Bearing capacity from SPT numbers

    One of most commonly method for determining allowable soil bearing capacity is from standard penetration test (SPT) numbers. It is simply because SPT numbers are readily available from soil boring. The equations that are commonly used were proposed by Meryerhof based on one inches of foundation settlement. Bowles revised Meyerhof’s equations because he believed that Meryerhof’s equation might be conservative.

Meryerhof’s equations:

For footing width, 4 feet or less:Qa = (N/4) / K [1.12]For footing width, greater than 4 ft:

Qa = (N/6)[(B+1)/B]2 / K [1.13]

Bowles’ equations:

For footing width, 4 feet or less:Qa = (N/2.5) / K [1.14]For footing width, greater than 4 ft:Qa = (N/4)[(B+1)/B]2 / K [1.15]Qa: Allowable soil bearing capacity, in kips/ft2.N: SPT numbers below the footing.B: Footing width, in feetK = 1 + 0.33(D/B) £ 1.33D: Depth from ground level to the bottom of footing, in feet. Example 7: Determine soil bearing capacity by SPT numbersGiven

Soil SPT number: 10 Footing type: 3 feet wide strip footing, bottom of footing at 2 ft below ground

surface. Requirement: Estimate allowable soil bearing capacity based on. Solution:Meryerhof's equationK = 1+0.33(D/B) = 1+0.33*(2/3) = 1.22 Qa = (N/4) / K = (10 /4) /1.22 = 2 kips/ft2Bowles’ equation: Qa = (N/2.5) / K = (10 /2.5) /1.22 = 3.3 kips/ft2

Example 8: Determine soil bearing capacity by SPT numbers

Given: Soil SPT number: 20 Footing type: 8 feet wide square footing, bottom of footing at 4 ft below

ground surface. Requirement: Estimate allowable soil bearing capacity based on Meryerhof’s equation.Solution:

Meryerhof’s equationK = 1+0.33(D/B) = 1+0.33*(4/8) = 1.17Qa = (N/6)[(B+1)/B]2 / K = (20/6)[(8+1)/8]2 /1.17 = 3.6 kips/ft2Bowles’ equation:Qa = (N/4)[(B+1)/B]2 / K = (20/4)[(8+1)/8]2 /1.17 = 5.4 kips/ft2 

Bearing capacity Failure mechanisms and derivation of equations Bearing capacity of shallow foundations Presumed bearing values Bearing capacity of piles

The ultimate load which a foundation can support may be calculated using bearing capacity theory. For preliminary design, presumed bearing values can be used to indicate the pressures which would normally result in an adequate factor of safety. Alternatively, there is a range of empirical methods based on in situ test results.

The ultimate bearing capacity (qf) is the value of bearing stress which causes a sudden catastrophic settlement of the foundation (due to shear failure).

The allowable bearing capacity (qa) is the maximum bearing stress that can be applied to the foundation such that it is safe against instability due to shear failure and the maximum tolerable settlement is not exceeded. The allowable bearing capacity is normally calculated from the ultimate bearing capacity using a factor of safety (Fs).

When excavating for a foundation, the stress at founding level is relieved by the removal of the weight of soil. The net bearing pressure (qn) is the increase in stress on the soil. qn = q - qo qo = D where D is the founding depth and is the unit weight of the soil removed.        

Failure mechanisms and derivation of equations Bearing capacity

Upper and lower bound solutions Semi-circular slip mechanism Circular arc slip mechanism

A relatively undeformed wedge of soil below the foundation forms an active Rankine zone with angles (45º + '/2).

The wedge pushes soil outwards, causing passive Rankine zones to form with angles (45º - '/2).

The transition zones take the form of log spiral fans.

