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Effective Stress in the ground
When a load is applied to soil, it is carried by the water in the pores as well as the solid grains.
The increase in pressure within the porewater causes drainage (flow out of the soil), and the
load is transferred to the solid grains.
The rate of drainage depends on the permeability of the soil.
The strength and compressibility of the soil depend on the stresses within the solid granular
fabric. These are called effective stresses.
Use the menu on the left to navigate throught the notes and simple exercises on stress in the
ground.
Stress in the ground
Total stress Pore pressure Effective stress Calculating vertical stress in the ground
When a load is applied to soil, it is carried by the water in the pores as well as the solid grains. The increase in pressure within the porewater causes drainage (flow out of the soil), and the load is transferred to the solid grains. The rate of drainage depends on the permeabilityof the soil. The strength and compressibility of the soil depend on the stresses within the solid granular fabric. These are called effective stresses.
Total stress
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In a homogeneous soil mass In a soil mass below a river or lake In a multi-layered soil mass In a soil mass which is unsaturated In a soil mass with a surface surcharge load
The total vertical stress acting at a point below the ground surface is due to the weight of everything lying above: soil, water, and surface loading. Total stresses are calculated from the unit weight of the soil.
Unit weight ranges are:
dry soil (^) d 14 - 20 kN/m³ (average 17kN/m³)
saturated soil g 18 - 23 kN/m³ (average 20kN/m³)
water (^) w 9.81 kN/m³ (^) ( 10 kN/m³)
See Description and classification
Any change in vertical total stress (v) may also result in a change in the horizontal total stress
(h) at the same point. The relationships between vertical and horizontal stress are complex.
Total stress in homogeneous soil
total stress
Total stress increases with depth and with unit weight: Vertical total stress at depth z, v = .z Simple total stress calculator
z v 20 3 60 The symbol for total stress may also be written z, i.e. related to depth z. The unit weight, , will vary with the water content of the soil. d g
Total stress below a river or lake
total stress
The total stress is the sum of the weight of the soil up to the surface and the weight of water above this: Vertical total stress at depth z,
Just above the water table the soil will remain saturated due to capillarity, but at some distance
above the water table the soil will become unsaturated, with
a consequent reduction in unit weight (unsaturated unit
weight = u)
v = w. zw + g(z - zw)
The height above the water table up to which the soil will
remain saturated depends on the grain size.
See Negative pore pressure (suction).
Total stress with a surface surcharge load
total stress
The addition of a surface surcharge load will increase the total stresses below it. If the surcharge loading is extensively wide, the increase in vertical total stress below it may be considered constant with depth and equal to the magnitude of the surcharge. Vertical total stress at depth z, v = .z + q For narrow surcharges, e.g. under strip and pad foundations, the induced vertical total stresses will decrease both with depth and horizontal distance from the load. In such cases, it is necessary to use a suitable stress distribution theory - an example is Boussinesq's theory.
Pore pressure
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Groundwater and hydrostatic pressure Water table, phreatic surface Negative pore pressure (suction) Pore water and pore air pressure
The water in the pores of a soil is called porewater. The pressure within this porewater is called pore pressure (u). The magnitude of pore pressure depends on:
the depth below the water table the conditions of seepage flow
Groundwater and hydrostatic pressure
Pore pressure
Under hydrostatic conditions (no water flow) the pore pressure at a given point is given by the
hydrostatic pressure:
u = w .hw where hw = depth below water table or overlying water surface It is convenient to think of pore pressure represented by the column of water in an imaginary standpipe; the pressure just outside being equal to that inside.
Water table, phreatic surface Pore pressure
The natural static level of water in the ground is called the water table or the phreatic surface (or sometimes the groundwater level ). Under conditions of no seepage flow, the water table will be horizontal, as in the surface of a lake. The magnitude of the pore pressure at the water table is zero. Below the water table, pore pressures are positive. u = w .hw In conditions of steady-state or variable seepage flow, the calculation of pore pressures becomes more complex. See Groundwater
Negative pore pressure (suction)
Pore pressure
Below the water table, pore pressures are positive. In dry soil, the pore pressure is zero. Above the water table, when the soil is saturated, pore pressure will be negative. u = - w .hw
The height above the water table to which the soil is saturated is called the capillary rise , and
this depends on the grain size and type (and thus the size of pores):
· in coarse soils capillary rise is very small
· in silts it may be up to 2m
· in clays it can be over 20m
Ground movements and instabilities can be caused by changes in total stress (such as loading due to foundations or unloading due to excavations), but they can also be caused by changes in pore pressures (slopes can fail after rainfall increases the pore pressures).
In fact, it is the combined effect of total stress and pore pressure that controls soil behaviour such
as shear strength, compression and distortion. The difference between the total stress and the
pore pressure is called the effective stress:
effective stress = total stress - pore pressure
or ´ = - u
Note that the prime (dash mark ´ ) indicates effective stress.
