# Geotech Engg. Ch#05 bearing capacity

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# Geotech Engg. Ch#05 bearing capacity

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### Geotech Engg. Ch#05 bearing capacity

1. 1. GEOTECHNICAL ENGINEERING - II Engr. Nauman Ijaz Bearing Capacity of the Soil Chapter # 05 UNIVERSITY OF SOUTH ASIA
2. 2. FOUNDATION It is the bottom most structural element of the sub structure which transmits the structural load including its own weight on to and / into the soil underneath/surrounding with out casing shear failure or bearing capacity failure (sudden collapse) and excessive settlement.
3. 3. CONTACT PRESSURE The pressure generated by the structural loading and self weight of the member on to or into the soil immediately underneath is called Contact pressure (σo). σo = Q / A The contact pressure is independent of soil parameters; it depends only on the load and the x-sectional area of the element carrying the load.
4. 4. Q = 1000KN σo = Q / A = 1000/(0.5 × 0.5) = 4000 Kpa A A 0.5m Fig # 01 0.5m Sec A-A
5. 5. Super-Structure and Sub- Structure The part of the structure which is above the GSL and can be seen with naked eye is known as Super-Structure. That part of structure which is below the GSL and can not be seen with naked eyes is known as Sub-Structure.
6. 6. Q = 1000KN Super- Structure GSL Sub- Structure Df B×L (2×2.5 m²) σo = Q / A Fig # 02 = 1000/(2 × 2.5) = 200 Kpa
7. 7. Foundation Depth (Df) It is the depth below the lowest adjacent ground to the bottom of the foundation. Need or Purpose of a Foundation Foundation is needed to transfer the load to the underlying soil assuming safety against bearing capacity failure and excessive settlement.
8. 8. This can be done by reducing the contact pressure such that it is either equal to or less than allowable bearing capacity (ABC) of soil. i.e σo < qa. In Fig- 1, the contact pressure under the concrete column is 4000Kpa which is much less than 21MPa (crushing strength of concrete) but much greater than 200KPa (ABC) of soil and needed to be reduced prior to transfer it to the soil underneath the column. The reduction can be achieved by;
9. 9. Lateral spreading of load using a large pad underneath the column (Fig # 02) σo = 1000 /5 = 200Kpa = ABCof soil The larger pad is known as Spread footing. FLOATING FOUNDATION Balance Partly or completely the load added to the load removed due to excavation is known as Floating foundation.i.e Provide basements.
10. 10. Types of Foundation Foundation may be characterized as being either “ Shallow” or “Deep”. Shallow Foundation Are those located just below the lowest part of the super structure which they support ( and get support from the soil just beneath the footing) and a least width generally greater than their depth beneath the ground surface, i.e Df / B < 1 Df = 3 m (generally)
11. 11. Deep Foundations Are those which extend considerably deeper into the earth ( and get supported from the side friction (skin friction) and / or bottom (end bearing) and generally with a foundation depth to width ratio (D/B) exceeding five.
12. 12. TYPES OF FOUNDATION Shallow foundations may be classified in several ways as below; SPREAD FOOTING OR INDIVIDUAL FOOTING This type of foundation supports one column only as shown below. This footing is also known as Pad footing or isolated footing. It can be square or rectangular in shape. This type of footing is the easiest to design and construct and most economical therefore.
13. 13. For this type of footing, length to breadth ratio (L/B) < 5. PLAN GSL ELEVATION
14. 14. ISOLATED FOOTING
15. 15. CONTINUOUS FOOTING If a footing is extended in one direction to support a long structure such as wall, it is called a continuous footing or a wall footing or a strip footing as shown below. Loads are usually expressed in force per unit length of the footing. For this type of footing , Length to Breadth ratio (L/B) > 5.
16. 16. A strip footing is also provided for a row of columns which are closely spaced that their spread footings overlap or nearly touch each other. In such a case it is more economical to provide a strip footing than a number of spread footing in one line.
17. 17. COMBINED FOOTING A combined footing is a larger footing supporting two or more columns in one row. This results in a more even load distribution in the underlying soil or rock, and consequently there is less chances of differential settlement to occur. While these footings are usually rectangular in shape, these can be trapezoidal ( to accommodate unequal column loading or close property lines)
18. 18. STRAP FOOTING Two or more footings joined by a beam (called Strap) is called Strap Footing. This type is also known as a cantilever footing or pump-handle foundation. This form accommodates wide column spacing's or close property lines. Strap is designed as a rigid beam to with stand bending moments, shear stresses. The strap simply acts as a connecting beam and does not take any soil reaction. To make this sure, soil below is dug and made loose.