For purely cohesive soils ( = 0) the transition zones become circular for which Prandtl had shown in 1920 that the solution is qf = (2 + ) su = 5.14 su

This equation is based on a weightless soil. Therefore if the soil is non-cohesive (c=0) the bearing capacity depends on the surcharge qo. For a footing founded at depth D below the surface, the surcharge qo = . Normally for a shallow foundation (D<B), the shear strength of the soil between the surface and the founding depth D is neglected. radius of the fan r = r0 .exp[.tan']. is the fan angle in radians (between 0 and /2) ' is the angle of friction of the soil ro = B/[2 cos(45+'/2)]

Upper and lower bound solutions

Failure mechanisms and derivation of equations

The bearing capacity of a soil can be investigated using the limit theorems of ideal rigid-perfectly-plastic materials.

The ultimate load capacity of a footing can be estimated by assuming a failure mechanism and then applying the laws of statics to that mechanism. As the mechanisms considered in an upper bound solution are progressively refined, the calculated collapse load decreases.

As more stress regions are considered in a lower bound solution, the calculated collapse load increases.

Therefore, by progressive refinement of the upper and lower bound solutions, the exact solution can be approached. For example, Terzaghi's mechanism gives the exact solution for a strip footing.        

Semi-circular slip mechanism

Failure mechanisms and derivation of equations

Suppose the mechanism is assumed to have a semi-circular slip surface. In this case, failure will cause a rotation about point O. Any surcharge qo will resist rotation, so the net pressure (q - qo) is used. Using the equations of statics: Moment causing rotation

= load x lever arm = [(q - qo) x B] x [½B]

Moment resisting rotation = shear strength x length of arc x lever arm = [s] x [.B] x [B]

At failure these are equal:

(q - qo ) x B x ½B = s x .B x B Net pressure (q - qo ) at failure

= 2 x shear strength of the soil This is an upper-bound solution.

Circular arc slip mechanism

Failure mechanisms and derivation of equations

Consider a slip surface which is an arc in cross section, centred above one edge of the base. Failure will cause a rotation about point O. Any surcharge qo will resist rotation so the net pressure (q - qo) is used. Using the equations of statics:     Moment causing rotation

= load x lever arm = [ (q - qo) x B ] x [B/2]

Moment resisting rotation = shear strength x length of arc x lever arm = [s] x [2R] x [R]

At failure these are equal: (q - qo) x B x B/2 = s x 2 R x R

Since R = B / sin : (q - qo ) = s x 4 /(sin )²

The worst case is when tan=2 at = 1.1656 rad = 66.8 deg

The net pressure (q - qo) at failure = 5.52 x shear strength of soil

Bearing capacity of shallow foundations Bearing capacity

Bearing capacity equation (undrained) Bearing capacity equation (drained) Factor of safety

The ultimate bearing capacity of a foundation is calculated from an equation that incorporates appropriate soil parameters (e.g. shear strength, unit weight) and details about the size, shape and founding depth of the footing. Terzaghi (1943) stated the ultimate bearing capacity of a strip footing as a three-term expression incorporating the bearing capacity factors: Nc, Nq and N, which are related to the angle of friction (´).

qf =c.Nc +qo.Nq + ½.B .Ng

For drained loading, calculations are in terms of effective stresses; ´ is > 0 and N c, Nq and N are all > 0. For undrained loading, calculations are in terms of total stresses; the undrained shear strength (su); Nq = 1.0 and N = 0

c = apparent cohesion intercept qo = D  (i.e. density x depth) D = founding depth B = breadth of foundation = unit weight of the soil removed.

Bearing capacity equation (undrained)

Bearing capacity of shallow foundations

Skempton's equation is widely used for undrained clay soils: qf = su .Ncu + qo where Ncu = Skempton's bearing capacity factor, which can be obtained from a chart or by using the following expression: Ncu = Nc.sc.dc where sc is a shape factor and dc is a depth factor. Nq = 1,  N = 0, Nc = 5.14 sc = 1 + 0.2 (B/L)   for B<=L dc = 1+ Ö(0.053 D/B )  for D/B < 4

Bearing capacity equation (drained)

Bearing capacity of shallow foundations

Bearing capacity factors Shape factors Depth factors

Terzaghi (1943) stated the bearing capacity of a foundation as a three-term expression incorporating the bearing capacity factors Nc, Nq and N. He proposed the following equation for the ultimate bearing capacity of a long strip footing: qf =c.Nc +qo.Nq + ½.B .N

This equation is applicable only for shallow footings carrying vertical non-eccentric loading. For rectangular and circular foundations, shape factors are introduced. qf = c .Nc .sc + qo .Nq .sq + ½ .B .N .sg

Other factors can be used to accommodate depth, inclination of loading, eccentricity of loading, inclination of base and ground. Depth is only significant if it exceeds the breadth.        

