Design of Mat Foundations Hemant Kumar Bhaskar Roll

Design of Mat Foundations Hemant Kumar Bhaskar Roll No: -0610421

Types of Foundations v. Shallow Foundations versus Deep Foundations Shallow Foundations Spread Footings 11/27/2020 Mat Foundations Deep Foundations Driven Piles CE-533 Advanced Foundation Engineering Drilled Shafts Auger Cast Piles 2

Mat/Raft Foundation? v. A foundation system in which essentially the entire building is placed on a large continuous footing. v. Usually large concrete slab supporting many columns. v. Commonly used as foundation for silos, chimneys, large machinery. v. It is a flat concrete slab, heavily reinforced with steel, which carries the downward loads of the individual columns or walls. 11/27/2020 CE-533 Advanced Foundation Engineering 3

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Mat Foundation often considered to be used when dealing with the following conditions: v. The spread footings cover 50% of the foundation area because of large column loads. v. The soil is soft with a low bearing capacity. v. Hydrostatic uplift resistance is needed etc. 11/27/2020 CE-533 Advanced Foundation Engineering 5

Mat/raft foundation 11/27/2020 CE-533 Advanced Foundation Engineering 6

Types of Mat Foundations 11/27/2020 CE-533 Advanced Foundation Engineering 7

To Design Mat Foundation: Determine the capacity of the foundation Determine the settlement of foundation Determine the differential settlement Determine the stress distribution beneath the foundation 5. Design the structural component of the mat foundation using the stress distribution obtain from 4. 1. 2. 3. 4. 11/27/2020 CE-533 Advanced Foundation Engineering 8

Bearing capacity of the Foundation § Bearing Capacity Analysis follows the same approach as for spread footings § Factor of Safety (Das, 2004): Under normal Dead loads = 3. 0(Min) Under extreme loads = 1. 75 -2. 0(Min) 9

2). Settlement of foundation The settlement tends to be controlled via the following: v. Use of a larger foundation to produce lower soil contact pressures. v. Displaced volume of soil (flotation effect); theoretically if the weight of excavation equals the combined weight of the structure and mat, the system "floats" in the soil mass and no settlement occurs. 10

v. Bridging effects attributable to a. Mat rigidity. b. Contribution of superstructure rigidity to the mat. Foundation type Expected maximum settlement, mm Expected differential settlement, mm Spread 25 20 Mat 50 20 By IS Code – 2950 (Part-1) 11

Design of Mat Foundations Differential Settlement of Mat Foundations (American Concrete Institute Committee 336, 1988) Modulus of Elasticity of Material used in Structure Rigidity Factor, Modulus of Elasticity of Soil Moment of inertia of structure per unit length at right angles to B Width of raft 12

Design of Mat Foundations Differential Settlement of Mat Foundations (American Concrete Institute Committee 336, 1988) 13

Structural Design of Mat Foundations Approximate Method Flexible Method Finite Difference Method Finite Element Method 11/27/2020 CE-533 Advanced Foundation Engineering 14

AN APPROXIMATE METHOD: The mat is divided into strips loaded by a line of columns and resisted by soil pressure. This strip is then analyzed as a combined footing. (This method can be used where the mat is very rigid and the column pattern is fairly uniform in both spacing and loads. ) This method is not recommended at present because of the substantial amount of approximations and the wide availability of computer programs that are relatively easy to use. 11/27/2020 CE-533 Advanced Foundation Engineering 15

FLEXIBLE METHOD: 1. Compute the plate rigidity D 2. Compute the radius of effective stiffness L (Note: the approximate zone of any column influence is ~ 4 L). 3. Compute the radial and tangential moments, the shear, and deflection. 11/27/2020 CE-533 Advanced Foundation Engineering 16

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FINITE DIFFERENCE METHOD The finite-difference method uses the fourth-order differential equation based on theory of plates and shells [Timoshenko and Woinowsky-Krieger (1959)]: 11/27/2020 CE-533 Advanced Foundation Engineering 18

