FOUNDATION ENGINEERING UNIT III FOOTINGS AND RAFTS

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1 1 FOOTINGS AND RAFTS FOUNDATION ENGINEERING UNIT III Types of foundation Contact pressure distribution below footings & raft - Isolated and combined footings types proportioning - mat foundation types use - proportioning floating foundation. S.NO Part A PAGE.NO. 1 State the types of shallow foundations 4 Define spread or Isolated footing 4. 3 Define Combined footing and Raft footing. 4 4 Define Strap (or) Cantilever footing. 4 5 Define Raft or mat foundation 4 6 Define Eccentric loading. 5 7 What are the circumstances necessitating combined footing? 5 8 Under what circumstances a rectangular and trapezoidal combined footings are adopted 5 9 Under what circumstances a strap footing is adopted 6 10 Where the Raft or Mat Foundation would be used? 6 11 What is the condition for selecting the critical section for bending moment of a spread or isolated footing?. 1 What is the condition for selecting the critical section for checking diagonal shear and punching shear of a spread (or) isolated footing? How the overall depth of an isolated footings are determined 7 14 What are assumptions made in the design of strap footing 7 15 What are the two methods of design of raft foundation as per IS 7 16 What are assumptions made in the conventional method of design of raft foundation 8

2 17 State the criteria for selecting P.C.C. and R.C.C. strip footings 8 18 Define differential settlement 8 19 Define Tilt or angular distortion 8 0 Define contact pressure. 9 1 What is modulus of sub grade reaction (Ks) 9 S.NO Part B PAGE.NO. State the Principles of proportioning of footings Explain the general procedure for designing the footing 10 3 Explain the Procedure for designing the P.C.C. strip footings 10 4 Explain the Procedure for designing the R.C.C. strip footings Explain the procedure for the Design of spread or Isolated footings. 1 6 Explain the Procedure for proportioning and designing of the rectangular combined footings Explain the Procedure for proportioning and designing of the Trapezoidal combined footings Design a trapezoidal Footing for the two columns shown in fig. Take allowable soil pressure as 00kN/m 16 9 Explain the Procedure for proportioning and designing of the strap footings Design a strap footings for the two columns shows in fig 19 Explain the Procedure of conventional design of the raft footings The plan of a mat foundation with 9 column down in fig. assuming that the mat is rigid, determine the soil pressure distribution. All the columns are of size 0.6m x 0.6m 13 What are the Causes for the settlement of foundation 4 14 Define Differential settlement and enumerate its causes 5

3 3 15 What are the Effects of differential settlement 6 16 Enumerate the Remedial measures against harmful settlements Explain the different modes of contact pressure distribution for different nature of foundation soil. A footing foundation of 7

4 4 PART - A 1. State the types of shallow foundations. (I) Strip footing or wall footing (II) Spread footing or isolated footing (a) single footing, (b) stepped footing, (c) Sloped footing. (III) Combined footing (a) Rectangular combined footing, (b) Trapezoidal combined footing. (IV) Strap footing or Cantilever footing (V) Raft or mat foundation.. Define spread or isolated footing Spread footing is a type of shallow foundation which is used to transmit the load of an isolated column. According to shape, it may be square or rectangular. 3. Define combined footing and Raft footing. Combined footing: A combined footing is a long footing supporting two or more columns in one row. According to shape, it may be Rectangular or Trapezoidal. 4. Define Strap (or) Cantilever footing. Strap footing: A strap footing normally comprises two footings connected by a beam called a strap Beam. This type is also known as cantilever footing or a pump-handle foundation. 5. Define Raft or mat foundation Raft (or) mat foundation: A raft or a mat foundation is a large footing, usually supporting several columns in two or more rows. 6. Define Eccentric loading. When the resultant of loads on a footing does not pass through the center of the footing, the footing is subjected to what is called as eccentric loading.

