7/28/2019 17.1_Bearing Capacity - Meyerhof

1/2

BC7

General Shear Failure Bearing Capacity:

o Form of Terzaghi equation essentially correct: bearing factors and extensions improvedo Desirable to analyze deeper footings (Df > B), inclined loads, eccentric loads, sloped

ground, and tilted footing baseo Several important solutions available:

Meyerhof (1963) uses = (45 + /2) and includes shear strength in soil abovefooting, inclined and eccentric loads

Hansen (1970) similar to Meyerhof, adds slope and tilted base

Vesic (1973) similar to Hansen with modified inclination, slope, and tilt factors

All three methods use same Nc and Nq, but have different N

Do not mix the methods , compare if time & project dictate extra effort

Meyerhof Bearing Capacity Equation: (for general shear failure)

qu= (qc + qq + q) = cNccscdci + qNqqsqdqi + BNsdi

where: qu = ultimate bearing capacityc = cohesion (qc due to c)

q = stress at depth of foundation = Df (qq due to q)

= average unit weight of soil under footing (q due to )

(if completely submerged, use = = b)

B = width of foundation (= diameter for circular foundation)

cs, qs, s = shape factors

cd, qd, d = depth factors

ci, qi, i = load inclination factors

Nc, Nq, N = bearing capacity factors

Shape Factors (s):

for ( = 0) cs

+=

L

B20.01 qs = s = 1.00

for (0

7/28/2019 17.1_Bearing Capacity - Meyerhof

2/2

BC8

Inclination Factors (i): for ( = 0) ci = qi = i = 1.00

for ( = 0) ci = qi

2

901

= i = 0

for ( > 0) ci = qi

2

901

= i

2

1

= (= 0 if > )

Bearing Factors (N): )2/45(taneN2tan

q +=

( in radians)

=

tan

1NN

q

c , Nc = 5.14 for = 0

)4.1tan()1N(N q =

Note: in above equations should be the plane strain value, ps, (from a direct shear test) if

(L/B> 1) and the triaxial value, tr, if (L/B = 1). The following approximate correlation may

be used if needed:

for tr 34 ps = 1.5tr 17

for tr < 34 ps = tr (Lade and Lee, 1976)

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Friction Angle , degrees

Bearing

CapacityFactor,

N

Terzaghi

Meyerhof

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Friction Angle , degrees

Bearing

CapacityFactor,

N

Terzaghi

Meyerhof

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Friction Angle , degrees

Bearing

CapacityFactor,

N

Terzaghi

Meyerhof