# CE-632 Foundation Analysis and Design

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1 CE-63 Foundation Analysis and Design Shallow Foundations 1 SUMMARY of Terminology Gross Loading Intensity Total pressure at the level of foundation including the weight of superstructure, foundation, and the soil above foundation. Net Loading Intensity Pressure at the level of foundation causing actual settlement due to stress increase. This includes the weight of superstructure and foundation only. Q + Q + Q q = g superstructure Foundation soil AFoundation q = q γ D n g f Ultimate Bearing capacity: Maximum gross intensity of loading that the soil can support against shear failure is called ultimate bearing capacity. q u from Bearing capacity calculation Net Ultimate Bearing Capacity: Maximum net intensity of loading that the soil can support at the level of foundation. qnu = qu γ Df SUMMARY of Terminology Net Safe Bearing capacity: Maximum net intensity of loading that the soil can safely support without the risk of shear failure. Gross Safe Bearing capacity: Maximum gross intensity of loading that the soil can safely support without the risk of shear failure. Safe Bearing Pressure: Maximum net intensity of loading that can be allowed on the soil without settlement exceeding the permissible limit. q ρs qnu qns = FOS qgs = qns +γ Df from settlement analysis Allowable Bearing Pressure: Maximum net intensity of loading that can be allowed on the soil with no possibility of shear failure or settlement exceeding the permissible limit. qa netminimum of bearing capacity and settlement analysis 3 1

2 Common Types of Footing Strip footing Spread Footing 4 Common Types of Footing Combined Footing Raft or Mat footing 5 General Requirements of Foundation Location and Depth of Foundation Bearing Capacity of Foundation Settlement of Foundation DONE DONE 6

3 Location and depth of Foundation The following considerations are necessary for deciding the location and depth of foundation As per IS: , minimum depth of foundation shall be 0.50 m. Foundation shall be placed below the zone of The frost heave Excessive volume change due to moisture variation (usually exists within 1.5 to 3.5 m depth of soil from the top surface) Topsoil or organic material Peat and Muck Unconsolidated material such as waste dump Foundations adjacent to flowing water (flood water, rivers, etc.) shall be protected against scouring. The following steps to be taken for design in such conditions Determine foundation type Estimate probable depth of scour, effects, etc. Estimate cost of foundation for normal and various scour conditions Determine the scour versus risk, and revise the design accordingly 7 Location and depth of Foundation IS: recommendations for foundations adjacent to slopes and existing structures When the ground surface slopes downward adjacent to footing, the sloping surface should not cut the line of distribution of the load (H:1V). In granular soils, the line joining the lower adjacent edges of upper and lower footings shall not have a slope steeper than H:1V. In clayey soil, the line joining the lower adjacent edge of the upper footing and the upper adjacent edge of the lower footing should not be steeper than H:1V. 1V H 1V H 8 Location and depth of Foundation Other recommendations for footing adjacent to existing structures Minimum horizontal distance between the foundations shall not be less than the width of larger footing to avoid damage to existing structure If the distance is limited, the principal of H:1V distribution should be used so as to minimize the influence to old structure Proper care is needed during excavation phase of foundation construction beyond merely depending on the H:1V criteria for old foundations. Excavation may cause settlement to old foundation due to lateral bulging in the excavation and/or shear failure due to reduction in overburden stress in the surrounding of old foundation 9 3

5 13 Safe Bearing Capacity: National Building Code of India (1983) 14 Safe Bearing Capacity: National Building Code of India (1983) 15 5

6 Other considerations for Shallow Foundation Design For economical design, it is preferred to have square footing for vertical loads and rectangular footing for the columns carrying moment Allowable bearing pressure should not be very high in comparison to the net loading intensity leading to an uneconomical design. It is preferred to use SPT or Plate load test for cohesion less soils and undrained shear strength test for cohesive soils. In case of lateral loads or moments, the foundation should also be checked to be safe against sliding and overturning. The FOS shall not be less than 1.75 against sliding and.0 against overturning. When wind/seismic loads are considered the FOS is taken as 1.5 for both the cases. Wall foundation width shall not be less than [wall thickness + 30 cm]. Unreinforced foundation should have angular spread of load from the supported column with the following criteria V:1H for masonry foundation 3V:H for lime concrete 1V:1H for cement concrete foundation The bottom most layer should have a thickness of atleast 150 mm. 16 Combined Footings Combined footing is preferred when The columns are spaced too closely that if isolated footing is provided the soil beneath may have a part of common influence zone. The bearing capacity of soil is such that isolated footing design will require extent of the column foundation to go beyond the property line. Types of combined footings Rectangular combined footing Trapezoidal combined footing Strap beam combined footing 17 Rectangular Combined Footing x Q 1 +Q Q 1 Q If two or more columns are carrying almost equal loads, rectangular combined footing is provided Proportioning of foundation will involve the following steps Area of foundation Q1+ Q A = qa net QS Location of the resultant force x = Q1+ Q L 1 S L For uniform distribution of pressure under the foundation, the resultant load should pass through the center of foundation base. Length of foundation, L= ( L1 + S) Offset on the other side, L = L S L1 > 0 The width of foundation, B = AL 18 6

