BEARING CAPACITY OF SOIL

Transcription

1 BEARING CAPACITY OF SOIL Dr. S. K. Prasad Professor of Civil Engineering S. J. College of Engineering, Mysore 7.0 Syllabus. Definition of ultimate, net and safe bearing apaities, Allowable bearing pressure 2. Terzaghi s and Brinh Hansen s bearing apaity euations Assumptions and Limitations 3. Bearing apaity of footings subjeted to eentri loading 4. Effet of ground water table on bearing apaity 5. Plate load test, Standard Penetration Test, Cone Penetration Test (8 Hours) 7. Definitions Bearing apaity is the power of foundation soil to hold the fores from the superstruture without undergoing shear failure or exessive settlement. Foundation soil is that portion of ground whih is subjeted to additional stresses when foundation and superstruture are onstruted on the ground. The following are a few important terminologies related to bearing apaity of soil.

2 Fig. 7. : Main omponents of a struture inluding soil 7.. Ultimate Bearing Capaity ( f ) : It is the maximum pressure that a foundation soil an withstand without undergoing shear failure Net ultimate Bearing Capaity ( n ) : It is the maximum extra pressure (in addition to initial overburden pressure) that a foundation soil an withstand without undergoing shear failure. n = f - o Here, o represents the overburden pressure at foundation level and is eual to D for level ground without surharge where is the unit weight of soil and D is the depth to foundation bottom from Ground Level Safe Bearing Capaity ( s ) : It is the safe extra load the foundation soil is subjeted to in addition to initial overburden pressure. Here. F represents the fator of safety. n s = + F o 7..4 Allowable Bearing Pressure ( a ) : It is the maximum pressure the foundation soil is subjeted to onsidering both shear failure and settlement Foundation is that part of the struture whih is in diret ontat with soil. Foundation transfers the fores and moments from the super struture to the soil below suh that the stresses in soil are within permissible limits and it provides stability against sliding and overturning to the super struture. It is a transition between the super struture and foundation soil. The job of a geotehnial engineer is to ensure that both foundation and soil below are safe against failure

3 and do not experiene exessive settlement. Footing and foundation are synonymous. 7.2 Modes of shear failure Depending on the stiffness of foundation soil and depth of foundation, the following are the modes of shear failure experiened by the foundation soil.. General shear failure (Ref Fig. 7.a) 2. Loal shear failure (Ref Fig. 7.b) 3. Punhing shear failure (Ref Fig. 7.) Shear failure in foundation soil P urve in different foundation soils Fig. 7. : Footing on ground that experienes a) General shear failure, b) Loal shear failure and ) Punhing shear failure 7.2. General Shear Failure This type of failure is seen in dense and stiff soil. The following are some harateristis of general shear failure.. Continuous, well defined and distint failure surfae develops between the edge of footing and ground surfae. 2. Dense or stiff soil that undergoes low ompressibility experienes this failure. 3. Continuous bulging of shear mass adjaent to footing is visible.

4 4. Failure is aompanied by tilting of footing. 5. Failure is sudden and atastrophi with pronouned peak in P urve. 6. The length of disturbane beyond the edge of footing is large. 7. State of plasti euilibrium is reahed initially at the footing edge and spreads gradually downwards and outwards. 8. General shear failure is aompanied by low strain (<5%) in a soil with onsiderable (>36 o ) and large N (N > 30) having high relative density (I D > 70%) Loal Shear Failure This type of failure is seen in relatively loose and soft soil. The following are some harateristis of general shear failure.. A signifiant ompression of soil below the footing and partial development of plasti euilibrium is observed. 2. Failure is not sudden and there is no tilting of footing. 3. Failure surfae does not reah the ground surfae and slight bulging of soil around the footing is observed. 4. Failure surfae is not well defined. 5. Failure is haraterized by onsiderable settlement. 6. Well defined peak is absent in P urve. 7. Loal shear failure is aompanied by large strain (> 0 to 20%) in a soil with onsiderably low (<28 o ) and low N (N < 5) having low relative density (I D > 20%) Punhing Shear Failure This type of failure is seen in loose and soft soil and at deeper elevations. The following are some harateristis of general shear failure.. This type of failure ours in a soil of very high ompressibility. 2. Failure pattern is not observed.