19. 19. MAT OR RAFT FOOTING A large slab supporting a number of columns not all of which are in a straight line is known as Mat or Raft or Mass foundation. These are usually considered where the base soil has a low bearing capacity and / or column loads are so large that the sum of areas of all individual or combined footings exceeds one half the total building area ( to economize on frame costs).
20. 20. Furthermore, mat foundations are useful in reducing the differential settlements on individual columns. A particular advantage of mat for basement at or below ground water table is to provide a water barrier.
21. 21. SELECTION OF FOUNDATION TYPE The selection of the type of foundation for a given structure-subsoil system is largely a matter of judgment/elimination based on both an analysis of scientific data and experience. It is not possible to establish rigorous regulations and detailed recommendations for the solution of all soil problems, as the planning and designing of foundations for structures is more of an art than a science.
22. 22. 1. The type of foundation most appropriate for a given structure depends on several factors but commonly the principal factors are three which are as follow: The function of the structure and the loads it must carry. – Purpose of the structure i.e residential, office, industrial, bridge etc – Service life – Loading number of stories, basement. – Type i.e framed RCC, masonry, column spacing etc. – Construction method and schedule.
23. 23. 2. Sub-surface Condition. – Thickness and sequence of soil strata with subsoil parameters. – GWT position and function limits. – Presence of any underground anomalies. 3. The cost of foundation in comparison with the cost of the super structure i.e funds available for the construction and foundation.
24. 24. COMPARISON OF SHALLOW AND DEEP FOUNDATIONS Sr/No DESCRIPTION SHALLOW FOUNDATION DEEP FOUNDATION 1 Depth Df / B < 1 Df / B > 4+ 2 Load Distribution Lateral Spread Lateral and/or Vertical spread. •For end bearing lateral spread. •For frictional vertical spread. •Generally both. 3 Construction •Open pit construction. •Easy control and the best QA/QC. •Less skill labour is required. •Min. Disturbance. •During construction dewatering is required for shallow GWT. •In hole or driven •Difficult QA/QC. •Very skilled labour is required. •Max.disturbance. •Dewatering may or may not be required.
25. 25. Sr/No DESCRIPTION SHALLOW FOUNDATION DEEP FOUNDATION 4 Cost Less as compared with deep foundations. Usually 3 times or more costly than shallow. 5 Structural Design Consideration Flexural bending Axial Compression 6 Settlement More than that of deep foundation. Usually 50% of the shallow foundation for similar loading. 7 Environmental Suitability Does not suit to all environments specially for off shores sites. Suitable for all environment including off shore.
26. 26. CRITERIA FOR FOUNDATION DESIGN 1. 2. When designing foundation; there are two criteria which must be considered and satisfied separately. There must be accurate factor of safety against a bearing capacity failure in the soil i.e soil shouldn’t fail in shear. The settlement and particularly the differential settlement must be kept within reasonable limits.
27. 27. Causes of Deformation Deformation of an element of soil is a function of a change in effective stress (change in volume) not change in total stress. Various causes of deformation of a structure are listed as follow; 1. 2. 3. 4. 5. Application of structural loads. Lowering of the ground water table. Collapse of soil structure on wetting. Heave of swelling soils. Deterioration of the foundation ( Sulphate attack on concrete, corrosion of steel piles, decay of timber piles).
28. 28. 6. Vibration of sandy soil. 7. Seasonal moisture movement. 8. The effect of frost action.
29. 29. DEFINITIONS OF BEARING PRESSURE Gross Bearing Pressure (q gross): The intensity of vertical loading at the base of foundation due to all loads above that level. 2. Net Bearing Pressure: (q net): The difference between q gross and the total overburden pressure Po at foundation level (i.e q net = q gross – Po). Usually q net is the increase in pressure on the soil at foundation level. 1.
30. 30. 3. Gross Effective Burden Pressure (q’gross): The difference between the qgross and the pore water pressure (u) at foundation level. (i.e q’gross = qgross – u). 4. Net Effective Bearing Pressure (q’net): The difference between q’gross and the effective over burden pressure Po at foundation level. (i.e q’net = q’gross – Po). 5. Ultimate Bearing Pressure (qf): The value of bearing pressure at which the ground fails in shear. It may be expressed as gross or net or total effective pressure.
31. 31. 6. Maximum Safe Bearing Pressure (qs): The value of bearing pressure at which the risk of shear failure is acceptably low; may be expressed as gross or net or effective pressure. 7. Allowable Bearing Pressure (qa): Takes account the tolerance of the structure to settlement and may be much less than qs. 8. Working Bearing Pressure (qw): Bearing Pressure under working load. May be expressed as gross or net or total or effective pressure.