Terzaghi's principle and equation
Effective stress
Karl Terzaghi was born in Vienna and subsequently became a professor of soil mechanics in the USA. He was the first person to propose the relationship for effective stress (in 1936):
All measurable effects of a change of stress, such as
compression, distortion and a change of shearing
resistance are due exclusively to changes in effective
stress. The effective stress ´ is related to total stress
and pore pressure by ´ = - u.
The adjective 'effective' is particularly apt, because it is effective stress that is effective in causing
important changes: changes in strength, changes in volume, changes in shape. It does not
represent the exact contact stress between particles but the distribution of load carried by the soil
over the area considered.
Mohr circles for total and effective stress Effective stress
Mohr circles can be drawn for both total and effective stress. The points E and T represent the
total and effective stresses on the same plane. The two circles are displaced along the normal
stress axis by the amount of pore pressure ( n = n' + u) , and their diameters are the same. The
total and effective shear stresses are equal ( ´ = ).
The importance of effective stress
Effective stress
The principle of effective stress is fundamentally important in soil mechanics. It must be treated as the basic axiom, since soil behaviour is governed by it. Total and effective stresses must be distinguishable in all calculations: algebraically the prime should indicate effective stress, e.g. ´
Changes in water level below ground (water table changes) result in changes in effective stresses
below the water table. Changes in water level above ground (e.g. in lakes, rivers, etc.) do not
cause changes in effective stresses in the ground below.
Changes in effective stress Effective stress
Changes in strength Changes in volume
In some analyses it is better to work in changes of quantity, rather than in absolute quantities; the effective stress expression then becomes: ´ = - u
If both total stress and pore pressure change by the same amount, the effective stress remains
constant. A change in effective stress will cause: a change in strength and a change in volume.
Changes in strength
Changes in effective stress
The critical shear strength of soil is proportional to the effective normal stress; thus, a change in effective stress brings about a change in strength.
Therefore, if the pore pressure in a soil slope increases, effective stresses will be reduced by '
and the critical strength of the soil will be reduced by - sometimes leading to failure.
Vertical total stress v = 32.0 + 20.0 x 3.0 = 92.0 kPa
Pore pressure u = 9.81 x 3.0 = 29.4 kPa
Vertical effective stress ´v = v - u = 92.0 - 29.4 = 62.6 kPa
Effect of changing water table
Calculation of vertical stress
The figure shows soil layers on a site. The unit weight of the silty sand is 19.0 kN/m³ both above and below the water table. The water level is presently at the surface of the silty sand, it may drop or it may rise. The following calculations show the effects of this:
Water table
Stresses under foundations
Calculation of vertical stress
From an initial state, the stresses under a foundation are first changed by excavation, i.e. vertical
stresses are reduced. After construction the foundation loading increases stresses. Other changes
could result if the water table level changed.
The figure shows the elevation of a foundation to be constructed in a homogeneous soil. The
change in thickness of the clay layer is to be calculated and so the initial and final effective
stresses are required at the mid-depth of the clay.
Unit weights: sand above WT = 16 kN/m³, sand below WT = 20 kN/m³, clay = 18 kN/m³.
Calculations for initial stresses final stresses
Calculation of vertical stress
Short-term and long-term stresses
Initially, before construction Immediately after construction Many years after construction
The figure shows how an extensive layer of fill will be placed on a certain site.
The unit weights are: clay and sand = 20kN/m³ , rolled fill 18kN/m³ , assume water = 10 kN/m³. Calculations are made for the total and effective stress at the mid-depth of the sand and the mid-depth of the clay for the following conditions: initially, before construction; immediately after construction; many years after construction.
Short-term and long-term stresses
Initially, before construction
Initial stresses at mid-depth of clay (z = 2.0m)
Vertical total stress
v = 20.0 x 2.0 = 40.0kPa
Pore pressure
u = 10 x 2.0 = 20.0kPa
Vertical effective stress
´v = v - u = 20.0kPa
Many years after construction
Short-term and long-term stresses
After many years, the excess pore pressures in the clay will have dissipated. The pore pressures
will now be the same as they were initially.
Initial stresses at mid-depth of clay (z = 2.0 m)
Vertical total stress
v = 20.0 x 2.0 + 72.0 = 112.0 kPa
Pore pressure
u = 10 x 2.0 = 20.0 kPa
Vertical effective stress
´v = v - u = 92.0 kPa
(i.e. a long-term increase)
Initial stresses at mid-depth of sand (z = 5.0 m)
Vertical total stress
v = 20.0 x 5.0 + 72.0 = 172.0 kPa
Pore pressure
u = 10 x 5.0 = 50.0 kPa
Vertical effective stress
´v = v - u = 122.0 kPa
(i.e. no further change)
Steady-state seepage conditions Calculation of vertical stress
The figure shows seepage occurring around embedded sheet piling.
In steady state, the hydraulic gradient,
i = / = 4 / ( 7 + 3 ) = 0.
Then the effective stresses are:
´A = 20 x 3 - 2 x 10 + 0.4 x 10 = 44 kPa
´B = 20 x 3 - 2 x 10 - 0.4 x 10 = 36 kPa