5 3. Bulging of soil around the footing is absent. 4. Failure is haraterized by very large settlement. 5. Continuous settlement with no inrease in P is observed in P urve. Fig. 7.2 presents the onditions for different failure modes in sandy soil arrying irular footing based on the ontributions from Vesi (963 & 973) Fig. 7.2 : Modes of failure at different Relative densities & depths of foundations Distintion between General Shear & Loal or Punhing Shear Failures The basi distintions between general shear failure and punhing shear failure are presented in Table 7.. Table 7. : Distintion between General Shear & Loal Shear Failures General Shear Failure Loal/Punhing Shear Failure Ours in dense/stiff soil Ours in loose/soft soil >36 o, N>30, I D >70%, C u >00 kpa <28 o, N<5, I D <20%, C u <50 kpa

6 Results in small strain (<5%) Results in large strain (>20%) Failure pattern well defined & lear Failure pattern not well defined Well defined peak in P- urve No peak in P- urve Bulging formed in the neighbourhood of No Bulging observed in the footing at the surfae neighbourhood of footing Extent of horizontal spread of Extent of horizontal spread of disturbane at the surfae large disturbane at the surfae very small Observed in shallow foundations Observed in deep foundations Failure is sudden & atastrophi Failure is gradual Less settlement, but tilting failure observed Considerable settlement of footing observed 7.3 Terzaghi s bearing Capaity Theory Terzaghi (943) was the first to propose a omprehensive theory for evaluating the safe bearing apaity of shallow foundation with rough base Assumptions. Soil is homogeneous and Isotropi. 2. The shear strength of soil is represented by Mohr Coulombs Criteria. 3. The footing is of strip footing type with rough base. It is essentially a two dimensional plane strain problem. 4. Elasti zone has straight boundaries inlined at an angle eual to to the horizontal. 5. Failure zone is not extended above, beyond the base of the footing. Shear resistane of soil above the base of footing is negleted. 6. Method of superposition is valid. 7. Passive pressure fore has three omponents (P PC produed by ohesion, P P produed by surharge and P P produed by weight of shear zone). 8. Effet of water table is negleted.

7 9. Footing arries onentri and vertial loads. 0. Footing and ground are horizontal.. Limit euilibrium is reahed simultaneously at all points. Complete shear failure is mobilized at all points at the same time. 2. The properties of foundation soil do not hange during the shear failure Limitations. The theory is appliable to shallow foundations 2. As the soil ompresses, inreases whih is not onsidered. Hene fully plasti zone may not develop at the assumed. 3. All points need not experiene limit euilibrium ondition at different loads. 4. Method of superstition is not aeptable in plasti onditions as the ground is near failure zone. Fig. 7.3 : Terzaghi s onept of Footing with five distint failure zones in foundation soil

8 7.3.3 Conept A strip footing of width B gradually ompresses the foundation soil underneath due to the vertial load from superstruture. Let f be the final load at whih the foundation soil experienes failure due to the mobilization of plasti euilibrium. The foundation soil fails along the omposite failure surfae and the region is divided in to five zones, Zone whih is elasti, two numbers of Zone 2 whih are the zones of radial shear and two zones of Zone 3 whih are the zones of linear shear. Considering horizontal fore euilibrium and inorporating empirial relation, the euation for ultimate bearing apaity is obtained as follows. Ultimate bearing apaity, f = N + DN BN If the ground is subjeted to additional surharge load, then f = N + ( D + ) N BN Net ultimate bearing apaity, n = N + D( N ) BN n = N + DN BN D Safe bearing apaity, = [ N + D( N ) + 0.5BN ] + D Here, F = Fator of safety (usually 3) = ohesion = unit weight of soil D = Depth of foundation = Surharge at the ground level B = Width of foundation N, N, N = Bearing Capaity fators s F Table 7.2 : Bearing apaity fators for different N N N g N ' N ' N ' g

9 Fig. 7.4 : Terzaghi s Bearing Capaity Fators for different

10 7.4 Effet of shape of Foundation The shape of footing influenes the bearing apaity. Terzaghi and other ontributors have suggested the orretion to the bearing apaity euation for shapes other than strip footing based on their experimental findings. The following are the orretions for irular, suare and retangular footings Cirular footing =.3N + DN + 0. BN f Suare footing f =.3N + DN BN Retangular footing B B = ( ) N + DN + ( 0.2 )0. BN L L f Summary of Shape fators Table 7.2 gives the summary of shape fators suggested for strip, suare, irular and retangular footings. B and L represent the width and length respetively of retangular footing suh that B < L. Table 7.3 : Shape fators for different shapes of footing Shape s s s Strip Suare Round Retangle B B ( ) ( 0.2 ) L L 7.5 Loal shear failure

