5 th IGC 5 th INDIAN GEOTECHNICAL CONFERENCE 17 th 19 th DECEMBER 215, Pune, Maharashtra, India Venue: College of Engineering (Estd. 1854), Pune, India PERFORMANCE ENHANCEMENT OF ISOLATED FOOTING WITH MICRO-PILES Jagat Jyoti Mandal 1, Payel Chaudhuri 2 ABSTRACT In traditional foundation design, it is customary to consider first the use of shallow foundation, such as an isolated footing. If it is not adequate, combined footing and raft are tried. When shallow foundation fails to provide adequate safety and serviceability of the structure, deep foundations such as a fully piled foundation are opted for the structure. In case of isolated footings, sometimes the top soil is not good enough to provide the safe bearing capacity of the soil required for the foundation. Even if the safe bearing capacity is satisfactory, settlement may be excessive (more than the permissible limit) and is not acceptable due to serviceability requirements. Probable solution is to improve the ground by adopting suitable techniques or by stabilizing the soil up to the influence zone. The problem can be tackled by installing micro-piles. Micro-piles improve and stabilize the existing soil by acting as reinforcement to the soil mass. Installation of micro piles in a systematic manner under the isolated footing reduces settlements to acceptable values. In addition to settlements, the bearing capacity of the soil also improves. This foundation combination further reduces the thickness required for the isolated footing. It is seen that isolated footing with micro piles is an economical solution in foundation design for soil condition where such design is applicable. 1 Professor_ Jagat Jyoti Mandal, Civil Engineering Department, NITTTR Kolkata, Kolkata, West Bengal, jjm_civil3@yahoo.co.in 2 Ph.D Scholar_Payel Chaudhuri, Civil Engineering Department, IIT, Kharagpur, Kolkata, West Bengal, payelce@gmail.com
Jagat Jyoti Mandal & Payel Chaudhuri Isolated footing with micro piles for small structures is quite a new concept from construction point of view. Introduction of micro pile/ micro piles under isolated footings is an alternative solution for combined footing, raft and deep foundations for soil having low bearing capacity and having high compressibility characteristics. For buildings, isolated footing with micro piles foundation can provide an alternative and economical foundation option instead of adopting some other ground improvement techniques where the performance of the isolated footing alone does not satisfy the design requirements. It is also advantageous where the soil condition beneath is poor. The present study is limited to the performance enhancement of isolated square footing with micro piles with respect to its elastic settlement. Comparison of isolated footing under a service load is made for different micro pile arrangement. Parametric studies are carried out in this regard. A coupled Finite Element Boundary Element approach has been used to determine the stiffness matrix of the combined foundation system. The isolated footing has been considered as a thick plate. Boundary Element Method and Finite Element Method have been employed to find out the soil stiffness matrix and plate stiffness matrix respectively where the soil has been considered as the elastic continuum. The micro pile stiffness has been represented by the spring of equivalent stiffness based on elastic theory. The micro pile has been considered as a small shaft in half space. Combined stiffness of the soil- micro pile footing system has been obtained by summing up the stiffness of the soil footing system and the stiffness contribution of the micro piles at their locations underneath the footing. Computer programs have been developed in FORTRAN language. The study can be further extended to study performance enhancement of other shallow foundations with slight modifications. Keywords: Isolated footing Micro piles, Finite element method, Boundary element method, Settlement, Elastic theory
5 th IGC 5 th INDIAN GEOTECHNICAL CONFERENCE 17 th 19 th DECEMBER 215, Pune, Maharashtra, India Venue: College of Engineering (Estd. 1854), Pune, India PERFORMANCE ENHANCEMENT OF ISOLATED FOOTING WITH MICRO- PILES J.J. Mandal, Professor, Civil Engineering Department, NITTTR Kolkata, jjm_civil3@yahoo.co.in P. Chaudhuri, Ph.D Scholar, Civil Engineering Department, IIT- Kharagpur, payelce@gmail.com ABSTRACT: Present study is aimed to study the performance enhancement of isolated square footing with micro piles with respect to its elastic settlement for different micro pile arrangements. A coupled Finite Element Boundary Element approach have been employed to find out the soil stiffness matrix and footing stiffness matrix respectively. The micro pile stiffness has been determined based on elastic theory. Combined stiffness of the soil- micro pile footing system has been obtained by summing up the stiffness of the soil footing system and the stiffness contribution of the micro piles. Computer code have been developed in FORTRAN language for this study, which shows very good convergence. Study indicates largely improved performance of the footing-soil-micro pile system