5 5 7. What are the circumstances necessitating combined footing? When two columns, transmitting heavy loads on to a weak soil are spaced closely, the footings, which are necessarily large, overlap each other, under which circumstances it is not practicable to have individual footings, hence combined footings can be provided. When a foundation is built closer to an existing building or the property line. There may not be sufficient space for equal projections on the sides of the exterior column. This results in an eccentric loading on the footing. It may lead to the fitting of the foundation, To counteract this tilting tendency, a combined footings is provided which joins the exterior column with an interior column 8. Under what circumstances a rectangular and trapezoidal combined footings are adopted Sufficient space, beyond each column ---- Rectangular combined footing interior Coolum relatively heavier (Rectangular combined footing) One column is near property line Interior column relatively light, (Trapezoidal combined footing) {the selection of shape is based on to keep the resultant of the column loads through the centre of gravity of the footing. 9. Under what circumstances a strap footing is adopted Necessity 1. When x 1< L 3. When the distance between two columns is so large, then a combined footing becomes excessively long and narrow, in this condition a strap footing can be provided. A strap footing consists of two spread footings joined by a rigid beam known as a strap. The strap is not subjected to any direct soil pressure

6 6 from below. Its main function is to transfer the moment from the exterior footing to the interior footing 10. Where the Raft or Mat Foundation would be used? Raft foundations are normally used (i) Where the soil has low bearing capacity; and (ii) Where the total area occupied by individual footings is not less than 50 percent of the loaded area of the building. (iii) The soil characteristic is such that the differential settlement would be difficult to control 11. What is the condition for selecting the critical section for bending moment of a spread or isolated footing? The critical section for B.M is taken as under (i) (ii) at the face of the column or pedestal monolithic with the footing when no metal plate is used. Halfway between the face of the column or pedestal and the edge of the metal plate on which the column or pedestal rests The maximum B.M for the case (i) given by, M = q B (B- b) o 8 1. What is the condition for selecting the critical section for checking diagonal shear and punching shear of a spread (or) isolated footing? For checking diagonal shear, the critical section is taken at a distance of difference depth of footing from the face of the column. For punching shear, the critical section is taken at a distance of d/ from the face of the column. 13. How the overall depth of an isolated footings are determined Generally the overall depth (d o ) of the footing is determined from the punching shear considerations. d o = q o B - (b 4(b + d)j sp d) + J sp safe punching shear

7 7 In the case of rectangular footings, the length and width should be so chosen that the bending moment in each of the adjacent projections is equal to the moment of resistance of the footing. The thickness of the footing at the edge shall be not less than 150 mm, for footings on soil and it should not be less than 300 mm above the top of piles, for footings on piles 14. What are assumptions made in the design of strap footing Strap footings are designed on the basis of the following assumptions: 1. The strap is infinitely stiff. It serves to transfer the column loads on to the soil with equal and uniform soil pressure under both the footings.. The strap is a pure flexural member and does not take soil reaction. To avoid bearing on the bottom of the strap a few centimeters of the underlying soil may be loosened up prior to the placement of concrete. 15. What are the two methods of design of raft foundation as per IS (a) Conventional method (b) Elastic method or soil line method 16. What are assumptions made in the conventional method of design of raft foundation The conventional method is based on the following two basic assumptions: (i) (ii) The foundation is infinitely rigid and, therefore, the actual deflection of the raft does not influence the pressure distribution below the raft. The soil pressure is assumed to be planer such that the centroid the soil pressure coincides with the line of action of the resultant force of all the loads acting on the foundation 17. State the criteria for selecting P.C.C. and R.C.C. strip footings 13. Plain cement concrete strip footings selected loads are light & soil is good. 14. Reinforced concrete footings when loads are heavy and soil condition is not favourable

8 8 18. Define differential settlement Differential settlement is the difference of maximum and minimum settlements produced below the building due to imposed load. 19. Define Tilt or angular distortion Tilt or angular distortion is the ratio between the differential settlement and Horizontal distance between the points of maximum and minimum settlements. differntial settlement Horizontal distance between the points of maximum and minimum settlements 0. Define contact pressure The actual pressure transmitted from the foundation to the soil is called contact pressure. The contact pressure is uniform for flexible footing and it is varying for rigid footing. 1. What is modulus of sub grade reaction (Ks) The ratio of the soil reaction (P) to the deflection y at any point is defined as the modulus of sub grade reaction or soil modulus or the co-efficient of sub grade reaction