11 The euation for bearing apaity explained above is appliable for soil experiening general shear failure. If a soil is relatively loose and soft, it fails in loal shear failure. Suh a failure is aounted in bearing apaity euation by reduing the magnitudes of strength parameters and as follows. 2 tanφ = tanφ 3 = Table 7.3 summarizes the bearing apaity fators to be used under different situations. If is less than 36o and more than 28o, it is not sure whether the failure is of general or loal shear type. In suh situations, linear interpolation an be made and the region is alled mixed zone. 2 3 Table 7.4 : Bearing apaity fators in zones of loal, mixed and general shear onditions. Loal Shear Failure Mixed Zone General Shear Failure < 28 o 28 o < < 36 o > 36 o N, N, N N m, N m m, N N, N, N 7.6 Effet of Water Table flutuation The basi theory of bearing apaity is derived by assuming the water table to be at great depth below and not interfering with the foundation. However, the presene of water table at foundation depth affets the strength of soil. Further, the unit weight of soil to be onsidered in the presene of water table is submerged density and not dry density. Hene, the redution oeffiients R W and R W2 are used in seond and third terms of bearing apaity euation to onsider the effets of water table.

12 D Z W Influene of R W B 0.5 < R W < D B Z W2 B Influene of R W2 Fig. 7.5 : Effet of water table on bearing apaity Ultimate bearing apaity with the effet of water table is given by, f = N + DN R + w 0. 5BN Rw2 Here, R Z = + w 2 D w where Z W is the depth of water table from ground level.. 0.5<R w < 2. When water table is at the ground level (Z w = 0), R w = When water table is at the base of foundation (Z w = D), R w = 4. At any other intermediate level, R w lies between 0.5 and

13 Here, R Z = + w 2 B w2 2 where Z W2 is the depth of water table from foundation level.. 0.5<R w2 < 2. When water table is at the base of foundation (Z w2 = 0), R w2 = When water table is at a depth B and beyond from the base of foundation (Z w2 >= B), R w2 = 4. At any other intermediate level, R w2 lies between 0.5 and 7.7 Effet of eentri foundation base D D Conentri Resultant of superstruture pressure D D e Eentri B Fig. 7.6 : Effet of eentri footing on bearing apaity The bearing apaity euation is developed with the idealization that the load on the foundation is onentri. However, the fores on the foundation may be eentri or foundation may be subjeted to additional moment. In suh situations, the width of foundation B shall be onsidered as follows. B = B 2e If the loads are eentri in both the diretions, then

14 B 2 = B e B & L = L 2eL Further, area of foundation to be onsidered for safe load arried by foundation is not the atual area, but the effetive area as follows. A = B XL In the alulation of bearing apaity, width to be onsidered is B where B < L. Hene the effet of provision of eentri footing is to redue the bearing apaity and load arrying apaity of footing. 7.8 Fator of Safety It is the fator of ignorane about the soil under onsideration. It depends on many fators suh as,. Type of soil 2. Method of exploration 3. Level of Unertainty in Soil Strength 4. Importane of struture and onseuenes of failure 5. Likelihood of design load ourrene, et. Assume a fator of safety F = 3, unless otherwise speified for bearing apaity problems. Table 7.5 provides the details of fators of safety to be used under different irumstanes.

15 Table 7.5 Typial fators of safety for bearing apaity alulation in different situations 7.9 Density of soil : In geotehnial engineering, one deals with several densities suh as dry density, bulk density, saturated density and submerged density. There will always be a doubt in the students mind as to whih density to use in a partiular ase. In ase of Bearing apaity problems, the following methodology may be adopted.. Always use dry density as it does not hange with season and it is always smaller than bulk or saturated density. 2. If only one density is speified in the problem, assume it as dry density and use. 3. If the water table orretion is to be applied, use saturated density in stead of dry density. On portions above the water table, use dry density.

