Lecture No.11

Consolidation of soils I:

Principle of effective stress

（土の圧密 I: 有効応力の原理）

■ Consolidation （圧密） and ground settlement （地盤沈下） 1

Differential settlement （不同沈下）

When soil is compressed （圧縮）…

① Soil particles and substances in the pores (water, air, etc.) shrink. （土粒子・間隙物質の圧縮）

② Substances in the pores are ejected. ←

（間隙物質の排出）

Original volume

Volume

reduction

Water, air,

etc. are

ejected

Compressive

stress

■ Consolidation （圧密） 2

The two mechanisms

① Soil particles and substances in the pores (water, air, etc.) shrink.

② Substances in the pores are ejected.

Compressibility （圧縮性） of water is very low:

The bulk modulus （体積圧縮係数） of water at 20oC is 2200 MPa.

i.e. If 1m3 of water descend to 100m deep, it becomes 0.99996m3

■ Consolidation （圧密） 3

The framework composed of soil particles:

When compression of soil particles and water

can be ignored （土粒子と水の圧縮が無視できるとき）:

Consider stress on this plane

(Area: A). （この仮想断面において応力を考える）

① Sum of forces by soil particles: F'

（土粒子による力）

② Force by pore water pressure, u: uA

（間隙水圧uによる力）

Total force:

Total stress:

s : Total stress （全応力）

s' : Effective stress （有効応力） u : Pore water pressure

（間隙水圧）

F

■ Effective stress （有効応力） 4

Total force

Principle of effective stress （有効応力の原理）

By Karl Terzaghi （テルツァギ）

Deformation of soil skeleton is solely described

by changes in effective stress. （土骨格の変形は有効応力の変化のみにより記述される）

■ Principle of effective stress （有効応力と土の変形） 5

Soil

Total stress：s =100 kN/m2

Pore water pressure： u = 40 kN/m2

① If total stress increases, with constant pore water pressure:

Effective stress increases

② If total stress is constant, with pore water increasing:

Effective stress decreases

③ If total stress and pore water pressure increase by same amount:

No change in effective stress

■ Example 6

Depth z

Example 1:

Ground water level （地下水位）

= Surface level （地表面）

(Vertical) total stress:

sv =

Pore water pressure:

u =

(Vertical) effective stress:

sv' =

g ' = gsat – gw : Submerged unit weight （水中単位体積重量）

sv u

■ Vertical effective stress profile （鉛直有効応力の分布） 7

Depth z

gsat

Example 2:

Ground water level （地下水位）

< Surface level （地表面）

gw

(Vertical) total stress :

sv =

Pore water pressure:

u =

(Vertical) effective stress :

sv' =

sv'

sv u

zgwl

Unsaturated:

s' undefined （不飽和帯： s' は定義されず）

■ Vertical effective stress profile （鉛直有効応力の分布） 8

■ Soil skeleton compression and effective stress 9

e

log sv'

A B

C D

E

F

e

sv'

A B

C D

E

F

Semi-log scale

Is commonly used

• Bi-linear, elasto-plastic （弾塑性） behaviour

注） 教科書ではsv'の代わりにpを用いている

■ Soil skeleton compression and effective stress 10

e

log sv'

A B

C D

E

F

① On NCL

② Left of NCL

③ Right of NCL

■ Compressibility of soil skeleton （土骨格の圧縮性）

Cs

e

log sv'

A B

C D

E

F

1

Cc

1

11

Defined in semi-logarithmic scale

Larger Cc

More compressible

Similarly,

Another expression of compressibility:

DV = DVv （negative）

（Dev：Vertical strain, positive in compression)

（圧縮を正と定義）

V0

Vs

Vv0 Vv

■ Compressibility of soil skeleton （土骨格の圧縮性） 12