7 Trapezoidal Combined Footing If one of the columns is carrying much larger load than the other one, trapezoidal combined footing is provided Proportioning of foundation will involve the following steps if L, and L 1 are known Q1+ Q Area of foundation A = qa net QS Location of the resultant force x = Q1+ Q x Q 1 +Q Q 1 Q L 1 S L For uniform distribution of pressure under the foundation, the resultant load should pass through the center of foundation base. This gives the relationship, B1+ B L x+ L1 = B1+ B Area of the footing, B 1+ B L = A 3 B 1 B Solution of these two equations gives B 1 and B 19 Strap Combined Footing M Strap footing is used to connect an eccentrically loaded column footing to an interior column so that the moment can be transferred through the beam and have uniform stress distribution beneath both the foundations. Q 1 Q This type of footing is preferred over the rectangular or trapezoidal footing if distance between the columns is relatively large. Some design considerations: Strap must be rigid: I strap /I footing >. Footings should be proportioned to have approximately equal soil pressure in order to avoid differential settlement Strap beam should not have contact with soil to avoid soil reaction to it. 0 Example: Strap Footing S Q 1 Q B 1 B R 1 R L d c1 1 7

8 Raft or Mat Foundations Where is it needed? Structures like chimneys, silos, cooling towers, buildings with basements where continuous water proofing is needed For foundations where differential settlement can be a major concern For soft soils strata or site with pockets of weak soil In situations where individual footings may touch or overlap each other. Types of Raft Foundation Plane Slab Rafts: For fairly small and uniform spacing of columns and when the supporting soil is not too compressible. Beam and Slab: For large column spacing and unequal column loads. Slab with Column Pedestals: For columns with heavy loads which may require large shear strength or flexural strength of slab. Cellular Rafts: For compensated foundations to avoid differential settlements in weak soils. Piled Rafts: For heavy structures on soft soils in order to share the loads with piles. Strip Rafts or Grid Rafts: For economical design where a complete slab may be avoided. 3 General Considerations for Raft Foundation The depth of foundation shall not be less than 1.0 m. Punching shear failure for raft foundation on cohesionless soils is not an option so it shall not be considered for analysis. The design is mostly governed by settlement criteria. For raft foundations on cohesive soils, stability against deep seated failure shall be analyzed. The effect of long term settlement due to consolidation shall also be considered. The uplift due to sub-soil water shall be considered in design. The construction below water table shall be checked for floatation Foundations subjected to heavy vibratory loading should preferably be isolated 4 8

9 Rigidity of Soil-Structure Structure System Performance of raft depends on the relative rigidity of its three components Super structure Raft Soil Distribution of contact pressures depends on the relative rigidity idit of the foundation with respect to soil It is important that the rigidity of superstructure also matches with the rigidity of foundation Rigid Superstructure with Rigid Foundation: Does not allow differential settlement so it is good Rigid Superstructure with Flexible Foundation: Large deformations in the foundation which is not suitable for superstructure Flexible Superstructure with Rigid Foundation: It may acceptable but not necessary Flexible Superstructure with Flexible Foundation: This is also good 5 Flexural Rigidity of Structure, EI ( ' + ' ) EIb I u I l b l l EI = + EIb 1 + H ( I' b+ I' u+ I' f ) l Terms on next slide The summation is to be done over all the floors, including foundation beam of raft. For top layer I u ' becomes zero. For foundation beams I f ' replaces I b and I l becomes zero 6 7 9