16 4. If water table is some where in between, use euivalent density as follows. In the ase shown in Fig. 7a, e should be used for the seond term and sat for the third term. In the ase shown in Fig. 7b, d should be used for seond term and e for the third term.. e D + 2D2 = D + D 2 D D 2 D B B (a) Water table above base (b)water table below base Fig. 7.7 : Evaluation of euivalent density 7.0 : Fators influening Bearing Capaity Bearing apaity of soil depends on many fators. The following are some important ones.. Type of soil 2. Unit weight of soil 3. Surharge load 4. Depth of foundation 5. Mode of failure 6. Size of footing 7. Shape of footing 8. Depth of water table 9. Eentriity in footing load 0. Inlination of footing load. Inlination of ground 2. Inlination of base of foundation

17 7. Brinh Hansen s Bearing Capaity euation As mentioned in previous setion, bearing apaity depends on many fators and Terzaghi s bearing apaity euation doers not take in to onsideration all the fators. Brinh Hansen and several other researhers have provided a omprehensive euation for the determination bearing apaity alled Generalised Bearing Capaity euation onsidering the almost all the fators mentioned above. The euation for ultimate bearing apaity is as follows from the omprehensive theory. = N s d i + N s d i + 0. BN s d i f 5 Here, the bearing apaity fators are given by the following expressions whih depend on. N N N = ( N = ( e π tan φ =.5( N = )ot φ 2 φ ) tan (45 + ) 2 ) tanφ Euations are available for shape fators (s, s, s ), depth fators (d, d, d ) and load inlination fators (i, i, i ). The effets of these fators is to redue the bearing apaity. 7. Determination of Bearing Capaity from field tests Field Tests are performed in the field. You have understood the advantages of field tests over laboratory tests for obtaining the desired property of soil. The biggest advantages are that there is no need to extrat soil sample and the onditions during testing are idential to the atual situation. Major advantages of field tests are Sampling not reuired Soil disturbane minimum

18 Major disadvantages of field tests are Labourious Time onsuming Heavy euipment to be arried to field Short duration behavior 7.. Plate Load Test Sand Bags Platform for loading Dial Gauge Testing Plate Foundation Level Foundation Soil Fig. 7.8 : typial set up for Plate Load test assembly. It is a field test for the determination of bearing apaity and settlement harateristis of ground in field at the foundation level. 2. The test involves preparing a test pit up to the desired foundation level. 3. A rigid steel plate, round or suare in shape, 300 mm to 750 mm in size, 25 mm thik ats as model footing. 4. Dial gauges, at least 2, of reuired auray (0.002 mm) are plaed on plate on plate at orners to measure the vertial defletion. 5. Loading is provided either as gravity loading or as reation loading. For smaller loads gravity loading is aeptable where sand bags apply the load.

19 6. In reation loading, a reation truss or beam is anhored to the ground. A hydrauli jak applies the reation load. 7. At every applied load, the plate settles gradually. The dial gauge readings are reorded after the settlement redues to least ount of gauge (0.002 mm) & average settlement of 2 or more gauges is reorded. 8. Load Vs settlement graph is plotted as shown. Load (P) is plotted on the horizontal sale and settlement () is plotted on the vertial sale. 9. Red urve indiates the general shear failure & the blue one indiates the loal or punhing shear failure. 0. The maximum load at whih the shear failure ours gives the ultimate bearing apaity of soil. Referene an be made to IS The advantages of Plate Load Test are. It provides the allowable bearing pressure at the loation onsidering both shear failure and settlement. 2. Being a field test, there is no reuirement of extrating soil samples. 3. The loading tehniues and other arrangements for field testing are idential to the atual onditions in the field. 4. It is a fast method of estimating ABP and P behaviour of ground. The disadvantages of Plate Load Test are. The test results reflet the behaviour of soil below the plate (for a distane of ~2Bp), not that of atual footing whih is generally very large. 2. It is essentially a short duration test. Hene, it does not reflet the long term onsolidation settlement of layey soil. 3. Size effet is pronouned in granular soil. Corretion for size effet is essential in suh soils. 4. It is a umbersome proedure to arry euipment, apply huge load and arry out testing for several days in the tough field environment.