9 9 PART - B 1. State the Principles of proportioning of footings. It is essential to estimate the dead load live load and other loads. An estimate about length, depth & width of footing is necessary for determining bearing capacity of the soil. Axial load + Bending moment (due to wind ie., the moment changes with the direction ) square footing Axial load + Bending moment which doesn t change direction (due to earth pr, eccentricity due to brackets in column) Rectangular footing. For determining bearing capacity using a value, the value of N to be used is the average of the N values from the base of footings to a depth to width of the footing.. Explain the general procedure for designing the footing 1. SBC is determined.. footings is proportioned using SBC as found in (1) 3. maximum settlement is determined, also Diff.settlement 4. Angular distortion between various parts of the structure is found out. 5. Max, diff.settlement, angular distortion is checked with allowable values. 6. If the values are not with in the limits, SBC is revised & the procedure is repeated. 7. Stability of footing is checked against sliding and overturning 3. Explain the Procedure for designing the P.C.C. strip footings. PCC strip footing (i) Width Load per metre run. Width of the footing B = Allowable soil pressure q na

10 10 If the theoretical width of the footing is different from actual width, the actual pressure is given by, (ii) Thickness q o = Actual width - it should be adequate to minimize the development of tension on the underside of the projection acting as a cantilever x length of projection from the wall face at the edge of the footing thick ness </ 150mm at the edge of the footing thick ness for cohesive soil </ 300 mm ( to resist swelling pressure 4. Explain the Procedure for designing the R.C.C.strip footings. RCC ship footing In R.C.C. strip footing, the reinforcement should be in the transverse direction Width B = (as given for pcc) q s Reinforcement (i) Bending moment is essential Thickness (i) critical section 1. face of the monolithic wall the thickness should be adequate to resist bending and cliagonal shear. For monolithic walls, the max B.M. is given by M = B width of fooling, b = width of the wall, q o actual soil pressure. q B (B- b) o, 8 For checking diagonal shear, critical section is taken at a distance equal to the effective depth (d) of footing from the face of wall

11 11 Diagonal shear is given by F = q o B- b d 5. Explain the procedure for the Design of spread or isolated footings Spread footings are used for distributing concentrated column loads over a large area so that the bearing pressure is less than or equal to the allowable soil pressure. (i) plain concrete footings A = q na (ii) Same as that of strip footing reinforced concrete footing Area of the footing A = q na Actual pressure q o = A o Column land na allowable soil pressure Ao area of actual size of footing provided ( rounded ) The critical section for B.M is taken as under a. at the face of the column or pedestal monolithic with the footing when no metal plate is used. b. Halfway between the face of the column or pedestal and the edge of the metal plate on which the column or pedestal rests The maximum B.M for the case (i) given by, M = q B (B- b) o 8 For checking diagonal shear, the critical section is taken at a distance of difference depth of footing from the face of the column. For punching shear, the critical section is taken at a distance of d/ from the face of the column. Generally the overall depth (d o ) of the footing is determined from the punching shear considerations.

12 1 d o = q o B - (b 4(b + d)j sp d) + J sp safe punching shear In the case of rectangular footings, the length and width should be so chosen that the bending moment in each of the adjacent projections is equal to the moment of resistance of the footing. The thickness of the footing at the edge shall be not less than 150 mm, for footings on soil and it should not be less than 300 mm above the top of piles, for footings on piles. 6. Explain the Procedure for proportioning and designing of the rectangular combined footings. Design procedure Length and width of the footing are selected such that the centroid of the footing and the resultant of the column loads coincide. The shear force and bending moment diagrams are drawn thickness of the footing id found out from Bending moment & shear stress. The footing is designed, as a continuous beam supported by two columns is longitudinal direction. 1. determine the total column loads = 1 + where 1 Exterior column load (lighter) interior column load (heavier). Find the base area of the footings Area of the footing A = q na q na allowable soil pressure 3. Locate the line of action of the resultant of the column loads. 4. Determine the total length of the footings

13 13 L = + b 1 5. Find the width of the footing B = L A x b 1 = width of the exterior column. 6. Round off the length and breadth (calculate) & find actual pr. q = A c 7. Draw the shear force and bending moment diagram. 8. Determine the bending moment at the face of columns and the maximum bending moment at the point of zero shear. 9. Thickness of footing for maximum B.M Check for diagonal shear & punching shear Check for bond at the point of contraflaxure 10. Determine the longitudinal reinforcement for the maximum B.M. 7. Explain the Procedure for proportioning and designing of the Trapezoidal combined footings. Trapezoidal footing Design procedure 1. Determine the total column loads = 1 +. Find the base area of the footing A = q na 3. Locate the line of action of the resultant of column loads. x x = 4. Determine the distance x of the resultant from the outer face of the exterior column. x 1 = x + b 1