10 Relative Stiffness of Structure and Foundation Soil Relative Stiffness Factor: For K > 0.5, the foundation may be considered as rigid with the ratio of differential to total settlement (δ) being equal to zero. For K = 0, ratio δ may be taken as 0.1, and for K < 0.5, it can be taken as 0.35 for square and 0.5 for long mat foundations. 8 Characteristic Length and Critical Column Spacing The characteristic coefficient λ, as used in classical solution of beams on elastic foundation, can be obtained as Characteristic Length Parameter, L e 1 = λ 9 Characteristic Length and Critical Column Spacing Rigidity of foundation can be defined by the spacing between columns, L L< 1.75 Le Foundations may be treated as short beam, hence rigid L> ( 3π ) Le Foundations may be treated as long beam, hence flexible 1.75 L < L< 3π L Foundations may be treated as finite beam e ( ) Hetenyi s (1946) recommendations e with intermediate rigidity L< 0.8 L L> 3 L e e 0.8 L < L> 3 L e Rigid Foundation Flexible Foundation e Intermediate Flexibility of Foundation 30 10

11 Determination of Modulus of Elasticity from Plate Load Test 1 ν Es = qb I s f q = intensity of contact pressure ν = Posson's ratio B = Plate width s = settlement I = Influence factor f Elastic Modulus of granular soil below foundation considering scale effects: B f Bf + B p Esf = EsP B P B f 31 Modulus of Subgrade Reaction from Plate Load Test Cohesive Soil Cohesionless Soil 3 Raft Foundation: Rigid Beam Analysis Assumptions Foundation is rigid relative to soil and compressible layer is relatively shallow. The contact pressure is planar such that centroid of the contact pressure coincides with the line of action of resultant force. The above conditions are satisfied if Relative stiffness factor > 0.5 Spacing between the columns is less than 1.75xL e Types of Analysis Flat Slab Analysis: Flat plate with regular layout of vertical loads can be analyzed assuming beam with the width of distance between mid-span width when ground settlement due to structural loads are not large. Strip 33 11

12 Raft Foundation: Rigid Beam Analysis Types of Analysis (Continued ) Equivalent Frame Analysis: If adjacent loads or column spacing exceed 0% of their higher value, the perpendicular beams as defined above may be treated as part of a frame structure and dthe analysis is performed dfor this equivalent frame. Beam and Slab Analysis: For the raft with added perpendicular beams to increase rigidity of foundation, an elemental analysis may be performed by cutting it into pieces as beams and slabs. Slab is designed as two way slab and beam as T-beam. 34 Raft Foundation: Rigid Beam Analysis Types of Analysis (Continued ) Deep Cellular Raft: This involves raft slab with beams and structural walls. Cross walls act as beam between the columns with net loading from soil pressure minus the self weight of wall and slab section beneath. A simple elemental analysis may be performed as in the previous case. An arbitrary value of ±wl /10 for positive and negative moment can give reasonable results. 35 Raft Foundation: Rigid Beam Analysis Pressure distribution: 36 1

13 Raft Foundation: Rigid Beam Analysis Modification Factor for Column Loads and Soil Reaction : e x e y Q The total soil reaction = q Total load from columns = B L.. av 1 Q1+ Q + Q3+ Q4 Total load from columns is slightly different than the total soil reaction due to the fact that no consideration has been given to the shear between adjacent strips. Therefore column loads and soil reaction need to adjusted. B 1 q av Q 1 Q Q 3 Q 4 L Q 1 Q Q 3 Q 4 37 Raft Foundation: Rigid Beam Analysis Modification Factor for Column Loads and Soil Reaction : Average Load = ( ) q. B. L+ Q + Q + Q + Q av Modified Soil Reaction ( qav ) modified qav qav 1 Average Load q = q. B. L Column load modification factor F Average Load = Q + Q + Q + Q Modified Column Loads: ( Q ) i m = FQ i 38 Raft Foundation: Rigid Beam Analysis - Example 1.0m 6.0m Q1 = 00kN Q = 370kN Q3 = 40kN Q4 = 30kN Q5 = 370kN Q6 = 740kN Q7 = 900kN Q8 = 40kN 6.0m e x e y 6.0m 1.0m Q9 = 370kN Q Q1 = 370kN 10 = 740kN Q11 = 740kN Q13 = 00kN Q14 = 370kN Q15 = 370kN Q16 = 00kN 1.0m 6.0m 6.0m 6.0m 1.0m 39 13

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