vis- a-vis only footing-soil system. INTRODUCTION In traditional foundation design, it is customary to consider first the use of shallow foundation such as an isolated footing, combined footing, etc. In case of isolated footings, sometimes the top soil is not good enough to provide the safe bearing capacity of the soil required for the foundation. Probable solution is to improve the ground by adopting suitable techniques or by stabilizing the soil up to the influence zone. The problem can be tackled by installing micropiles to improve and stabilize the existing soil by acting as reinforcement to the soil mass. Installation of micro piles in a systematic manner under the isolated footing reduces settlements to acceptable values. In addition to settlements, the bearing capacity of the whole system of foundation also improves and micro piles can be used as structural elements as well as a reinforcing element to the soil mass. It is seen that isolated footing with micro piles to be economical solution in foundation design for soil condition where such design is applicable. Isolated footing constructed with micro piles for small structures is quite a new concept from construction point of view and can be an alternative solution for combined footing, raft and deep foundations for soil having low bearing capacity Micro-Piles Micro-piles are defined as small diameter, drilled, cast-in-place, or grouted piles that are typically reinforced. It is widely assumed that the range of diameter of micro piles is limited to less than 3 mm. Micro-piles can withstand axial and/or lateral loads, and may be considered as a substitute for conventional piles or as one component in a composite soil - pile mass, depending upon the design concept employed. Due to its relatively large flexibility, it can be effective in resisting seismic loads also. Due to the small pile diameter, the endbearing contribution in micro piles is generally neglected.
Jagat Jyoti Mandal & Payel Chaudhuri MATHEMATICAL FORMULATION In the present study, the analysis will be carried out by Plates on Piles and Continuum approach [5, 6]. The isolated footing is idealized as a thick plate freely resting on soil which is idealized as a semiinfinite, isotropic and homogeneous elastic half - space. The behavior of micro pile is idealized as a structural pile being considered as a shaft in elastic half - space. And the stiffness of micro pile is represented by spring on equivalent stiffness, which is determined from simplified approach by considering it to as a shaft in the half-space as done in normal pile settlement analysis. A FE BE (finite element boundary element) coupling technique is used in the calculation of the combined stiffness matrix of the foundation combination concerned. Boundary element method [3] is used to find out the soil stiffness matrix and finite element method is employed to find out the plate stiffness matrix. The half-space response is based on the solution given by Mindlin (1936) [4] for a point load in half space and it allows taking into account the effect of embedment of the plate. The plate and the half- space are two separate models in unilateral and frictional contact at the interface [2]. namely vertical displacement and two orthogonal rotations. The half-space is also discretized into the similar elements to maintain continuity and the node to node connectivity at the plate-soil interface. The stiffness matrix of the soil is obtained by boundary element method (by inverting the flexibility matrix). For compatibility at the interface, suitable transformation is carried out before coupling matrices obtained from two different approaches. Thus solution of the system can be obtained for any load distribution on the plate. After the deformations of the plate are obtained from the above procedure, the stresses can be estimated by back substitution. The stiffness of the micro-pile is determined by using elastic theory [1] by obtaining the settlement of micro pile and the micro pile is considered as a shaft in the half-space. In this method, the micro pile is divided into a number of uniformly loaded elements and a solution is obtained by imposing compatibility between the displacements of the micro pile and the adjacent soil for each element of the micro pile. The displacements of the micro pile are obtained by considering the compressibility of the micro pile under axial loading. The soil displacements are obtained in most cases by using Mindlin s equations for the displacements within a soil mass caused by loading within the mass. Fig. 1 Elastic Continuum Two-dimensional isoparametric quadrilateral elements are used to discretize the plate-half space interface. The plate is discretized into eight noded isoparametric plate-bending finite elements based on Mindlin s plate bending theory, which allows transverse shear deformation. Each node of the plate bending element has three degrees of freedom, Fig. 2 Micro-pile in elastic continuum Combined stiffness of isolated footing enhanced with micro-pile system is obtained by summing up the stiffness of the soil footing system and the stiffness contribution at the micro pile locations.