Bearing capacity factors Bearing capacity equation (drained)

The bearing capacity factors relate to the drained angle of friction ('). The c.Nc term is the contribution from soil shear strength, the qo.Nq term is the contribution from the surcharge pressure above the founding level, the ½.B..Ng term is the contribution from the self weight of the soil. Terzaghi's analysis was based on an active wedge with angles ' rather than (45+'/2), and his bearing capacity factors are in error, particularly for low values of '. Commonly used values for Nq and Nc are derived from the Prandtl-Reissner expression giving

Exact values for Ng are not directly obtainable; values have been proposed by Brinch Hansen (1968), which are widely used in Europe, and also by Meyerhof (1963), which have been adopted in North America. Brinch Hansen:

N = 1.8 (Nq - 1) tan' Meyerhof:

N = (Nq - 1) tan(1.4 ')

Shape factors Bearing capacity equation (drained)

Terzaghi presented modified versions of his bearing capacity equation for shapes of foundation other than a long strip, and these have since been expressed as shape factors. Brinch Hansen and Vesic (1963) have suggested shape factors which depend on '. However, modified versions of the Terzaghi factors are usually considered sufficiently accurate for most purposes.

  sc sq s

square 1.3 1.2 0.8circle 1.3 1.2 0.6rectangle (B<L) 1+ 0.2(B/L) 1+ 0.2(B/L) 1 - 0.4(B/L)B = breadth, L = length        

Depth factors Bearing capacity equation (drained)

It is usual to assume an increase in bearing capacity when the depth (D) of a foundation is greater than the breadth (B). The general bearing capacity equation can be modified by the inclusion of depth factors.

qf = c.Nc.dc + qo.Nq.dq + ½ B..d for D>B:

dc = 1 + 0.4 arctan(D/B) dq = 1 + 2 tan('(1-sin')² arctan(B/D) d = 1.0

for D=<B: dc = 1 + 0.4(D/B) dq = 1 + 2 tan('(1-sin')² (B/D) d = 1.0

Factor of safety Bearing capacity of shallow foundations

A factor of safety Fs is used to calculate the allowable bearing capacity qa from the ultimate bearing pressure qf. The value of Fs is usually taken to be 2.5 - 3.0.

The factor of safety should be applied only to the increase in stress, i.e. the net bearing pressure qn. Calculating qa from qf only satisfies the criterion of safety against shear failure. However, a value for Fs of 2.5 - 3.0 is sufficiently high to empirically limit settlement. It is for this reason that the factors of safety used in foundation design are higher than in other areas of geotechnical design. (For slopes, the factor of safety would typically be 1.3 - 1.4).

Experience has shown that the settlement of a typical foundation on soft clay is likely to be acceptable if a factor of 2.5 is used. Settlements on stiff clay may be quite large even though ultimate bearing capacity is relatively high, and so it may be appropriate to use a factor nearer 3.0.        

Presumed bearing values Bearing capacity

For preliminary design purposes, BS 8004 gives presumed bearing values which are the pressures which would normally result in an adequate factor of safety against shear failure for particular soil types, but without consideration of settlement.

