3.2.1 In situ lateral stress
Horizontal（lateral）stress in soils is usually described and quantified by means of a lateral earth pressure coefficient，K：
where
p′v is the effective overburden pressure；
σ′h is the horizontal（lateral）effective stress at the same point within the soil mass.
The effective overburden pressure p′v is given by
where
γis the bulk density；
z is the depth below；
u is the pore water pressure；
q is any uniform surcharge at the ground surface.
Unlike some other retaining walls，embedded walls usually retain predominantly natural ground.So the pre⁃existing or in situ horizontal（lateral）earth pressure，as modified by wall installation，is potentially important.The symbol K0 is used to denote the earth pressure coefficient describing the initial in situ stress state in the ground before the wall is installed.
The in situ earth pressure coefficient may be of particular concern in a clay deposit，in which K0，like the specific volume，depends on the stress history.Deposition（or burial under a glacier）corresponds approximately to one⁃dimensional（1D）compression，during which the horizontal effective stressσ′h increases in proportion to the effective overburden pressure p′v.Clays may also become consolidated by desiccation（drying）on exposure to air，by vegetation or by freezing，where the effective stress is increased through a reduction in pore water pressure while the total stress remains constant，as shown in Figure 3.2.
Figure 3.2 Schematic stress history of an overconsolidated clay deposit
On unloading（e.g.due to the erosion of overlying soil，re⁃saturation after desiccation，the melting of an overlying glacier or a rise in groundwater level），the horizontal effective stress，σ′h，tends to remain“locked⁃in”，decreasing proportionately less quickly than the effective overburden pressure，p′v.So the in situ earth pressure coefficient K0 in an overconsolidated clay stratum is usually greater than unity.In heavily overconsolidated clays，a zone of soil extending to a depth of several meters from the surface maybe be close to its limiting passive pressure because of geological unloading.
The earth pressure coefficient in granular material or weak rock is not uniquely related to the stress history of the deposit as it is in clay.
In situ lateral earth pressure may be estimated using an equation of the form：
where
φ′is the drained angle of shearing resistance；
OCR is the over consolidation ratio；
βis the slope angle（to the horizontal）of the soil surface.
For normally consolidated deposit（OCR＝1）and level ground（β＝0），this reduces to Jaky's empirical formula K0＝（1－sinφ′）.