32. 32. FAILURE MODES A soil underneath any foundation may fail in one or a combination of the following three modes; 1. General Shear Failure. 2. Punching Shear Failure. 3. Local Shear Failure. (an intermediate mode of failure between conditions a and b)
33. 33. GENERAL SHEAR FAILURE Results in sudden catastrophic associated with plastic flow and lateral expulsion of soil.
34. 34. Failure usually accompanied by tilting and failure signs are imminent around the footing. The soil adjacent to the footing bulges Failure load is well defined on the load settlement graph. Shallow foundations on dense/hard soil and footing on saturated NCC under undrained loading. Relative density RD > 70% Void Ratio < 0.55 dense.
35. 35. PUNCHING SHEAR FAILURE Failure Mechanism, relatively slow ,no lateral expulsion, failure is caused by compression of soil underneath the footing.
36. 36. Failure is confined underneath the footing and no signs of failure are visible around the foundation. No tilting the footing settle almost uniformly. Failure load is difficult to be defined from the shape of load-settlement graph. There is continuous increase in load with settlement. Foundation in and/or on loose/soft soils placed at relatively shallow depth undergoes such type of failure. Footing on saturated NCC under drained loading. RD < 20%, Void Ratio > 0.75 loose.
37. 37. LOCAL SHEAR FAILURE Failure is between the General shear and Punching shear. Footing on saturated NCC under drained loading undergoes such type of failure. RD < 20%, Void ratio > 0.75, loose.
38. 38. SOURCES OF OBTAINING BEARING CAPACITY VALUES 1. 2. 3. 4. 5. Building codes, official regulations and civil engineering handbooks (Prescriptive method). Soil Load Test. Laboratory Testing. Method based on observations ( used for embankment design). Analytical Method (Bearing Capacity theories)
39. 39. BUILDING CODES In building codes bearing capacity values are tabulated for various type of soil. These values are based on many years of observation in practice as shown in table represents presumptive (Presumed) bearing capacity values of National Building Code (NBC). These values may be used for preliminary of feasibility design.
40. 40. MERITS AND DEMERITS OF CODE VALUES MERITS: 1. These values are used for preliminary design because of their readily availability and economy. 2. For small jobs in the areas for which the code values have been listed, final designs may be based on these values.
41. 41. DEMERITS: 1. The tabulated values neglect to report the effects of moisture, density and other soil properties which are known to have influence on bearing capacity. 2. The Building Codes do not indicate how and what methods are used to arrive at these values. 3. Effect of shape, size and depth of foundation is ignored. 4. Values of building Codes are not usually updated. 5. Type of structure is not taken into account.
42. 42. PRESUMPTIVE BEARING CAPACITY VALUES OF NATIONAL BUILDING CODE SOIL TYPE MAX. BEARING CAPACITY (TSF) CLAY: SOFT MEDIUM STIFF 1 TO 1.5 2.5 COMPACT (FIRM) 2 HARD 5 SAND: FINE, LOOSE 2 COARSE, LOOSE 3 COMPACT,COARSE 4 TO 6 GRAVEL: LOOSE 4 TO 6 SAND – GRAVEL MIXTURE COMPACT 6 VERY COMPACT 10
43. 43. SOIL TYPE MAX. BEARING CAPACITY (TSF) SAND-CLAY MIX., COMPACT 3 SAND-CLAY MIX, LOOSE,SATURATED 1 HARD PAN, COMPACTED OR CEMENTED 10 to 12 ROCK: SOFT 8 MEDIUM HARD 40 HARD 60 SEDIMENTARY ROCK: SHALE 8 to 10 HARD SHALE 8 to 10 LIME STONE 10 to 20 SAND STONE 10 to 20 Chalk 8 IGNEOUS ROCKS: GRANITE,LAVA,BASALT,DIORITE etc 20 to 40 to 100
44. 44. TERZAGHI’S THEORY Terzaghi modified the Prandtl’s theory and presented a classic bearing capacity equation (1943) which is still in use in its original form and in many modified forms proposed by various research workers. ASSUMPTIONS: 1. Footing base is rough. 2. Footing is shallow; i.e Df / B < 1 and shear along CD is neglected. 3. Footing is a strip footing i.e L/B > 10 and the stress distribution is assumed to be plain.