Category Types of rocks and soils Presumed bearing value

Non-cohesive soils Dense gravel or dense sand and gravel >600 kN/m²

 Medium dense gravel,  or medium dense sand and gravel

<200 to 600 kN/m² 

  Loose gravel, or loose sand and gravel  <200 kN/m²

  Compact sand >300 kN/m²

  Medium dense sand 100 to 300 kN/m²

  Loose sand<100 kN/m² depends on  degree of looseness

Cohesive soils Very stiff bolder clays & hard clays 300 to 600 kN/m²

  Stiff clays 150 to 300 kN/m² 

  Firm clay  75 to 150 kN/m² 

  Soft clays and silts  < 75 kN/m² 

  Very soft clay  Not applicable

Peat   Not applicable

Made ground   Not applicable

Presumed bearing values for Keuper Marl

Weathering Zone DescriptionPresumed bearing value

Fully weathered IVb Matrix only as cohesive soil

Partially weathered

IVaMatrix with occasional pellets less than 3mm

125 to 250 kN/m²

III Matrix with lithorelitics up to 25mm 250 to 500 kN/m²

IIAngular blocks of unweathered marl with virtually no matrix

500 to 750 kN/m²

Unweathered 1 Mudstone (often not fissured) 750 to 1000 kN/m²

Bearing capacity of piles Bearing capacity

Driven piles in non-cohesive soil Bored piles in non-cohesive soil Driven piles in cohesive soil Bored piles in cohesive soil Carrying capacity of piles in a layered soil Effects of ground water

The ultimate bearing capacity of a pile used in design may be one three values: the maximum load Qmax, at which further penetration occurs without the load increasing; a calculated value Qf given by the sum of the end-bearing and shaft resistances; or the load at which a settlement of 0.1 diameter occurs (when Qmax is not clear).

For large-diameter piles, settlement can be large, therefore a safety factor of 2-2.5 is usually used on the working load.

A pile loaded axially will carry the load: partly by shear stresses (s) generated along the shaft of the pile and partly by normal stresses (qb) generated at the base.

The ultimate capacity Qf of a pile is equal to the base capacity Qb plus the shaft capacity Qs.

Qf  =  Qb + Qs   =  Ab . qb + (As . s) where Ab is the area of the base and As is the surface area of the shaft within a soil layer.

Full shaft capacity is mobilised at much smaller displacements than those related to full base resistance. This is important when determining the settlement response of a

pile. The same overall bearing capacity may be achieved with a variety of combinations of pile diameter and length. However, a long slender pile may be shown to be more efficient than a short stubby pile. Longer piles generate a larger proportion of their full capacity by skin friction and so their full capacity can be mobilised at much lower settlements.

The proportions of capacity contributed by skin friction and end bearing do not just depend on the geometry of the pile. The type of construction and the sequence of soil layers are important factors.        

Driven piles in non-cohesive soil Bearing capacity of piles

Ultimate pile capacity Standard penetration test Cone penetration test

Driving a pile has different effects on the soil surrounding it depending on the relative density of the soil. In loose soils, the soil is compacted, forming a depression in the ground around the pile. In dense soils, any further compaction is small, and the soil is displaced upward causing ground heave. In loose soils, driving is preferable to boring since compaction increases the end-bearing capacity.

In non-cohesive soils, skin friction is low because a low friction 'shell' forms around the pile. Tapered piles overcome this problem since the soil is recompacted on each blow and this gap cannot develop.

Pile capacity can be calculated using soil properties obtained from standard penetration tests or cone penetration tests. The ultimate load must then be divided by a factor of safety to obtain a working load. This factor of safety depends on the maximum tolerable settlement, which in turn depends on both the pile diameter and soil compressibility. For example, a safety factor of 2.5 will usually ensure a pile of diameter less than 600mm in a non-cohesive soil will not settle by more than 15mm.

Although the method of installing a pile has a significant effect on failure load, there are no reliable calculation methods available for quantifying any effect. Judgement is therefore left to the experience of the engineer.        

Ultimate pile capacity Driven piles in non-cohesive soil

The ultimate carrying capacity of a pile is: Qf = Qb + Qs

The base resistance, Qb can be found from Terzaghi's equation for bearing capacity, qf = 1.3 c Nc + qo Nq + 0.4 B N The 0.4 term may be ignored, since the diameter is considerably less than the depth of the pile. The 1.3 c Nc term is zero, since the soil is non-cohesive.