5 th IGC Settlement (mm) 5 th INDIAN GEOTECHNICAL CONFERENCE 17 th 19 th DECEMBER 215, Pune, Maharashtra, India Venue: College of Engineering (Estd. 1854), Pune, India [K pr ] = [K p ] + [K fp ] + [[M][A 1 ]] (1) Where, [Kpr] is the combined stiffness matrix of the combined system of foundation, [Kp] is the assembled stiffness matrix of the plate and [Kfp] is the stiffness of floating micro pile, [A] is the soil flexibility matrix and [M] is the transformation matrix. The force- displacement equation of the foundation can be written as {(u i ) c } = [K pr ] 1 P c (2) {(ui)c}is the generalised displacement at the nodes and Pc is the externally applied load at the nodes. By solving the above equations, displacement parameters can be obtained. A computer program is developed, based on the procedure described above for analysis of square plate. It allows for most of the practical load cases and produces accurate results RESULTS AND DISCUSSION Convergence study is carried out to assess the accuracy and effectiveness of the formulation. The result shows a faster convergence and very good accuracy. The analysis of square footing under central concentrated load with or without micropiles have been carried out and the settlement curves obtained are studied. The effect of number, length and diameter of micro-piles have also been considered. Comparative study of square footing An example has been taken up and solved to validate the methodology and computer program used in the present study. In order to assess convergence of the solution algorithm and computer code, a square footing size of size 4 m 4 m having a thickness of.3m is considered. Footing modulus (Ep) is 2.5 1 7 KN/m 2, Poisson s ratio of footing material (μr) is.2. Soil modulus (Es) is 6 KN/m 2, Poisson s ratio of soil medium (μs) is.3. Loading is a centrally concentrated load of 2KN. The elastic modulus of the pile material (Ep) is 2.5 1 7 KN/m 2. Poisson s ratio of pile material (μp) is.3. The elastic displacement of the given square footing obtained from the analysis by varying the number of elements chosen for discretization and the rigid plate displacement is plotted in Figure 3 69 68 67 66 65 64 63 62 4 16 36 64 No of elements Central settlement Rigid plate displaceme nt Fig. 3 Convergence of the displacement of square footing with rigid displacement It can be observed that the solution converges very fast and the displacement value is very close to the rigid plate displacement when 36 numbers of elements chosen for discretization of the footing. Discretization by 36 number of elements can be chosen for further analysis of the foundation. Analysis of a square footing with micro-piles A square footing of dimension 4 m 4 m having a thickness of.3m is considered. Footing modulus (Ep) = 2.5 1 7 KN/m 2, Poisson s ratio of footing material (μr) =.2. Soil modulus (Es) = 6 KN/m 2, Poisson s ratio of soil medium (μs) =.3. Loading; Central Concentrated Load (2KN). The elastic modulus of the pile material (Ep) is = 2.5 1 7 KN/m 2.Poisson s ratio of pile material (μp) =.3. Performance study is carried for various number, length and diameters of micro piles.
Settlement (mm).33.67 1 1.33 1.67 2 2.33 2.67 3 3.33 3.67 4 Settlement (mm) Jagat Jyoti Mandal & Payel Chaudhuri The discretization of the footing and corresponding location of the micro piles are shown in Figs. 4-6 for five, seven and nine numbers respectively. The evaluated elastic settlements of the footing for different number of micro piles having length 5m and diameter.15m along one centre line of the footing has been plotted in Fig. 7. 8 6 5 4 3 2 1 FOOTIN G 5 nos. Piles 7 nos. Piles 9 nos. Piles Fig. 4 Discretisation of footing with 5 micropiles Distance along the center line (m) Fig. 7 Elastic settlements for varying number of micro piles It can be observed that the settlement of the footing decreases significantly with increase in the number of piles. The evaluated elastic settlement for different length of micro piles are shown in Fig. 8 considering nine (9) numbers and.15m diameter of micro-piles. Fig. 5 discretisation of footing with 7 micropiles 8 6 FOOTING 5 4 3 2 1 1 2 3 4 Distance along the center line of footing (m) Pile length= 2m Pile length= 3m Pile length= 4m Pile length= 5m Fig. 8 Elastic Settlement for Varying Length of Micro Piles Fig. 6 discretisation of footing with 7 micropiles