45. 45. FOOTING MODEL USED BY TERZAGHI TO DETERMINE qult
46. 46. In fig zone I forms wedge under the footing and moves downward with footing. The soil in zone II and III are in state of general shear failure and move up and away from the footing as it moves down into the soil. Terzaghi considered the equilibrium of the wedge ABC and summing up the vertical forces ΣFv = 0 produced the following equation for (c-ϕ) soil. qult = c Nc cohesion + q Nq + 0.5 γ B Nγ overburden Friction Where; qult = Gross ultimate bearing capacity including the effect of Terzaghi overburden pressure, q = γDf Ni = Bearing capacity factors, the values of which depends on angle of internal friction ϕ.
47. 47. The first term is the cohesion term and accounts for cohesive resistance along failure surface. The 2nd term is the surcharge term and accounts for the resistance supplied by the mass of soil above the base of footing. The third term is the self weight term and accounts for frictional resistance generated along failure surface. The self weight is a function of the footing width B because increasing the footing width increases volume of soil in zone II and III, thereby increasing the normal forces acting on the failure surface in turn increases the resistance along the failure surface.
48. 48. The safe bearing capacity values are computed by dividing the ultimate values of gross or net bearing capacity by an appropriate factor of safety usually 3 or more. qs net = Safe bearing capacity = qult net / FOS qs = Safe gross bearing capacity = qult net / FOS + γDf
49. 49. BEARING CAPACITY FACTORS OF TERZAGHI
50. 50. Later on Terzaghi proposed shape factors Sc and Sγ for the first and last terms of equation to account for the different shapes of the footings such as circular, square, rectangular etc. SHAPE FACTOR STRIP CIRCULAR Square Rectangular Sc 1 1.3 1.3 1 + 0.2 (B/L) Sγ 1 0.6 0.8 1- 0.2 (B/L)
51. 51. Terzaghi's bearing capacity Eq. has been modified for other types of foundations by introducing the shape factors. The equations are: – Square Foundations: – Circular Foundations: – Rectangular Foundations:
52. 52. MAYERHOFF GENERAL BEARING CAPACITY EQUATION
53. 53. M A Y E R H O F ’ S B E A R I N G CAPACITY FACTORS ϕ Nc Nq Nγ 0 5.1 1 0 5 6.5 1.6 0.1 10 8.3 2.5 0.4 15 11 3.9 1.2 20 14.9 6.4 2.9 25 20.7 10.7 6.8 30 30.1 18.4 15.1 35 46.4 33.5 34.4 40 75.3 64.1 79.4
54. 54. EFFECT OF GROUND WATER TABLE If there is enough water in the soil to develop a ground water table, and this ground water table is within the potential shear zone, then pore water pressure will be present, the effective stress and shear strength along the failure surface will be smaller and the ultimate bearing capacity will be reduced. When exploring the sub-surface conditions, we determine the current location of the ground water table and worst case (highest) location that might reasonably be expected during the life of the proposed structure.
55. 55. We have three cases that describes the worst-case field conditions. Case – I : Ground water table is at or above base of footing (Dw < D). We simply compute γ’ = γb = γ - γw Case – II : Ground water table is below the base of the footing, but still within the potential Shear zone, below the footing (D < Dw < D+B), we interpolate γ’ between buoyant unit weight and unit weight using, γ’ = γ – γw [1 – (Dw – D)/ B]
56. 56. Case # I Ground water table above base of footing Case # II Ground water table In this zone Case # III Ground water table Deeper than D+B
57. 57. Case – III : Ground water table is below the potential shear zone below the footing (D + B < Dw ), no ground water correction is necessary. γ’ = γ
58. 58. NUMMERICAL PROBLEM : Compute the FOS against a bearing capacity failure for the square spread footing as shown in the figure with ground water table at position A.
59. 59. SOLUTION : D = 2ft Dw = 7ft D + B = 6ft D+B < Dw, so ground water Case#III applies γ’ = γ. From the table ; Nc = 40.40, Nq = 25.30, Nγ = 23.70 when ϕ’ = 31o Terzaghi’s equation for square footing; qu = 1.3×0×40.4 + 121×2×25.3 + 0.4×121×4×23.70 qu = 10,710 lb/ft2
60. 60. q = P/A + γc D - u q = 76000/(4×4) + (150×2) – 0 q = 5050 lb/ft2 Factor of safety = FOS = F = qult / q F = 10,710/5050 F = 2.1
61. 61. NUMMERICAL PROBLEM : Compute the FOS against a bearing capacity failure for the square spread footing as shown in the figure with ground water table at position B.