20 7..2 Standard Penetration Test 750 mm 65 kg Hammer Tripod Bore Hole Split Spoon Sampler Fig. 7.8 : typial set up for Standard Penetration test assembly. Referene an be made to IS for details on Standard Penetration Test. 2. It is a field test to estimate the penetration resistane of soil. 3. It onsists of a split spoon sampler 50.8 mm OD, 35 mm ID, min 600 mm long and 63.5 kg hammer freely dropped from a height of 750 mm. 4. Test is performed on a lean hole 50 mm to 50 mm in diameter. 5. Split spoon sampler is plaed vertially in the hole, allowed to freely settle under its own weight or with blows for first 50 mm whih is alled seating drive. 6. The number of blows reuired for the next 300 mm penetration into the ground is the standard penetration number N 7. Apply the desired orretions (suh as orretions for overburden pressure, saturated fine silt and energy)

21 8. N is orrelated with most properties of soil suh as frition angle, undrained ohesion, density et. Advantages of Standard Penetration Test are. Relatively uik & simple to perform 2. Euipment & expertise for test is widely available 3. Provides representative soil sample 4. Provides useful index for relative strength & ompressibility of soil 5. Able to penetrate dense & stiff layers 6. Results reflet soil density, fabri, stress strain behavior 7. Numerous ase histories available Disadvantages of Standard Penetration Test are. Reuires the preparation of bore hole. 2. Dynami effort is related to mostly stati performane 3. SPT is abused, standards regarding energy are not uniform 4. If hard stone is enountered, diffiult to obtain reliable result. 5. Test proedure is tedious and reuires heavy euipment. 6. Not possible to obtain properties ontinuously with depth Cone Penetration Test

22 Fig. 7.9 : typial set up for Stati Cone Penetration test assembly. Referene an be made to IS 4968 (P3) 987 for details on Standard Penetration Test. 2. Cone Penetration Test an either be Stati Cone Penetration Test or Dynami Cone Penetration Test. 3. Continuous reord of penetration resistane with depth is ahieved. 4. Consists of a one 36 mm dia (000 mm 2 ) and 60 o vertex angle. 5. Cone is arried at the lower end of steel rod that passes through steel tube of 36 mm dia. 6. Either the one, or the tube or both an be fored in to the soil by jaks. 7. Cone is pushed 80 mm in to the ground and resistane is reorded, steel tube is pushed up to the one and resistane is reorded. Further, both one and tube are penetrated 200 mm and resistane is reorded. Total resistane ( ) gives the CPT value expressed in kpa.

23 8. Cone resistane represents bearing resistane at the base and tube resistane gives the skin fritional resistane. Total resistane an be orrelated with strength properties, density and deformation harateristis of soil. 9. Corretion for overburden pressure is applied. 0. Approximately, N = 0 (kpa) Advantages of SCPT are. Continuous resistane with depth is reorded. 2. Stati resistane is more appropriate to determine stati properties of soil. 3. Can be orrelated with most properties of soil. Disadvantages of SCPT are. Not very popular in India. 2. If a small rok piee is enountered, resistane shown is errati & inorret. 3. Involves handling heavy euipment. 7.2 Presumptive Safe Bearing Capaity It is the bearing apaity that an be presumed in the absene of data based on visual identifiation at the site. National Building Code of India (983) lists the values of presumptive SBC in kpa for different soils as presented below. A : Roks Sl Desription No Roks (hard) without laminations and defets. For e.g. granite, trap & diorite 2 Laminated Roks. For e.g. Sand stone and Lime stone in sound ondition 3 Residual deposits of shattered and broken bed roks and hard shale emented material SBC (kpa)

24 4 Soft Rok 440 B : Cohesionless Soils Sl Desription SBC (kpa) No Gravel, sand and gravel, ompat and offering resistane to 440 penetration when exavated by tools 2 Coarse sand, ompat and dry Medium sand, ompat and dry Fine sand, silt (dry lumps easily pulverized by fingers) 50 5 Loose gravel or sand gravel mixture, Loose oarse to medium 245 sand, dry 6 Fine sand, loose and dry 00 C : Cohesive Soils Sl Desription SBC (kpa) No Soft shale, hard or stiff lay in deep bed, dry Medium lay readily indented with a thumb nail Moist lay and sand lay mixture whih an be indented with 50 strong thumb pressure 4 Soft lay indented with moderate thumb pressure 00 5 Very soft lay whih an be penetrated several entimeters with 50 the thumb 6 Blak otton soil or other shrinkable or expansive lay in dry ondition (50 % saturation) Note :. Use d for all ases without water. Use sat for alulations with water. If simply density is mentioned use aordingly. 2. Fill all the available data with proper units. 3. Write down the reuired formula 4. If the given soil is sand, = Problems & Solutions. A suare footing is to be onstruted on a deep deposit of sand at a depth of 0.9 m to arry a design load of 300 kn with a fator of safety of 2.5. The ground water table may rise to the ground level during rainy season. Design

