QuickDefine
B:
width of footing; the smaller
of the 2 dimensions in the case of a rectangular footing
Df:
depth of soil from ground
surface to the bottom of foundation
D1:
depth to water table; of significance in
Case I of water table
existence
D2:
depth from water table to bottom of foundation; of significance in Case I
of water table existence
qu:
ultimate bearing capacity; the load per unit area at which a sudden failure in
the soil supporting the foundation will take place, and the failure surface in
the soil will extend to the ground surface.
H:
depth from the bottom of footing to top of the weaker soil layer
g:
unit weight of soil; the weight of soil per unit volume, W/V
gsat:
saturated or moist unit weight of soil; obtained by relating the weight of soil
solids and the moisture content to the total volume of a soil sample
gw:
unit weight of water
gbar:
weighted or effective unit weight of soil introduced into the third term of the
soil bearing capacity equation when a water table exists at a depth less than B
below the foundation base
e:
load eccentricity; in force the system equivalent to a moment and vertical
loading case, e is the distance M/Q (moment/load) from the center of the footing
Nc, Nq, and Ng:
bearing capacity factors;
first introduced by Terzaghi and later on verified/modified experimentally by
Meyerhof
N'c,
N'q, and N'g:
bearing capacity factors
obtained by replacing Φ in the equations of
Nc, Nq, and Ng
by: Φ’=tan-1 (2/3tanΦ).
qo: an equivalent surcharge
replacing the effect of soil above the bottom of the foundation
Kpg:
passive pressure coefficient
Fcs, Fqs, Fgs:
shape factors which account for rectangularity of the footing; empirical
relationships based on extensive laboratory tests by Da Beer & Hansen (1970)
Fcc, Fqc, Fgc:
soil compressibility factors derived by Vesic (1973) from the analogy of the
expansion of cavities
Fcd, Fqd, Fgd:
depth factors; empirical relations based extensive laboratory tests by Hansen
(1970) - Note that the factor tan-1(Df/B) is in radians
Fci, Fqi, Fgi:
inclination factors to account for the inclination of the load applied in case
the load is not vertical and at an angle
b from the vertical.
eB:
eccentricity along the width; in the force system equivalent to a moment and
vertical loading case, e is the distance M/Q (moment/load) from the center of
the footing
eL:
eccentricity along the
length; in the force system equivalent to a moment and vertical loading case, e
is the distance M/Q (moment/load) from the center of the footing
A’:
effective area; the effective area procedure was developed by Meyerhof (1953) to
evaluate the factor of safety for eccentrically loaded footings against bearing
capacity failure
B’: effective
width; the effective area procedure was developed by Meyerhof (1953) to evaluate
the factor of safety for eccentrically loaded footings against bearing capacity
failure
L’: effective
length; the effective area procedure was developed by Meyerhof (1953) to
evaluate the factor of safety for eccentrically loaded footings against bearing
capacity failure
B1, B2:
sub parameters for determining the effective width
L1, L2:
sub parameters
for determining the effective length
G: shear modulus
of the soil
q’: effective
overburden pressure at a depth of Df + B/2
b:
inclination of
load with respect to the vertical.
d:
depth from bottom of footing to water table level; of significance in Case
II of water table existence where it is located at depth (d) less
than B below foundation base level
Cohesion (c):
an average value of the
intermolecular attractive force acting between the grains of a given mass of
soil. It is this force that holds the mass of soil together. (Characteristic of
clayey soils; c approaches 0 as soil becomes more granular.)
Effective unit weight
g’: it is the unit weight
of soil taking into account the presence of water and the consequent buoyancy
Friction angle
f:
Stable angle of slope of soil or drained angle of internal friction; determined
using the direct-shear or triaxial tests (increases as soil becomes more
granular and equals 0 for saturated clays and silts)
Rigidity index Ir:
an indication of the soil’s
rigidity and is proportional to the shear modulus of the soil
Ir(cr):
critical rigidity index; the
rigidity index is an indication of the soil’s rigidity and is proportional to
the shear modulus of the soil
Ncq: for purely
cohesive soils, is function of the ratio of Df/B and the stability number Ns
where Ns=gH/c.
Ngq: for purely
granular soils, is function of the ratio of Df/B and the friction angle f of
soil.
Shallow
foundations: A foundation is
shallow when the depth Df of the foundation is less than or equal to the width
of the foundation. (It can be considered that foundations where Df equals 3-4
times the width of the foundation are also shallow foundations.)
Deep foundations:
Foundations where the depth is greater than 4 times the width are deep
Shear failure: The
shear strength of a soil mass is the internal resistance per unit area that the
soil mass can offer to resist failure and sliding along any plane inside it.
When sliding occurs along any plane inside the soil mass, then shear failure
takes place.
Settlement:
The deformation of soil under a certain applied load causes displacement in the
layers of soil. This deformation in the soil layer is called settlement.
Allowable bearing
capacity (qall): It
is the loading per
unit area that the soil is able to support without unsafe movement.
Strip/continuous
footing: A
strip footing is a footing where the width-to-length ratio approaches zero; an
infinitely long footing.
Terzaghi
(1883-1963):
A civil engineer who
founded the branch of civil engineering science known as soil mechanics, the
study of the properties of soil under stresses and under the action of water.
Water table level: the level at which the piezometric
head is equal to zero
Buoyancy force:
the vertical upward force
exerted on a body by a static fluid in which it is submerged or floating
General failure:
In the case of dense sand or stiff cohesive clay, when the applied load on the
footing is ultimate, sudden
failure occurs and the failure surface extends to the ground surface. This type
of failure is called general failure. In this type of failure, all points
forming the failure surface will have reached their peak value at the same time.
Local failure:
In the case of sand or clayey soil of medium
compaction, a further increase of
load (above ultimate) will be accompanied by a large increase of foundation settlement. The
failure surface will extend somewhere below the ground surface. Some of the points in
soil forming the failure surface will have already reached their peak value and
failed before others
Rough foundation
base: the
case in which the angle between the
foundation base and the sides of the triangular bulge is equal to the friction
angle of the soil (see figure 1.)
Smooth foundation base:
the case in which the angle between the foundation base and the sides of the
triangular bulge is equal to Φ/2 + 45 (see figure 1.) It has been experimentally
verified that this change in magnitude of the angle is more accurate and
representative of reality.