14 14 a trapezoidal footing is required if, L 3 < x 1 < L where L is the length of the trapezoidal footing (Limited) if x 1< L, strap footing is suitable 3 8. Design a trapezoidal Footing for the two columns shown in fig. Take allowable soil pressure as 00kn/m Total load = = 3500 q na 00 = 17.5 m L is restricted to 6.5 m x x = 1500x6 = =.57m 3500 x 1 = x + b =.57 + =.8 m L = 6.5 = as.17 < x 1 < 3.5 L 3.5m; =.17m 3 Trapezoidal footing can be provided B = A L 3x 1 1 L x17.5 3x.8 = 1 = 1.6m

15 15 A B 1 = B L x17.5 = 1.6 = 3.76m 6.5 let us provide B 1 = 3.8m & B = 1.65 m, 3500 Actual uplift pressure = ( ) x6.5 = 197.6k Pressure intensity at the left edge = x 3.8 = 750 kn/m Pressure intensity at the right edge = x 1.65 = 36 kn/m 9. Explain the Procedure for proportioning and designing of the strap footing footings. Design procedure 1. Eccentricity between the land 1 and Reaction R 1, on the exterior column is assumed.. Length of the footing of the exterior column L 1 = (e + 0.5b 1 ) 3. Reaction R1 is determined by taking moments about the line of action of R R 1 = 1 x S, R = ( 1 + ) R 1 X = distance between loads 1 & S = distance between reactions R 1 & R 4. Area A 1 & A are computed A 1 = R q 1 na 5. Width of footings B 1 = A L 1 ; B A 1

16 16 6. Design the individual footings as in the case of spread footings. 7. Determine the depth of the strap for diagonal shear & B.M 10. Design strap footings for the two columns shows in fig. The allowable soil pressure is 100kN/m. take the accentricity of the footing of column 1 as 1m. L 1 = (e + 0.5b 1 ) = ( x 0.4) =.4m. Taking moment about the section of R 1 x 5 = 600 x 6 =0 600x6 R 1 = = 70 kn 5 R = ( + 1 ) R 1 = R Area A 1 = 1 70 = = 7.m q na 100 R 880 A = 8.8 q = = m na 100 B 1 = B = A 1 L 1 = 7..4 = 3m A = 8.8 =.96m 3m 11. Explain the Procedure of conventional design of the raft footings. (a)conventional method (b)elastic method or soil line method Procedure for the conventional design 1. Determine the line of action of all the loads acting on the raft self wt of the raft is not considered, and directly by the soil.. Determine the contact pressure distribution as under

17 17 a. if the resultant passes through the centre the contact pr is given by, q = A b. q = A 3. Divide the slab into strips (bands) in a and y directions. Each strip is assumed to act as independent beam subjected to the contact pr and the column loads. 4. Draw the shear force and bending moment diagram for each strip. 5. Determine the modified column loads as below. It is found that the strip footing doesn t satisfy statics. i.e, the resultant of column loads and the resultant of contact pr are not equal and they do not Act in the same line. The reason is that the strips do not act independently as assumed and there is some shear transfer between adjoining strips. Let us consider the strip of width B 1 and length B carrying column loads 1, and 3. The average soil (contact) pressure on the strip be Average load on the strip. av = 1 (down word load + up word force) av = 1 ( q av B 1 B) The modified average soil pressure is given by F= av All the column loads are multiplied by F for that strip. For this strip, the column loads are F 1, F and F The bending moment and shear force diagrams are drawn for the modified column loads and the modified average soil pressure ( q av )

