Chapter 2 Bearing capacity of foundations
Chapter 2 Bearing capacity of foundations
2.1 Introduction The soil must be capable of carrying the loads from any engineered structure placed upon it without a shear failure and with the resulting settlements being tolerable for that structure. This chapter will be concerned with evaluation of the limiting shear resistance, 周 or ultimate bearing capacity quit,of the soil under a foundation load. 阳喝
2.1 Introduction ▪ The soil must be capable of carrying the loads from any engineered structure placed upon it without a shear failure and with the resulting settlements being tolerable for that structure. ▪ This chapter will be concerned with evaluation of the limiting shear resistance, or ultimate bearing capacity qult, of the soil under a foundation load
2.1 Introduction A soil shear failure can result in excessive building distortion and even collapse. Excessive settlements can result in structural damage to a building frame,cracks and equipment failure. In many cases settlement criteria will control the allowable bearing capacity,however,there are also a number of cases where base shear dictates the recommended beating capacity
2.1 Introduction ▪ A soil shear failure can result in excessive building distortion and even collapse. ▪ Excessive settlements can result in structural damage to a building frame, cracks and equipment failure. ▪ In many cases settlement criteria will control the allowable bearing capacity, however, there are also a number of cases where base shear dictates the recommended beating capacity
2.2 Bearing capacity for footings on layered soils It may be necessary to place footings on stratified deposits where the thickness of the top stratum from the base of the footing d is less than the H distance computed as H=B tana/2. In this case the rupture zone will extend into the lower layer(s)depending on their thickness and require some modification of quit There are three general cases of the footing on a layered soil as follows: Case 1.Footing on layered clays (all =0) a.Top layer weaker than lower layer(c1C2)
2.2 Bearing capacity for footings on layered soils ▪ It may be necessary to place footings on stratified deposits where the thickness of the top stratum from the base of the footing d1 is less than the H distance computed as H=B tanα/2. ▪ In this case the rupture zone will extend into the lower layer (s) depending on their thickness and require some modification of qult ▪ There are three general cases of the footing on a layered soil as follows: ▪ Case 1. Footing on layered clays (all φ=0) ▪ a. Top layer weaker than lower layer (c1c2 )
2.2 Bearing capacity for footings on layered soils Case 2.Footing on layered -c soils with a,b same with case 1. Case 3.Footing on layered sand and clay soils a.Sand overlying clay b.Clay overlying sand Experimental work to establish methods to obtain qult for these three cases seems to be based mostly on models- often with B<75mm. Several analytical methods exist as well. Button(1953)used a circular arc to search for the approximate minimum(for the trial circle all in the top layer),give N.=5.5<2T
2.2 Bearing capacity for footings on layered soils ▪ Case 2. Footing on layered φ-c soils with a, b same with case 1. ▪ Case 3. Footing on layered sand and clay soils ▪ a. Sand overlying clay ▪ b. Clay overlying sand ▪ Experimental work to establish methods to obtain qult for these three cases seems to be based mostly on modelsoften with B<75mm. ▪ Several analytical methods exist as well. ▪ Button (1953) used a circular arc to search for the approximate minimum (for the trial circle all in the top layer), give Nc=5.5<2π
2.2 Bearing capacity for footings on layered soils The use of trial circular arcs can be readily programmed for a computer for two or three layers using su for the layers. It is suggested that the circular arcs be limited to cases where the strength ratio CR=c2/c1 of the top two layers is on the order of 0.6<CR<1.3. where CR is much out of this range there is a large difference in the shear strength of the two layers,Nc is obtained using a method given by Brown and Meyerhof (1969)based on model tests as follows:equation (2.2)~(2.6)
2.2 Bearing capacity for footings on layered soils ▪ The use of trial circular arcs can be readily programmed for a computer for two or three layers using su for the layers. ▪ It is suggested that the circular arcs be limited to cases where the strength ratio CR=c2 /c1 of the top two layers is on the order of 0.6<CR≤1.3. ▪ where CR is much out of this range there is a large difference in the shear strength of the two layers, Nc is obtained using a method given by Brown and Meyerhof (1969) based on model tests as follows: equation (2.2)～(2.6)