25 the plan dimension of footing given sat = 20.8 kn/m 3, N = 25, N = 34 and N =32. (Feb 2002) Data C = 0 F = 2.5 D = 0.9 m R W = R W2 = 0.5 = 20.8 kn/m 3 N = 25 N = 34 N = 32 s = P A P = = 2 B [.3N + D( N ) R + 0.4BN R ] + D W W = B B B =.2 m F 2. What will be the net ultimate bearing apaity of sand having = 36 o and d = 9 kn/m 3 for (i).5 m strip foundation and (ii).5 m X.5 m suare footing. The footings are plaed at a depth of.5 m below ground level. Assume F = 2.5. Use Terzaghi s euations. (Aug 2003) N N N 35 o o By linear interpolation N = 65.38, N = 49.38, N = 54 at = 36 o Data B =.5 m D =.5 m = 9 kn/m 3

26 Strip Footing n = N + D( N ) BN n = kpa Suare Footing =.3N + D( N ) + 0. BN n 4 n = kpa 3. A suare footing 2.5 m X 2.5 m is built on a homogeneous bed of sand of density 9 kn/m 3 having an angle of shearing resistane of 36 o. The depth of foundation is.5 m below the ground surfae. Calulate the safe load that an be applied on the footing with a fator of safety of 3. Take bearing apaity fators as N = 27, N = 30, N = 35. (Feb 2004) Data C = 0 F = 3 B = 2.5 m D =.5 m = 9 kn/m 3 N = 27 N = 30 N = 35 s = P A P = = 2 B [.3N + D( N ) R + 0.4BN R ] + D W W 2 Safe load, P = s *B*B = kn 4. A strip footing 2 m wide arries a load intensity of 400 kpa at a depth of.2 m in sand. The saturated unit weight of sand is 9.5 kn/m 3 and unit weight above water table is 6.8 kn/m 3. If = 0 and = 35 o, determine the fator of safety with respet to shear failure for the following loations of water table. a. Water table is 4 m below Ground Level F

27 b. Water table is.2 m below Ground Level. Water table is 2.5 m below Ground Level d. Water table is at Ground Level. Using Terzaghi s euation, take N = 4.4 and N = (Feb 2005) Data C = 0 = 35 o B = 2 m D =.2 m b = 9.5 kn/m 3 (bottom) t = 6.8 kn/m 3 (top) N = 0 N = 4.4 N = 42.4 Safe load intensity = 400 kpa s = [ N + D( N ) R + 0.5BN R ] + D 400 = W W 2 a. Water table is 4 m below Ground Level R W = R W2 = = 6.8 kn/m 3 F = 4.02 b. Water table is.2 m below Ground Level R W =, R W2 = = X F [ 6.8X.2X 40.4X+ 0.5X9.5X 2X 42.4X 0.5] F = Water table is 2.5 m below Ground Level RW2 = 0.5(+.3/2) = X X 0.7 eff = = kn/m 3 2 F

28 400 = X F [ 6.8X.2X 40.4X+ 0.5X7.745X 2X 42.4X 0.825] F = d. Water table is at Ground Level R W = R W2 = 0.5 = 9.5 kn/m = X F F = [ 9.5X.2X 40.4X X9.5X 2X 42.4X 0.5] A suare footing loated at a depth of.3 m below ground has to arry a safe load of 800 kn. Find the size of footing if the desired fator of safety is 3. Use Terzaghi s analysis for general shear failure. Take = 8 kpa, N = 37.2, N = 22.5, N = 9.7. (Aug 2005) d = 8 kn/m 3 = 8 kpa F = 3 D =.3 m N = 37.2 N = 22.5 N = 9.7 P = 800 kn R W = R W2 = s = P A 47.28B P = = 2 B B B =.436 m 3 (Assumed) [.3N + D( N ) R + 0.4BN R ] + D W W = 0 6. A suare footing 2.8 m X 2.8 m is built on a homogeneous bed of sand of density 8 kn/m 3 and = 36 o. If the depth of foundation is.8 m, determine F