The net unit base resistance is therefore qnf = qf - qo = qo (Nq -1)

and the net total base resistance is Qb = qo (Nq -1) Ab

The ultimate unit skin friction (shaft) resistance can be found from qs = Ks .'v .tan where 'v = average vertical effective stress in a given layer = angle of wall friction, based on pile material and ´ Ks = earth pressure coefficient Therefore, the total skin friction resistance is given by the sum of the layer resistances: Qs = (Ks .'v .tan .As) The self-weight of the pile may be ignored, since the weight of the concrete is almost equal to the weight of the soil displaced. Therefore, the ultimate pile capacity is:

Qf = Ab qo Nq + (Ks .'v .tan .As)

Values of Ks and can be related to the angle of internal friction (´) using the following table according to Broms.

Material  Ks

low density high density

steel 20° 0.51.0

concrete 3/4 ´ 1.0 2.0timber 2/3 ´ 1.5 4.0

It must be noted that, like much of pile design, this is an empirical relationship. Also, from empirical methods it is clear that Qs and Qb both reach peak values somewhere at a depth between 10 and 20 diameters.

It is usually assumed that skin friction never exceeds 110 kN/m² and base resistance will not exceed 11000 kN/m².        

Standard penetration test Driven piles in non-cohesive soil

The standard penetration test is a simple in-situ test in which the N-value is the mumber of blows taken to drive a 50mm diameter bar

300mm into the base of a bore hole.

Schmertmann (1975) has correlated N-values obtained from SPT tests against effective overburden stress as shown in the figure. The effective overburden stress =  the weight of material above the base of the borehole - the wight of water e.g. depth of soil = 5m, depth of water = 4m, unit weight of soil = 20kN/m³, 'v = 5m x 20kN/m³ - 4m x 9.81kN/m³ 60 kN/m²

Once a value for ´ has been estimated, bearing capacity factors can be determined and used in the usual way.

Meyerhof (1976) produced correlations between base and frictional resistances and N-values. It is recommended that N-values first be normalised with respect to effective overburden stress:

Normalised N = Nmeasured x 0.77 log(1920/´v)

Pile type  Soil typeUltimate base resistance

qb (kPa)Ultimate shaft resistance

qs (kPa)

DrivenGravelly sand  Sand

40(L/d) N but < 400 N

2 Navg

 Sandy silt  Silt

20(L/d) N but < 300 N

 

Bored Gravel and sands13(L/d) N

but < 300 N

 

Navg

 Sandy silt Silt

13(L/d) N but < 300 N

 

L = embedded length d = shaft diameter Navg = average value along shaft    

Cone penetration test Driven piles in non-cohesive soil

End-bearing resistance The end-bearing capacity of the pile is assumed to be equal to the unit cone resistance (qc). However, due to normally occurring variations in measured cone resistance, Van der Veen's averaging method is used: qb = average cone resistance calculated over a depth equal to three pile diameters above to one pile diameter below the base level of the pile.

Shaft resistance The skin friction can also be calculated from the cone penetration test from values of local side friction or from the cone resistance value using an empirical relationship: At a given depth, qs = Sp. qc where Sp = a coefficient dependent on the type of pile     Type of pile Sp

Solid timber ) Pre-cast concrete ) Solid steel driven )

0.005 - 0.012

Open-ended steel 0.003 - 0.008

Bored piles in non-cohesive soil Bearing capacity of piles

The design process for bored piles in granular soils is essentially the same as that for driven piles. It must be assumed that boring loosens the soil and therefore, however dense the soil, the value of the angle of friction used for calculating Nq values for end bearing and values for skin friction must be those assumed for loose soil. However, if rotary drilling is carried out under a bentonite slurry ' can be taken as that for the undisturbed soil.        

Driven piles in cohesive soil Bearing capacity of piles

Driving piles into clays alters the physical characteristics of the soil. In soft clays, driving piles results in an increase in pore water pressure, causing a reduction in effective stress;.a degree of ground heave also occurs. As the pore water pressure dissipates with time and the ground subsides, the effective stress in the soil will increase. The increase in 'v leads to an increase in the bearing capacity of the pile with time. In most cases, 75% of the ultimate bearing capacity is achieved within 30 days of driving.

