w

4 downloads 126 Views 125KB Size Report
effective stress of soils, especially when. ○ S r of sand and soil is less than 20%; S r of clay is less than 85 .... (1998). ○ Volume change tests on expansive clays.
Consolidation Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University

z

z

Biot(1941) was the first person to suggest the volume and water content have a linear relationship with two independent stress variables Bishop(1959); Jennings and Burland(1962) found for most soils there is not a unique relationship between volume change and effective stress of soils, especially when z

Sr of sand and soil is less than 20%; Sr of clay is less than 85 - 90%

z

z

Bishop and Blight(1963): relationship between volume change and (σ – ua) and (ua – uw) Burland(1965): relationship between volume change and either (σ – ua) or (ua – uw) is independent

z

Volumetric strain based on Hooke’s law: 3  1 − 2µ  dε v = 3  d (σ mean − u a ) + d (u a − u w ) H  E 

dVv dε v = = Volumetric strain V σmean=(σx +σy +σz )/ 3= Mean effective stress E = Elastic modulus of soil μ= Poisson’s ratio H = Modulus of volume change due to matric suction

z

Change of water content can be separated from the volume change in the unsaturated soil: dVw d (u a − u w ) 3 d (σ mean − u a ) + = V0 Ew Hw Ew = Modulus of water related to (σ - ua) Hw = Volumetric modulus of water related to (ua – uw)

z

Relationship between volume change and water content:

de = at d (σ mean − ua ) + amd (ua − uw ) σ mean at =

Mean effective stress

∂e

∂ (σ mean − ua ) ∂e am = ∂ (u a − u w )

Coefficient of compressibility due to (σmean – ua) Coefficient of compressibility due to (ua– uw)

Change of water content

(

)

dw = bt d σ mean − ua + bm d (ua − uw ) bt =

∂w

∂ (σ mean − u a )

bm =

∂w

∂ (u a − u w )

Coefficient of change of water content due to (σmean – ua) Coefficient of change of water content due to (ua– uw)

z

The constitutive surface consists of volume change (or water content) and two stress variables has uniqueness z

z z

As long as the state of stress is the same, the volume or the water content will be the same, regardless of the stress path

The above statement has one prerequisite, it has to be monotonic deformation The deformation of unsaturated soil exhibits hysteresis characteristic

Uniqueness of continuity of the constitutive surface of the unsaturated soil

Fredlund (1993) z

z

z z z

Suggest a simple way to determine the four parameter of the constitutive surface: at, am, bt, bm: On the constitutive surface, we have the same deformation modulus under same e and w%, thus at can be obtained from the slope of e-(σ - ua) of 1-D consolidation test Æ at = av When fully saturated, e = Gsw, thus bt = at/Gs Get bm from slope of SWCC Get am from the slope of the e – w% curve of the shrinkage limit test Æ the slope = am/bm

z

Two conclusions from the 2-D constitutive surface: z

z

z

Effect of net applied stress (σ – ua) on the void ratio is greater than the effect of matric suction (ua – uw) Æ at > am Effect of matric suction on water content is greater than the effect of net applied stress Æ bm > bt

Thus: the volume change of soil depends on the net change of net applied stress; the change of water content depends on the matric suction

Matyas and Radhakrishna(1968) z z

z z

z

Observe the volume change of soil under isotropic loading Found lowering of matric suction caused the collapse of meta-stable soil Æ volume of soil decreased This was due to the lowering of the effective stress between the soil particles For soil with stable structure, the lowering of matric suction will lead to intake of water and increase of volume This proves the constitutive surface does not have uniqueness during the loading and unloading process

z

z

z

Fredlund et al(1975),Li and Selig(1994),Jin et al(1994),Phillip(1994),Drumm et al(1997),Oloo et al(1997) proves that the deformation modulus of soil increases when matric suction increases Alonso(1998) let specimens of compacted clay subject to wet/dry cycles Æ the volume change of specimens dry-of-optimum is less then that of the specimens wet-of-optimum All specimens dilate first and then compressed after taking in water under load

Bastos et al. (1998) z

z

Volume change tests on expansive clays under controlled suction Conclude that the deformation modulus of unsaturated soil is independent of the applied stress but instead dependent on the matric suction