62. 62. SOLUTION : D = 2ft Dw = 3ft D + B = 6ft D < Dw < D+B, so ground water Case#II applies. γ’ = γ – γw [1 – (Dw – D)/ B] γ’ = 121 – 62.4 [1 – (3 – 2)/ 4] = 74.2 lb/ft3 From the table ; Nc = 40.40, Nq = 25.30, Nγ = 23.70 when ϕ’ = 31o Terzaghi’s equation for square footing; qu = 1.3×0×40.4 + 121×2×25.3 + 0.4×74.2×4×23.70 qu = 8936 lb/ft2
63. 63. q = P/A + γc D - u q = 76000/(4×4) + (150×2) – 0 q = 5050 lb/ft2 Factor of safety = FOS = F = qult / q F = 8936/5050 F = 1.8
64. 64. NUMMERICAL PROBLEM : A1350KN column load is to be supported on a square spread footing founded in a clay with Su = 150Kpa. The depth of embedment, D will be 500mm, and the soil has a unit weight of 18.5KN/m3.The ground water table is at a considerable depth below the bottom of the footing. Using FOS of 3, determine the required footing width. Case # III applies. As ground water table is at considerable depth below the bottom of footing. γ’ = γ From the table ; Nc = 5.7, Nq = 1.0, Nγ = 0.0 when ϕ’ = 0o Terzaghi’s equation for square footing; qu = 1.3×150×5.7 + 18.5×0.5×1.0 + 0.4×18.5×B×0 qu = 1121 KPa
65. 65. Factor of safety = FOS = F = qult / qa qa = qult / F = 1121 / 3 = 374 Kpa qa = P/A + γc D - u 374 = 1350/(B2) + (23.6×0.5) – 0 B = 1.93 m Round up = 2m
66. 66. STANDARD PENETRATION TEST One of the oldest and most common in-situ test is the Standard Penetration test. It was developed in the late 1920’s and has been extensively used in North and South America, UK and Japan. ASTM Standard D 1586. It consists of Penetrometer having diameter 51mm and 600mm long tube. The penetrometer is connected to the surface with standard rods and is hammered into the ground with a tip hammer.
67. 67. TEST PRODEDURE 1. 2. 3. 4. The test procedure according to ASTM D1586 are as follow; Drill a 60-200mm (2.5 – 8inch) diameter exploratory boring to the depth of the first test. Insert the SPT sampler (also known as SPLIT-SPOON Sampler) into the boring. Shape and dimensions are shown in the figure. It is connected via steel rods to a 63.5Kg (140lb) hammer. Use either rope or an automatic tripping mechanism. Raise the hammer to a height 760mm (30inch) and allow it to fall. This energy derives the sampler into the bottom of the boring. Repeat the process until the sampler has penetrated a distance of 460mm (18inch), recording the number of hammer blows required for each 150mm (6inch) interval. Stop the test if more than 50 blows are required for any of the intervals or if more than 100 total blows are required.
68. 68. 5. Either of these events is known as Refusal and is noted on the boring logs. 6. Compute the N-value by summing the blow counts for the last 300mm (12inch) of penetration. The blow count for the first 150mm (6inch) is retained for reference purpose, but not used to compute N because the bottom of the boring is likely to be disturbed by the drilling process and may be covered with loose soil left in the boring. 7. Extract the SPT sampler, then remove and save the soil sample. 8. Drill the boring to the next test and repeat the same procedure.
69. 69. IMPORTANT POINTS Soft or very loose soil typically have NValues less than 5. Soil of average stiffness generally have 20< N <40. Very dense and hard soils have N of 50 or more. Very high N-values > 75 typically indicate very hard soil or rock.
70. 70. What is SPT – N value?? Number of blows required to penetrate split spoon sampler for 12inch penetration when a standard weight of 140lbs is dropped from a standard height of 30inches.
71. 71. ADVANTAGES 1. 2. 3. SPT does have at least three important advantages over other in-situ methods. First, it obtains a sample of the soil being tested. This permit direct soil classification. Most of the other methods do not include sample recovery. It is very fast and inexpensive test. Nearly all drill rigs used of soil exploration are equipped to perform this test. Whereas other insitu test requires specialize equipment that may not readily available.
72. 72. ASSIGNMENT A foundation 3.0m square is placed at 1.5m below the GSL on a uniform deposit of sandy gravel having following properties. 1. 2. 3. 4. c’ = 0, ϕ’ = 32o γ = 19.5 KN/m³ γ’ = 10.5 KN/m³ Calculate the gross ultimate bearing capacity for the following position of water table: GWT well below the zone of influence. GWT at the base of the footing. GWT rises to the GSL. GWT at 2m below the footing base.