The finite-difference method has several advantages: It has been widely used (and should be used as a check on alternative methods where it is practical). It is reliable if the mat can be modelled using a finite-difference grid. It is rapid since the input data are minimal compared with any other discrete method, and the computations to build the stiffness array are not so extensive as other methods. Usually only three to five lines of input data are needed compared with up to several hundred for the other methods. 11/27/2020 CE-533 Advanced Foundation Engineering 19

There also a number of disadvantages: v It is extremely difficult to model boundary conditions of column fixity. v. It is very difficult to model notches, holes, or re-entrant corners. v. It is difficult to apply a concentrated moment (as from a column) since the difference model uses moment/unit of width. 11/27/2020 CE-533 Advanced Foundation Engineering 20

FINITE ELEMENT METHOD: In the finite-element analysis, element continuity is maintained through use of displacement functions. The displacement function is of the form 11/27/2020 CE-533 Advanced Foundation Engineering 21

DESIGN OF MAT FOUNDATION USING SOFTWARES: Many types of software available to design mat foundation some are like ABAQUS V 6. 8, STAAD FOUNDATION, RISA FOUNDATION, ANSYS, etc. MODELLING OF MAT FOUNDATION Using STAAD Foundation 2006 11/27/2020 CE-533 Advanced Foundation Engineering 24

Some Highlight points of IS-2950 Part-1 (DESIGN AND CONSTRUCTION OF RAFT FOUNDATIONS ) For satisfactory design and construction of a raft foundation, the following information is necessary: v. Site Plan v. Loading Conditions v. Environmental Factors v. Geotechnical Information v. Limiting Value of Angular distortion and differential settlement v. Rigidity of foundation and Super structure 11/27/2020 CE-533 Advanced Foundation Engineering 25

METHODS OF ANALYSIS Rigidity of Superstructure And Foundation Modulus of Elasticity of Material used in Structure Modulus of Elasticity of Soil 11/27/2020 CE-533 Advanced Foundation Engineering Moment of inertia of structure per unit length at right angles to B Width of raft 26

Determination Of Critical Column Spacing Evaluation of the characteristics γ is made as follows: Where, k = modulus of subgrade reaction in KN/m 3 B = width of raft in cm Ec = modulus of elasticity of concrete in MPa Z = moment of inertia of the raft in m 4 Depth of Foundation : v The depth of foundation shall generally be not less than 1 m. 11/27/2020 CE-533 Advanced Foundation Engineering 27

Construction Practices Applicable to the Design of Mats. Thickness T is determined from two-way shear (punching shear); Typical mat thickness T: Stories B=45' B=90' B=120' < 5 24" 31" 39" 5 - 10 35" 47" 59” 10 - 20 59" 78" 98" 11/27/2020 CE-533 Advanced Foundation Engineering 28

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Conclusions: v The primary objective of this report is to discuss various methods of design of mat foundation with structural reinforcement view has been done starting from simple analysis to methods in research with rigorous analysis. v The use of software's to design mat foundation had been introduced to track the current era of computers. 11/27/2020 CE-533 Advanced Foundation Engineering 32

REFERENCES: v. Bowles, J. E. (2000) Foundation Analysis and Design. v. A. C. I. Committee 336, Suggested analysis and design procedures for combined footings and mats, ACI Struct J (1988), pp. 304– 324. v S. N. Shukla, A simplified method for design of mats on elastic foundations, ACI J (1984), pp. 469– 475. View Record in Scopus | Cited By in Scopus (2) v O. C. Zienkiewicz, The finite element method (3 rd ed. ), Mc. Graw-Hill, UK (1977). v. G. Bézine, A new boundary element method for bending of plate on elastic foundations, Int J Solids Struct 24 (1988), pp. 557– 565. Abstract | PDF (589 K) | View Record in Scopus | Cited By in Scopus (0) 11/27/2020 CE-533 Advanced Foundation Engineering 33

THANK YOU 11/27/2020 CE-533 Advanced Foundation Engineering 34