18 18 7. Design the individual strips for the bending moment and shear force found in step 6. the raft is designed As the analysis is approximate, the actual reinforcement Provided is twice the computed value. 1. The plan of a mat foundation with 9 column down in fig. assuming that the mat is rigid, determine the soil pressure distribution. All the columns are of size 0.6m x 0.6m. Total loads = = = 7400kn. Taking moments about the face AD, ( ) x ( ) ( ) x = 7400 x = 5.895m x Eccentricity e x = = 0.405m(int he vedirection). Taking moments about the face AB, y = ( ) + ( ) x8.3+ ( ) x16.3 = 7.98 m 16.6 ecc. (y) = = 0.3m (in the ( ve) direction) q =.ex.ey.x. y Iy y Ix x 7400x0.41 q = xx 16.6x1.6 3 q = x 0.5y 7400x0.3 xy 1.6x16.6 3

19 19 Pressure at point A (x = -6.3m, y = - 8.3m) q A = x (-6.3) 0.5 (-8.3) = 46.4 kn/m. Pressure at point B (x= 6.3m, y= -8.3) q B = x x (-8.3) = 3.6 kn/m Pressure at point C ( x = + 6.3m, y = 8.3) For the strip ABFE, q n = x (-6.3) 0.5 (8.3) = 38. kn/m qav = = 39.5kn /m q B B 1 3 ar 1 = [( downwardload ) + ( uploadforce )] = ) ( ) 1 = [( ) + ( 39.5x4.3x1.6 )] av = 180 kn Modified soil pressure = q av av q B B av q av = 39.5 = 39.5x1.6x4.3 Modified column loads F = av = = kn / m Modified column loads and pressure distribution can be shown as 14. Define Differential settlement and enumerate the Causes for differential settlement. Differential settlement can be defined as the difference of maximum and minimum settlements produced below the building due to imposed load.

20 0 (1) Geologic and physical non-uniformity, or anomalies, in type, structure, thickness, and density of the soil medium (Pockets of sand in clay, clay lenses in sand), an admixture of organic matter, peat; mud ) Non uniform pressure distribution from foundation to the soil due to non - uniform loading and incomplete loading of the foundations. 3) Water regimens at the construction site. 4) Overstressing of soil at adjacent site by heavy structures built next to light ones. 5) Overlap of soil at adjacent site by heavy structures built next to light ones. 6) Unequal expansion of the soil due to excavation for footings 7) Non uniform development of extrusion settlements. 8) Non uniform structural disruptions or disturbance of soil due to freezing and thawing, swelling and softening and drying of soils 15. What are the Effects of differential settlement Settlement cracks take place normally in diagonal position. Settlement cracks start from the top, bottom to the end of wall. If the end of the wall has settled more than the rest, then ctack will start from the top Good soil Clay Clay If the middle portion of a wall has settled more, the cracks will develop near the bottom of the wall. The settlement cracks will normally extend up to the edge of the wall because of the relative movement.

21 1 16. Enumerate the Remedial measures against harmful settlements. 1. Removal of soft strata, consistent with economy.. The use of properly designed and constructed pile foundations 3. Provision of lateral restraint against lateral expulsion of soil mass from underneath the footing of a foundation 4. Building slowly on cohesive soils to avoid lateral expansion of a soil mass and to give time for the pore water to be expelled by the surcharge load. 5. Reduction of contact pressure on the soil, more appropriately, proper adjustment between pressure, shape and size of the foundation in order to attain uniform settlements underneath the structure. 6. Pre consolidation of a building site long enough for the expected load, depending upon the tolerable settlements; alternatively, any other method of soil stabilization. 17. Explain the different modes of contact pressure distribution for different nature of foundation soil. The actual pressure transmitted from the foundation to the soil is called contact pressure. A uniformly loaded column will not necessarily transmit a uniform contact pressure to the soil. This is possible only if the foundation is perfectly flexible The contact pressure is uniform for a flexible foundation irrespective of the nature of the foundation soil. If the foundation is rigid, the contact pressure distribution depends upon the type of the soil below the foundation. For (Φ = 0) soil For a perfectly elastic material such as saturated clay, the contact pressure at the edge is infinite ( from theory of elasticity) But load yielding of soil makes the pressure at the finite. Under initial failure conditions, the pressure distribution tends to be practically uniform. For (c = 0)

22 For rigid foundation placed at ground surface on sand, the contact pressure at the edge is zero (no resistance to shear due to the absence of over burden pressure.) The pressure distribution is approximately parabolic. If the foundation is deep, shear resistance will be more due to overburden pressure, and hence the contact pressure tends to be more uniform. For (c Φ) Intermediate between the above two soils.