For piles driven into stiff clays, a little consolidation takes place, the soil cracks and is heaved up. Lateral vibration of the shaft from each blow of the hammer forms an enlarged hole, which can then fill with groundwater or extruded porewater. This, and 'strain softening', which occurs due to the large strains in the clay as the pile is advanced, lead to a considerable reduction in skin friction compared with the undisturbed shear strength (su) of the clay. To account for this in design calculations an adhesion factor, , is introduced. Values of can be found from empirical data previously recorded. A maximum value (for stiff clays) of 0.45 is recommended.

The ultimate bearing capacity Qf of a driven pile in cohesive soil can be calculated from: Qf = Qb + Qs

where the skin friction term is a summation of layer resistances Qs = ( .su(avg) .As)

and the end bearing term is Qb = su .Nc .Ab

Nc = 9.0 for clays and silty clays.        

Bored piles in cohesive soil Bearing capacity of piles

Following research into bored cast-in-place piles in London clay, calculation of the ultimate bearing capacity for bored piles can be done the same way as for driven piles. The adhesion factor should be taken as 0.45. It is thought that only half the undisturbed shear strength is mobilised by the pile due to the combined effect of swelling, and hence softening, of the clay in the walls of the borehole. Softening results from seepage of water from fissures in the clay and from the un-set concrete, and also from 'work softening' during the boring operation.

The mobilisation of full end-bearing capacity by large-diameter piles requires much larger displacements than are required to mobilise full skin-friction, and therefore safety factors of 2.5 to 3.0 may be required to avoid excessive settlement at working load.        

Carrying capacity of piles in layered soil Bearing capacity of piles

When a pile extends through a number of different layers of soil with different properties, these have to be taken into account when calculating the ultimate carrying capacity of the pile. The skin friction capacity is calculated by simply summing the amounts of resistance each layer exerts on the pile. The end bearing capacity is calculated just in the layer where the pile toe terminates. If the pile toe terminates in a layer of dense sand or stiff clay overlying a layer of soft clay or loose sand there is a danger of it punching through to the weaker layer. To account for this, Meyerhof's equation is used.

The base resistance at the pile toe is qp = q2 + (q1 -q2)H / 10B but £ q1

where B is the diameter of the pile, H is the thickness between the base of the pile and the top of the weaker layer, q2 is the ultimate base resistance in the weak layer, q1 is the ultimate base resistance in the strong layer.

       

Effects of groundwater Bearing capacity of piles

The presence and movement of groundwater affects the carrying capacity of piles, the processes of construction and sometimes the durability of piles in service.

Effect on bearing capacity In cohesive soils, the permeability is so low that any movement of water is

very slow. They do not suffer any reduction in bearing capacity in the presence of groundwater. In granular soils, the position of the water table is important. Effective stresses in saturated sands can be as much as 50% lower than in dry sand; this affects both the end-bearing and skin-friction capacity of the pile.

Effects on construction When a concrete cast-in-place pile is being installed and the bottom of the borehole is below the water table, and there is water in the borehole, a 'tremie' is used.

With its lower end lowered to the bottom of the borehole, the tremmie is filled with concrete and then slowly raised, allowing concrete to flow from the bottom. As the tremie is raised during the concreting it must be kept below the surface of the concrete in the pile. Before the tremie is withdrawn completely sufficient concrete should be placed to displace all the free water and watery cement. If a tremie is not used and more than a few centimetres of water lie in the bottom of the borehole, separation of

the concrete can take place within the pile, leading to a significant reduction in capacity.

A problem can also arise when boring takes place through clays. Site investigations may show that a pile should terminate in a layer of clay. However, due to natural variations in bed levels, there is a risk of boring extending into underlying strata. Unlike the clay, the underlying beds may be permeable and will probably be under a considerable head of water. The 'tapping' of such aquifers can be the cause of difficulties during construction.

