eb ci, eb mi, eb smi, eb fsi, eb csi, eb gi are the end bearing for clay, silt, sand-silt, fine sand, coarse sand and gravel layer for i th pile. For each pile there is one

6 GURDEEPAK SINGH, B. S. WALIA end bearing for a particular soil in which pile tip rest, end bearing for other soils is taken as zero. Q ui is ultimate load carrying capacity of i th pile which is computed from field pile load test data. The regression coefficients are multiplied with skin frictions and tip bearing capacity for respective soil type and equated to ultimate pile load capacity found from pile load tests. So a total of 50 simultaneous equations are solved by multiple regression analysis to get regression coefficients which are unique for a particular soil type. These regression coefficients are given in Table No. 4. The ratio of predicted to field ultimate load capacity is determined before multiple regression analysis and after regression analysis. It is found that there is improvement in statistical parameters before multiple regression analysis and after regression analysis. The results are given in Table No. 5. Table 4: Regression coefficients for major soil types. Sr. no. Type of soil Regression Coefficient 1 Gravel Coarse Sand Fine Sand Silt-Sand Silt Clay Table 5: Statistical parameters before multiple regression analysis and after regression analysis. Sr. no. Statistical parameters Before multiple regression analysis After multiple regression analysis 1 Minimum Maximum Average Standard Deviation Coefficient of Correlation Table 6: The equations for determination of unit skin friction, unit end bearing from cone penetration resistance. Sr. No. Type of Soil Unit skin friction (kn/m 2 ) Unit end bearing capacity (kn/m 2 ) 1 Clay (q c ) (q c ) (q c ) Silt (q c ) (q c ) (q c ) Silty Sand (q c ) (q c ) (q c ) (q c ) (q c ) Fine Sand (q c ) (q c ) (q c ) (q c ) Coarse sand (q c ) (q c ) (q c ) (q c ) Gravel (q c ) (q c ) (q c ) (q c ) (q c ) Results: The regression coefficients found in previous sections are used to obtain polynomial equations which can be used for the calculation of unit skin friction and unit end bearing capacity of bored piles from soil type and cone penetration resistance (MPa). These equations are given in Table No. 6. The variation of unit skin friction and unit end bearing with depth is calculated up to 30m depth and presented in form of polynomial equation. For unit skin friction the depth factor is D sf, which is calculated as follows: D sf = D D for 0< D< 30m and D sf 1 Where D is the depth of centre of layer of soil under consideration. For unit end bearing the depth factor is D eb, which is calculated as follows: D eb = L L for 0< L<30m and D eb 1 Where L is the length of pile. The unit skin friction and unit end bearing capacity are calculated as product of equation from Table No. 6 corresponding to the soil under consideration and depth factor given above.

7 Predicted to measured pile load capacity Qu(p)/ Qu(m) Prediction Model for Skin Friction and Tip Bearing Capacity of Bored Piles by FEM 9. Validation of predictive methods and discussion In order to investigate the performance of the proposed model, a statistical comparison has been made for CPT direct methods such as, de Ruiter and Beringen (European method), Bustamante and Gianeselli Method (LCPC/LCP Method), Aoki and De Alencar Method with proposed method. The ultimate pile load capacity (Q u ) is predicted by direct CPT methods and proposed method and compared with the measured pile load test values. The comparison of the minimum, maximum, average and coefficient of correlation of the ratio of estimated to measured ultimate pile load capacity is shown by Table No.7 for the quantitative assessment. It can be noted that CPT direct methods namely French method and Aoki method with the mean values of 0.59, and 0.37 considerably underestimate the pile load capacity. In contrast, the European method and the proposed method with the mean values of 0.92 and 1.06, respectively, show a good agreement between the predicted and the measured ultimate pile load capacity proposed European French Aoki Cumulative Probability (%) Fig. 3. Comparison of methods estimation for pile load capacity by the probability approach. Table 7: Statistical parameters of ratio of predicted ultimate pile load capacity, Q u (p) to measured ultimate pile load capacity, Q u (m) by various direct CPT methods and the proposed method. Statistical parameters European method French method Aoki method Proposed method Minimum of (Q u (p)/ Q u (m)) Maximum of (Q u (p)/ Q u (m)) Average of (Q u (p)/ Q u (m)) Coeff. of Correlation of (Q u (p)/ Q u (m)) The comparison is also presented by log normal plot of the ratio of the estimated values of ultimate pile load capacity (Q u ) to the measured values versus their cumulative average(which is known as cumulative probability) by Fig. 3 graphically. Long and Shimel (1989) have shown that using such statistical presentation will provide valuable insight and quantified measure of the prediction ability of empirical correlations. Hence, for the current set of data, the ratio of predicted to measured values of ultimate pile load capacity (Q u (p)/ Q u (m)), is arranged in ascending order numbered (1, 2, 3,...i,...m) and a cumulative probability, P, is determined for each pile shaft resistance value as P = i / (m+1) Where, i is the number of value considered in P. Fig. 3 shows the plot of estimated to measured ultimate pile load capacity (Q u (p)/ Q u (m)), values versus cumulative probability for the present datasets. For the probability of 50%, the (Q u (p)/ Q u (m)) value for the proposed method is close to unity, whereas the ratio for the European method, French method and Aoki method is about 0.58, 0.56 and 0.35 respectively demonstrating a trend toward underestimation. The proposed method exhibits a lower dispersion than the other CPT direct methods, as indicated by the flatter slope of the line. It is obvious that the results for the proposed method are closer to log-normal distribution than other methods. Conclusions: A database of case histories consisting of 50 fullscale pile loading tests is compiled with the information on soil types and CPT results. FEM is used to calculate unit skin friction and unit tip bearing capacity using CPT data for every soil type. The soil types used in study is clay, silt, sand-silt, fine sand, coarse sand and gravel. The equations for the calculation of unit skin friction and unit end bearing are developed which use cone penetration resistance. Statistical approach is used to validate the performance of the proposed method and the other direct CPT methods. The predictions of ultimate load carrying capacity of bored piles by direct CPT method and proposed method is compared with the measured values obtained from pile load test data. The minimum, maximum, average and coefficient of