2.2 Bearing capacity for footings on layered soils When the top layer is very soft with a small d /B ratio, consideration should be given to placing the footing deeper onto the stiff clay or to using some kind of soil improvement method. Model tests indicate that when the top layer is very soft it tends to squeeze out from beneath the base and when it is stiff it tends to punch into the lower softer layer [Meyerhf and Brown(1967)]. If quit >4c+q the soil may squeeze from beneath the footing (the "lower-bound"solution). It is suggested for -c soils to obtain modified pand c value as follows:①④ If the top layer is soft you should check for any squeezing using Eq.(a)
2.2 Bearing capacity for footings on layered soils ▪ When the top layer is very soft with a small d1 /B ratio, consideration should be given to placing the footing deeper onto the stiff clay or to using some kind of soil improvement method. ▪ Model tests indicate that when the top layer is very soft it tends to squeeze out from beneath the base and when it is stiff it tends to punch into the lower softer layer [Meyerhf and Brown (1967) ]. ▪ If qult >4c1+q the soil may squeeze from beneath the footing (the “lower-bound” solution). ▪ It is suggested for φ-c soils to obtain modified φand c value as follows: ①～④ ▪ If the top layer is soft you should check for any squeezing using Eq. (a)
2.2 Bearing capacity for footings on layered soils For bases on sand overlying clay or clay overlying sand,first check if the distance H will penetrate into the lower stratum.If H>d1 you might estimate qult as follows:①③ ■ A possible alternative for o-c soils with a number of thin layers is to use average values of c and o in the bearing capacity equations of Table 2.1 obtained as Eq.(c)and (d). A slope-stability program written by Bowles can be used to obtain the bearing capacity for layered soils. 超
2.2 Bearing capacity for footings on layered soils ▪ For bases on sand overlying clay or clay overlying sand, first check if the distance H will penetrate into the lower stratum. If H>d1 you might estimate qult as follows: ①～③ ▪ A possible alternative for φ-c soils with a number of thin layers is to use average values of c and φ in the bearing capacity equations of Table 2.1 obtained as Eq. (c) and (d). ▪ A slope-stability program written by Bowles can be used to obtain the bearing capacity for layered soils
2.3 Bearing capacity of footings on slopes When a footing locates on or adjacent to a slope,the lack of the soil on the slope side of the footing will tend to reduce the stability of the footing. The author developed Table 2.3 to solve the footing on or adjacent to a slope as follows: 1 Develop the exit point E for a footing,the angle of the exit is taken as 45-/2 since the slope line is a principle plane. 2 Compute a reduced Nc(Nc)based on the failure surface. 3 Compute a reduced Na(Na)based on the ratios of areas,when the distance b/B>1.5(or 2),Na=Na
2.3 Bearing capacity of footings on slopes ▪ When a footing locates on or adjacent to a slope, the lack of the soil on the slope side of the footing will tend to reduce the stability of the footing. ▪ The author developed Table 2.3 to solve the footing on or adjacent to a slope as follows: ▪ ① Develop the exit point E for a footing, the angle of the exit is taken as 45°-φ/2 since the slope line is a principle plane. ▪ ② Compute a reduced Nc (Nc ’ ) based on the failure surface. ▪ ③ Compute a reduced Nq (Nq ’ ) based on the ratios of areas, when the distance b/B>1.5(or 2), Nq ’= Nq
2.3 Bearing capacity of footings on slopes 4 The overall slope stability should be checked for the effect of the footing load.At least a few trial circles should touch point c(on the edge of base)as well as other trial entrance points on top of and on the slope. The ultimate bearing may be computed by any of the equation of Table 2.1;however,the author suggests using the Hansen equation modified to read as follows: qult=CNc'Scic+qNgSgig+1/2YBNy'syiy Obtain the Nc and Na factors from Table 2.3. The d factors are not included in the equation since the depth effect is included in the computation of the ratios of areas
2.3 Bearing capacity of footings on slopes ▪ ④ The overall slope stability should be checked for the effect of the footing load. At least a few trial circles should touch point c (on the edge of base) as well as other trial entrance points on top of and on the slope. ▪ The ultimate bearing may be computed by any of the equation of Table 2.1; however, the author suggests using the Hansen equation modified to read as follows: ▪ qult=cNc ’sc ic+qNq ’sq iq+1/2γBNγ ’ sγiγ ▪ Obtain the Nc ’ and Nq ’ factors from Table 2.3. ▪ The di factors are not included in the equation since the depth effect is included in the computation of the ratios of areas