8 Retaining structures and basement stability
8.15 Earth pressures
8.15.1 General
The determination of earth pressure involves consideration of both ground and groundwater with the method of interpretation varying according to whether undrained or drained conditions are being considered. It also includes consideration of appropriate limit modes (see Section 8.16), and associated movement and strain. The following information on earth pressures is based on soils; however, it can also be applied to soft and weathered or strong and highly fractured rocks which can be modelled in terms of soil parameters (c0and w0parameters).
Calculating the magnitude of earth pressures and the directions of resulting forces includes consideration of:
– surcharges and ground surface slope – wall inclination to the vertical
– water tables and groundwater seepage forces
– wall movement relative to the ground (mobilisation of friction between wall and supported/supporting ground)
– horizontal and vertical equilibrium of the wall
– ground properties (shear strength, unit weight, swelling potential and rock fabric/discontinuities)
– passive side softening and disturbance – wall and support stiffness
– wall roughness – shape of failure surface
– selected limit state (i.e. SLS or ULS)
– initial ground conditions and structural stiffness
– allowable wall and supported ground deformation at SLS.
The degree to which wall friction, sntan d, and/or adhesion a is mobilised should be considered in terms of:
– ground strength
– friction properties of the wall-ground interface – wall movement relative to the ground – capacity of wall to support vertical forces.
The mobilised shear strength t can be calculated as follows:
t ¼ sntan d þ a where:
sn is the normal stress on wall
a is the adhesion (a function of c0or cu; a ¼ 0 may be appropriate when using wcv)
d is the angle of shearing resistance at wall-ground interface (dd¼design value)
The following values for dd/wcv;dare given in EC7 Part 11: 0.667 (concrete panel or steel in sand or gravel)
1.0 (concrete cast against soil)
0.0 (steel sheet pile in clay under undrained conditions immediately after driving).
wcv is the critical state angle of shearing resistance (wcv;d¼design value) Whilst the prescribed use of wcvmay be logical given its relationship to f0and ultimate limit states, obtaining its value from standard laboratory testing is not easy. However, some guidance is given in Section 4.8 of PD 669434and in Section 2.2 of BS 800230along with example values.
8.15.2 At-rest earth pressure – K0
The at-rest earth pressure, taking account of stress history, is used when there is no movement of a wall relative to the ground. For normally
consolidated soil, at-rest conditions are normally assumed for movement of less than 0.0005 times the height of the wall.
There are several similar equations for calculation of K0, the suggested equation in EC7 is as follows:
K0¼(1 – sin w0)(1 þ sin b) ffiffiffiffiffiffi OCR p
where:
w0 is the angle of shearing resistance
b is the upwards slope angle of ground behind the wall (0 b w0) OCR is the over-consolidation ratio (it should be noted that the equation is
not appropriate for very high OCR values).
The resulting force is parallel to the ground surface.
CIRIA C58035presents details of assessment of K0for stiff over-consolidated clays along with suggestions of how wall installation modifies K0prior to the excavation phase of construction.
8.15.3 Intermediate earth pressure
If there is insufficient movement to mobilise the active or passive limits, intermediate values of earth pressure will occur. This should be considered to occur when, for example, struts, anchorages or similar elements restrain the movement of a retaining structure. The magnitude of movement required to mobilise the active and passive limits is presented in Section 8.7. Intermediate values of earth pressure may be determined using these movements and linear interpolation for active earth pressure or parabolic interpolation for passive earth pressure. Alternatively empirical rules, spring constant methods or finite element methods could be used to calculate appropriate active and passive side earth pressures based on wall movement and structural stiffnesses (wall and propping stiffnesses).
8.15.4 Limit earth pressures – Kaand Kp
The active and passive limit values of earth pressure on a vertical wall can be calculated as follows:
sa(z) ¼ Ka(g z þ q u) þ u c Kac
sp(z) ¼ Kp(g z þ q u) þ u þ c Kpc
where:
sa(z) is the stress normal to the wall at depth z (active earth pressure) sp(z) is the stress normal to the wall at depth z (passive earth pressure)
Ka is the coefficient of active earth pressure Kp is the coefficient of passive earth pressure g is the unit weight of ground
z is the depth
q is the surface surcharge u is the pore-water pressure
c is the cohesion of ground (c0drained, cuundrained)
Kac is the is the active earth pressure coefficient to model soil cohesion Kpc is the passive earth pressure coefficient to model soil cohesion
Kac¼min 2
For retaining walls the adhesion a is usually taken to be equal to 0kN/m2for drained analysis. For undrained analysis (temporary conditions in clays) the value of adhesion a is usually taken to be 0.5cu;dto allow for disturbance during wall installation35.
For drained soil Kaand Kpare functions of w0, d, b and u (angle of wall back from vertical) whereas for undrained conditions, Ka¼Kp¼1.
Figures 8.2a–8.2d1provide the horizontal component of Kaand Kpfor two common situations:
b ¼0, u ¼ 0, 0 d/w01.0 b .0, d/w0¼0.66, u ¼ 0
Relatively highly fractured or soft rock can potentially be modelled in terms of w0and c0using soil models. In relatively massive/hard rock where joint/
discontinuity orientation and spacing dominate, soil models are often not appropriate for use in retaining wall design; it is, however, possible to derive equivalent Kaand Kpparameters from rock mass parameters when rock mass structure is not aligned to active and passive failure surfaces.
Specialist advice should be sought where retention of rock masses is being considered.
In soft/normally consolidated soils it should be recognised that the active pressure on the back of a retaining wall may exceed the passive pressure on the front of a retaining wall for a significant depth below excavation level. This can lead to structural resistance and deformation issues which may require the installation of cross panels or jet grouting to limit wall depth and ground movements. Specialist advice should be sought in this situation. See also Brand and Brenner100.
8.15.5 Compaction pressures
Earth pressures behind a wall are to include pressures resulting from the placing and method of compaction of backfill. Appropriate compaction procedures and plant need to be specified by the designer with the aim of avoiding excessive additional earth pressures.
As a part of design it is necessary to state the compaction plant that has been allowed for in the design. This information must be included in construction information as it is related to safe construction of the wall (CDM issue, see Section 10.2).
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3
0.2 Horizontal component Ka
0.1
5° 10° 15° 20° 25° 30° 35° 40° 45°
ϕ′
δ/ϕ′ = 0 δ/ϕ′ = 0.66 δ/ϕ′ = 1.0 β = 0
Horizontal surface β = 0
δ > 0
Fig 8.2a Kachart – horizontal surface, d/w0variable (after Annex C EC7 Part 1)