29 the safe load that an be applied on the footing. Take F = 2.5, N = 27, N = 36, N = 35. (Feb 2007) Data d = 8 kn/m 3 = 0 (sand) F = 2.5 B = 2.8 m D =.8 m N = 27 N = 36 N = 35 P =? R W = R W2 = s = P A P = = 2 B P = s *B*B = 6023 kn [.3N + D( N ) R + 0.4BN R ] + D W W 2 7. A strip footing m wide and a suare footing m side are plaed at a depth of m below the ground surfae. The foundation soil has ohesion of 0 kpa, angle of frition of 26 o and unit weight of 8 kn/m 3. Taking bearing apaity fator from the following table, alulate the safe bearing apaity using Terzaghi s theory. Use fator of safety of 3. (July 2008) N N N 5 o o o F As = 28 o, the ground experienes loal shear failure C = (2/3)X0 = 6.67 kpa tan = (2/3) X tan

30 = 8.0 o By linear interpolation, N =5.79, N =5.97, N =4.0 B = m D = m = 8 kn/m 3 Strip footing s = [ N + D N ) + 0.5BN ] + D Suare footing s ( =94.96 kpa F [.3N + D( N ) + 0.4BN ] + D = =03.08 kpa F 8. A suare footing plaed at a depth of m is reuired to arry a load of 000 kn. Find the reuired size of footing given the following data. C = 0 kpa, = 38 o, = 9 kn/m 3, N = 6.35, N = 48.93, N = and F = 3. Assume water table is at the base of footing. (July 2007) Data C = 0 kpa = 38 o B =? D = m = 9 kn/m 3 N = 6.35 N = N = F = 3 R W = R W2 = 0.5 s B 3 = P A P = = 2 B + 6.4B 2 [.3N + D( N ) R + 0.4BN R ] + D W W = 0 F

31 B = 0.72 m 7.3 Exerise problems. Calulate the ultimate bearing apaity of 2 m wide suare footing resting on the ground surfae of sand deposit with the following properties; unit weight 8.6 kn/m 3, angle of internal frition 35 o, N = 4.4, N = Also alulate ultimate bearing apaity if same footing is plaed at a depth of m below ground surfae. (July 2006) 2. Determine the safe bearing apaity of a suare footing 2. m X 2. m plaed at a depth of.5 m in a soil with a moist unit weight of 7.5 kn/m 3, = 5 kpa and = 20 o. Take N =.8, N = 3.9 and N =.7. What is the hange in safe bearing apaity if the water table rises to 0.5 m above footing base if F = 3. (July 2002) 3. What will be the gross net bearing apaity of sand having = 36 o and dry unit weight of 9 kn/m 3 for the following ases a..5 m wide strip foundation b..5 m X.5 m suare footing m radius irular footing The footings are plaed at a depth of.5 m from ground surfae. Assume fator of safety of.5 and use Terzaghi s bearing apaity euations N N N Design a suare footing to arry a load of 500 kn. Assume ohesionless soil and adopt = 9 kn/m 3, = 38 o, N = 49, N = 44. and D =.5 m, F =3. (Feb 2009)

32 5. A suare footing.4 m X.4 m rests at a depth of m in a saturated lay layer 3 m deep. Take sat = 7.8 kn/m 3, N = 5.7, N =, F = 2.5. Determine the safe load if the unonfined ompressive strength is 50 kpa. 6. A suare footing 2m X 2m in plan and.5 m below ground level is eentrially loaded. The resultant is 0.2 m outside of entroid in one diretion. If = 0 kpa, = 40 o, =6kN/m 3, find the safe load arried by footing. What would have been the inrease in load arried, if the load was onentri. N N N A 3 m X 4 m retangular footing and.5 m below ground level is eentrially loaded. The resultant is 0.2 m outside of entroid widthwise, and 0.3 m outside of entroid lengthwise. If = 0 kpa, = 40 o, =6kN/m 3, find the safe load arried by footing. What would have been the inrease in load arried, if the load was onentri. N N N A 3 m X 4 m retangular footing is eentrially loaded. The resultant is 0.2 m outside of entroid widthwise, and 0.3 m outside of entroid lengthwise. If = 0 kpa, = 25 o, =6kN/m 3, find the safe load arried by footing. What would have been the inrease in load arried, if the load was onentri. Refer to IS for bearing apaity fators. Note : As < 28 o, the mode of failure is loal shear failure. Hene orretion for bearing apaity fators and are neessary 9. A irular footing is proposed on a ohesive ground with = 8 kpa, = 30 o, and = 6.5 kn/m 3. Find the safe load arried by the footing if the diameter is 2.5 m. Refer to IS for bearing apaity fators. 0. A suare footing is proposed at a site to arry a load of 600 kn. The standard penetration test indiated that the average N value after all the orretions