8 GURDEEPAK SINGH, B. S. WALIA correlation are quoted for quantitative assessment. The comparison demonstrated that the CPT direct methods, namely French method and Aoki method with the average values of 0.59 and 0.37 respectively underestimate piles shaft resistance. In contrast, the European method and the proposed approach with the mean values of 0.92 and 1.06 respectively, demonstrated better agreement with measured ultimate pile load capacity. Moreover, the proposed method gives the coefficient of correlation of 0.90 which is more than that obtained from the other CPT direct methods. The proposed method show better relationship with measured values obtained from pile load test data and is a definite progress in the prediction of ultimate load carrying capacity of bored piles in compression. Hence ultimate load carrying capacity of bored piles can be predicted by proposed method with better accuracy. References: [1] Alsamman, O The Use of CPT for Calculating Axial Capacity of Drilled Shaft. PhD Thesis, University of Illinois, Urbana [2] Aoki, N., de Alencar, D An Approximate Method to Estimate the Bearing Capacity of Piles In: Proceedings, the 5th Pan-American Conference of Soil Mechanics and Foundation Engineering, Buenos Aires, Vol.1, pp [3] Baziar, M.H., Ghorbani, A Evaluation of lateral spreading using artificial neural networks. Soil Dyn Earthq Eng. 25(1):1 9. [4] Bittar, Z., Sejnoha, J Numerical methods in structural mechanics. In: ASCE Press, Thomas Telford, New York, pp. 422 [5] Bustamante, M., Gianeeselli, L Pile Bearing Capacity Predictions by Means of Static Penetrometer CPT In: Proceedings of the 2nd European Symposium on Penetration Testing, ESOPT-II, Amsterdam, Vol. 2, pp [6] Campanella, R. G Interpretation of piezocone test data for geotechnical design, Soil Mechanics Series No. 157, Dept of Civil Engg, The University of British Columbia. [7] Campanella, R.G., Robertson, P.K Current status of the piezocone test. In: Proceedings of 1st international symposium on penetration testing, ISOPT-1, Orlando, March 22 24, vol. 1 pp [8] Chin, F.K Estimation of the ultimate load of piles from tests not carried to failure. In: Proceedings of the Second SE Asian Conference on Soil Engineering, Singapore, pp [9] de Ruiter, J., Beringen, F.L Pile Foundations for Large North Sea Structures. Marine Geotechnology, 3(3): [10] Desai, C.S Numerical design analysis for piles in sands. Journal of Geotechnical Engineering Division, ASCE 100 (GT6): [11] Eslami, A Bearing Capacity of Piles from Cone Penetration Data. PhD Thesis, University of Ottawa, Ottawa, Ontario [12] Eslami, A., Fellenius, B.H Pile capacity by direct CPT and CPTu methods applied to 102 case histories. Can Geotech J 34: [13] Fleming, W A new method of single pile settlement and analysis. Geotechnique, 42(3): [14] Jaksa, M.B., Maier, H.R., Shahin, M.A Future challenges for artificial neural network modelling. In:The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics, pp [15] Keaveny, J.M., Mitchell, J.K Strength of finegrained soils using the piezocone In: Proc. of. ASCE Special Conference In Situ86, Blacksburg, pp [16] Lambe, T.W., Whitman, R.V Soil Mechanics, Wiley, New York, pp. 160 [17] Long, J.H., Shimel, I.S Drilled shafts, a database approach. In: ASCE proceedings of the foundation engineering congress: current principles and practices, Evanston, Ill, June 25 29, In: Kulhawy FH, editor. Geotechnical special publication 22, vol. 2. American Society of Civil Engineers. pp [18] Mayne, P.W., Peuchen, J., and Bouwmeester, D Estimation of soil unit weight from CPTs. Proc. 2nd International Symposium on Cone Penetration Testing, (CPT 10, Huntington Beach, CA), Vol 2, pp [19] Olsen, R,S., and Farr, J.V Site characterization using the cone penetration test. In: Proc. ASCE Special Conference - In Situ '86: Use of In Situ Tests in Geotechnical Engineering, Blacksburg, pp [20] Owuama, C.O A comprehensive method of interpretation of static cone data. NSE Technical Transactions, vol. 35, No. 1, pp [21] Pooya Nejad, F., Jaksa, M.B., Kakhi, M., McCabe, B.A Prediction of pile settlement using artificial neural networks based on standard penetration test data. Comput Geotech 36(7): [22] Poulos, H.G., Davis, E.H Pile Foundation Analysis and Design. Wiley. [23] Randolph, M.F., Wroth, C.P Analysis of deformation of vertically loaded piles. Journal of Geotechnical Engineering, Division 104, pp [24] Robertson, P.K., Campanella, R.G Interpretation of cone penetration tests, Part 1: Sand. Canadian Geotechnical Journal, 20(4): [25] Soares, J.M Evaluation of soil-structure interaction and design. Ph.D. Thesis. Geotechnical Post-Graduation Program, Civil and Environmental Engineering Department, University of Brasília. [26] Vesic, A.S Design of pile foundations. In: National Cooperative Highway Research Program, Synthesis of Practice No.42, Transportation Research Board, Washington, DC.