5 th IGC Settlement (mm) Maximum Settlements (mm) Settlement (mm) Maximum Settlements (mm) 5 th INDIAN GEOTECHNICAL CONFERENCE 17 th 19 th DECEMBER 215, Pune, Maharashtra, India Venue: College of Engineering (Estd. 1854), Pune, India It can be observed that the reduction of settlement of the foundation is not that significant with the increase in the length of piles. The elastic settlement curve obtained for different diameter of micro-piles considering micro-piles of nine (9) numbers and length of 2m are shown in Fig. 9. 8 6 5 4 3 2 1 Fig. 9 Elastic settlement for varying micro pile diameters It can be observed that the influence of diameter on settlement is not very significant. Elastic settlement for various modulus of elasticity has been plotted in Fig. 1. 8 6 5 4 3 2 1.67 1.33 2 2.67 3.33 4 Distance along the center line of the footing (m).67 1.33 2 2.67 3.33 4 Distance along the center line of footing (m) FOOTING Pile dia=.15m Pile dia=.2m Pile dia=.25m Pile dia=.3m Es=6KN/ m^2 Es=8KN/ m^2 Es=1KN /m^2 WITH PILE Es=6KN/ m^2 Es=8KN/ m^2 Es=1KN /m^2 Fig. 1 Settlement for varying soil modulus of elasticity along the center line of footing The influence of soil modulus of elasticity on the settlement indicates that introduction of micro piles is very effective for soft soils. The predicted maximum settlement of the foundation have been plotted against the number of micro piles in Fig. 11. 8 6 5 4 3 2 1 5 7 9 No. of Micropiles Maximum settlement(mm) Fig. 11 Predicted Maximum settlement against numbers of micro piles The predicted maximum settlement values have been plotted against the length of micro piles in Fig. 12. 8 6 5 4 3 2 1 2 3 4 5 Length of Micropiles (m) Thickness=.3 m Fig. 12 Predicted maximum settlement against lengths of micro piles The predicted maximum settlement have been plotted against the diameter of the micro piles used for analysis in Fig.13.
Maximum settlement (mm) Jagat Jyoti Mandal & Payel Chaudhuri 8 6 5 4 3 2 1.15.2.25.3 Diameter of Micropiles (mm) Maximum settlement(m m) Fig. 13 Predicted maximum settlement against the diameters of micro piles The arrangement of micro piles chosen in the example reduces settlement far below the allowable values. Therefore, a set of nine numbers of micro piles having pile length 2m and diameter.25m can be considered enough for improved performance when introduced with a square footing of 4m 4m.3m undergoing a central concentrated load of 2KN. CONCLUSIONS The primary objective of the present study is to predict the performances of isolated footing for various combination with respect to member number, size and orientation of micro piles. Based on the mathematical formulation, the developed computer program is used to predict the elastic settlement of the foundation. It is observed that with the use of micro piles there has been a significant reduction in the overall settlement and differential settlement of the footing. The effect of number of micro piles, length and diameter of micro piles on the performances of the isolated footing have been studied through the examples and a conclusion can be drawn as below: a. For the analysis of the isolated footing with micro piles a couple BEM FEM formulation has been used which considered all the interactions between plate, micro piles and the soil. b. The computer program developed in this case shows good convergence with lesser numbers of elements for footing settlements. Discretization scheme is automatic with compatibility at footingsoil interface in vertical direction. This highlights the suitability of the coupled approach. c. The stiffness of the footing and the micro piles has a major contribution in the determining the settlements of the foundation combination. d. For soft soil, introduction of micro pile along with the footing reduces the differential settlement significantly and there after the overall settlement. The stiffness and the arrangement of the micro piles plays an important role in the differential settlement reduction for soft soils. e. From the present study it is observed that a footing with micro piles reduces the settlement considerably than the footing used alone. Hence the combination of square footing with micro piles can be effectively used to minimize the elastic settlement as required and optimum configuration can be obtained for a footing- soil micro pile combination. REFERENCES 1. Mandal, J. J. (1998), A Coupled FE BE Approach for Response Analysis of Raft Foundations, Dissertation for the degree of Doctor of Philosophy, Department of Civil Engineering, Indian Institute of Technology, Kharagpur. 2. Mandal, J. J. and Ghosh, D. P. (1999), Prediction of Elastic Settlement of Rectangular Raft Foundation A Coupled FE-BE Approach, Int. J. Numeri. Anal. Meth. Geomech, 23(3), 263-273 3. Mendonca, A. V. and Paiva, J. B. (23), An elastostatic FEM/BEM analysis of vertically loaded raft and piled raft foundation, Engineering Analysis with Boundary Elements, 27(9), 19-93. 4. Mindlin, R.D. (1936) Force at a Point in the Interior of a Semi-Infinite Solid, Physics, Vol. 7, 227-235. 5. Poulos, H.G. (21) Piled Raft Foundations: design and applications, ICE Publishing Journals, 51(2), 95-113. 6. Poulos, H.G. (21) Methods Of Analysis Of Piled Raft Foundations, A Report Prepared On Behalf Of Technical Committee TC18 on Piled Foundations, International Society of Soil Mechanics and Geotechnical Engineering.