33 was 30 and the ground was granular. Design the size of footing. Refer to IS The following are the results of plate load test on granular soil. P (kn) (mm) Find the allowable bearing pressure if B = 2 m, Bp = 0.3 m, permissible settlement in field = 2 mm. 2. The following are the results of plate load test on ohesive soil. P (kn) (mm) Find the allowable bearing pressure if B = 2 m, B p = 0.3 m, permissible settlement in field = 2 mm. 3. Find the safe bearing apaity of soil to support a 2 m X 3 m footing at a depth of.8 m when the load is inlined at 0 o to vertial. Take = 0 kpa, = 25 o, =6 kn/m 3. Find the safe load arried by the footing. Find the safe load supported by the footing if eentriities of 0. m widthwise and 0.2 m lengthwise exist. Further, find the drop in safe load arried if water table rises up to the base of footing. 4. A 2 m X 2 m suare footing is proposed on a ground with = 8 kpa, = 38 o, = 8 kn/m 3 at a depth of.5 m. If N = 6.35, N = 48.93, N = 74.03, find the safe bearing apaity of soil in different seasons of the year. The depth of Ground Water Table below Ground Level in January, Marh, May, July, September and November are respetively 4 m, 6 m, 0 m, m,.5 m, 2.5 m. 7.4 Additional Questions ) List the advantages and disadvantages of plate load test 2) Distinguish between Standard Penetration Test and Stati one penetration test

34 3) Distinguish between Stati one penetration test and dynami one penetration test 4) Distinguish between Standard Penetration Test and dynami one penetration test 5) Distinguish general shear failure from loal shear failure 6) List the assumptions of Terzaghi s bearing apaity theory 7) Mention the limitations of Terzaghi s bearing apaity theory 8) Explain the effet of shape of footing on bearing apaity 9) How does ground water table influene bearing apaity? Explain 0) Eentrially plaed footings perform better than onentrially plaed footings. Is the statement true or false? Justify your answer. ) Explain the effet of eentriity of footing on its load arrying apaity. Desribe the influene of one way and two way eentriities. 2) What is the influene of size of footing on ohesive soils? 3) How do you onsider loal shear effet in bearing apaity euation? 4) What are the advantages of Brinh Hansen s Theory over Terzaghi s theory of bearing apaity? 5) Distinguish Safe Bearing Capaity from Allowable Bearing Pressure 6) Distinguish Safe Bearing Capaity from Ultimate Bearing Capaity 7) Briefly explain Terzaghi s bearing apaity theory 8) Briefly explain Brinh Hansen s bearing apaity theory 9) A granular soil possesses = 30 o. Explain the proedure adopted to evaluate Safe Bearing Capaity. 20) How do you determine Safe Bearing Capaity at a site? Explain. 2) Explain whih unit weight of soil should be used in bearing apaity determination. Justify your answer. 22) A footing is designed to arry a speifi load of superstruture. It is deided to redesign the same to arry double the load. What ations would you take?

35 23) Disuss the fators influening bearing apaity of soil 24) Explain the test proedure for onduting plate load test as per Indian Standards 25) Explain the test proedure for onduting Standard Penetration test as per Indian Standards 26) Explain the test proedure for onduting Stati Cone Penetration test as per Indian Standards 27) Explain the test proedure for onduting Dynami Cone Penetration test as per Indian Standards 28) How do you interpret field test results for the determination of Safe Bearing Capaity reuired for foundation design? 29) Write short notes on a. Plate load test b. Standard Penetration test. Stati Cone Penetration test d. Dynami Cone Penetration test e. Loal shear failure f. General shear failure g. Punhing shear failure h. Effet of Ground Water Table on bearing apaity i. Shape of footing j. Eentri load on footing 7.5 Referenes. Bowles, J. E. (977) Foundation Analysis and Design, M Graw Hill Publiations, New York. 2. Craig, R. F. (983) Soil Mehanis, 3 rd Edition, English Language Book Soiety & Van nostrand Reinhold Co. Ltd., London.

36 3. Das, B. M. (2007) Priniples of Foundation Engineering, Thomson India Edition, New Delhi. 4. IS Punmia, B. C. (2005) Soil Mehanis and Foundations, Laxmi Publiations Pvt. Ltd., Bangalore 6. Som, N. N. and Das, S. C. (2003) Theory and Pratie of Foundation Design, Prentie Hall of India, New Delhi