Effects on piles in service The presence of groundwater may lead to corrosion or deterioration of the pile's fabric. In the case of steel piles, a mixture of water and air in the soil provides conditions in which oxidation corrosion of steel can occur; the presence of normally occurring salts in groundwater may accelerate the process. In the case of concrete piles, the presence of salts such as sulphates or chlorides can result in corrosion of reinforcement, with possible consequential bursting of the concrete. Therefore, adequate cover must be provided to the reinforcement, or the reinforcement itself must be protected in some way. Sulphate attack on the cement compounds in concrete may lead to the expansion and subsequent cracking. Corrosion problems are minimised if the concrete has a high cement/aggregate ratio and is well compacted during placement.

Input Data:

Cohesion, c = psf

Soil density, γ = pcf

Found. depth, D = ft

Ang. of repose, φ = °

Found. width, B = ft

Factor of Safety =

Results:

Nq =

Nγ =

Nc =

Ultimate bearing cap. = psf

Allowable bearing cap. = psf

Terzaghi’s Ultimate Bearing Capacity Equation

For saturated, submerged soils:

qu = qc + qq + qγ = cNc + qNq + ½γ'BNγ . . . for strip foundations

qu = qc + qq + qγ = cNc + qNq + 0.3γ'BNγ . . . for circular or square foundations

qc, qq, q . = load contributions from cohesion, soil weight and surcharge Nc, Nq, N . = bearing capacity factors for cohesion, soil weight and surcharge c = cohesion strength of soil q = soil weight γ’ = effective bulk density of soil ( γ' = γ - γw ) B = width of the foundation

Soil weight is calculated as q = γ'D, where D is the depth of penetration of the foundation

NOTE: γ’ is used only for the portion of the soil that is submerged, otherwise the bulk density γ is used (neither is a dry weight!)

For shallow foundations:

Nq = eπ tanφ tan2(45 + φ/2) Nγ = (Nq - 1) tan(1.4φ) Nc = (Nq - 1) cotφφ > 0 Nc = π + 2 = 5.14φ = 0, clay for deep foundations Nc ≈ 9

Allowable bearing capacity (qa)qa = qu / FS

For Sandy Soils

Cohesionless soil (80% or more sand), c = 0, φ from table:

Soil Type φ (degrees)

Loose sand 27-35

Medium sand 30-40

Dense sand 35-45

Gravel with some sand 34-48

Silt 26-35

For Clay Soils

Cohesive soil, assume φ = 0, c from table:

Consistency psf kN/m2

Very soft 0 - 500 0 - 48

Soft 500 - 1,000 48 - 96

Medium 1,000 - 2,000 96 - 192

Stiff 2,000 - 4,000 192 - 384

Very stiff 4,000 - 8,000 384 - 766

hard > 8,000 > 766

Blow Count (N, blows/ft or blows/30 cm)

N is the average blows per foot in the stratum, number of blows of a 140-pound hammer falling 30 inches to drive a standard sampler (1.42" I. D., 2.00" O. D.) one foot. The sampler is driven 18 inches and blows counted the last 12 inches.

Sand Clay

Density N N Undrained Compressive

strength (psf)

Very loose 0-4 <2 <500 Very soft

Loose 4-10 2-4 500-1,000 Soft

Medium 10-30 4-8 1,000-2,000 Medium

Dense 30-50 8-15 2,000-4,000 Stiff

Very dense >50 15-30 4,000-8,000 Very stiff

>30 >8,000 Hard

ESTIMATION OF SOIL PARAMETERS FROM STANDARD PENETRATION TESTS

Granular Soil (Sand)

Description Very Loose

Loose Medium Dense Very Dense

Standard penetration resistance corr’d, N'*

0 4 10 30 50

Approx. angle of internal friction, (φ)degrees**

25 – 30 27 – 32 30 – 35 35 – 40 38 – 43

Approx. range of moist unit weight, (γ)pcf**

70 – 100 90 – 115

110 – 130

120 – 140

130 – 150

* N' is SPT value corrected for overburden pressure.** Use larger values for granular material with 5% or less fine sand and silt.

Cohesive soils (Clay)

(Rather unreliable, use only for preliminary estimate purposes).

Consistency Very Soft

Soft Medium Stiff Very Stiff

Hard

qu, ksf 0 0.5 1.0 2.0 4.0 8.0

Field standard penetration Resistance, N

0 2 4 8 16 32

γ(moist) pcf 100 – 120

110 – 130 120 – 140

The bearing capacity of soils for shallow foundations generally follows the acceptable Terzaghi-Meyerhof equation.

Qult = 1/2*gamma*B*Ny + c*Nc + (Pq +gamma*Df)*Nq  where Q ult is the ultimate bearing capacity. To get the acceptable, you may use a factor of safety of 3.

Gamma is the overburden pressurec is the undrained shear strength or 0.5 of unconfined strength (for clay), c=o for sandy soilsDf = depth to foundation levelPq = additional surcharge load above ground, if required.

Ny,Nc and Nq are capacity factors, and need to be looked from a chart. It is a function of friction angle phiCorrection is required for  for size and depth of footing.

From here there are correlation from N values to estimated undrained shear strength (for cohesive soils).

For sandy soil, the above equation can be estimated to be :Qa = 0.11 Cn * NQa = allowable bearing pressure = Q ult/Factor of safety = Q ult/3Cn is overburden factor  Cn=1 if overbudern is about 1 tsf, Cn=2 if overburden is 0 tsf, Cn=0.5 if overbudern is 4.5 tsf.

If you want details, I suggest that you look at one of the soil mechanics or Foundation Engrg book, or visit the web site of US Army and read the text on bearing capacity of soils  Document number EM 1110-1-1905Address is http://www.usace.army.mil/inet/usace-docs/eng-manuals/em.htmYou can read the documents using acrobat (pdf file)

First to start, it is important that you know that predictions on bearing capacity using SPT are only moderately reliable, principally due to some inconsistencies in SPT test procedures. Furthermore, the standard penetration test are not too good for predict pile capacities in cohessive soils.By the way, your question is for shallow or deep (pile)foundations?For the second of them you could use these formulas:

MEYERHOFEnd bearing:qe = minor of 0,40*N'60(at toe)*D/B*sigma.r and 4*N'60(at toe)*sigma.r (Sands and gravels)qe = minor of 0,40*N'60(at toe)*D/B*sigma.r and 3*N'60(at toe)*sigma.r (Non plastic silts)

Skin Friction:fs = sigma.r/50*N60 (Large displacement piles)fs = sigma.r/100*N60 (Small displacement piles)

Where:qe= unit point resistancefs= unit lateral resistance sigma.r=100 KPa =2000 lb/ft2 D/B is the ratio pile embedment depth- diameter N'60 is the normalized value for the SPT, corrected for overburden pressures and field procedures.

N'60= CN*N60CN= 2/(1+sigma.v/sigma.r)sigma v= Overburden pressure

N60 is the SPT value corrected for field procedures. It assumes an standard of 60% of

efficiency of the penetration hammer. If you are not sure of the efficiency of the hammer, you can assume your N= N60. Off course, you can mislead if your efficiency is less than 60 %, because it will need the next transformation:

N60= N* % Efficiency/60

BRIAUD:qe= 19,7*sigma.r*(N60)^0,36fs= 0,224*sigma.r*(N60)^0,29

BOWLES:fs= Xm*N55 (or N60)Xm= 2,0 for large volume displacementXm= 1,0 for small volume displacement

SHIOI and FUKUI:fs= 10 N55 (KPa) Driven piles in clay

Riz (Structural) 12 Mar 01 8:56

Art,Yes, u can find relevant soil type according to the N values u get. Once the soil type is established u can than  read a suitable allowable bearing capacity.Look for:A. Hodgkinson, 1986,Foundation Design,Architectural Press, UKHowever, I would point out that u carry out from 1st principles the allowable bearing capacity based on N values u have. Its easy once u get going!Riz