The Concept of Effective Stress For Soil, Concrete and Rock
February 4, 2023 | Author: Anonymous | Category: N/A
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(σcell u ) (∆σcell ∆u ), ), u constant
(σcell u ), ), u
Initial condition
(a)
Linear compression of grains ⇒ volumetric compression of skeleton
∆V sks C sksV 0(∆σcell ∆u )
(σcell u ), ), u
Volumetric compression of grains (unless νgrains 0.5) ∆V gs C gsV 0(∆σcell ∆u )
(σcell u ) constant, u ∆u
Initial condition: grains in contact
∆V gu
(1 n )V 0C gu∆u
∆V sku V 0C sku∆u
(b1)
For grains in contact: (1 n )C gu C sku
(σcell u ) constant, u ∆u
(σcell u ), ), u
Solid rock with interconnected pores: `grains´ compress, but little compression of skeleton (1 n )C gu C sku
⇒
(b2) u
Initial condition
u ∆u
∆V w C wnV 0S ∆u and and S ∆V a nV 0 1 ∆ u u 2
(c)
Dial gauge
σcell
To volume change and cell pressure measuring device
3.2mm stainless steel pin
Water saturated cell
6.4mm stainl stainless ess steel cell wall
Stainless steel cap (and base)
0.6mm thick latex rubber membrane
1mm thick stainless steel plates cover holes on 4 sides of cube specimen
To volume change and pore pressure measuring device
σcell
∆V skeleton
u
∆V specimen
For incompressible grains: ∆V specimen ∆V skeleton (circular grains maintain their volumes) For compressible grains: ∆V grains ∆V skeleton ∆V specimen (circular grains compress into square grains)
described by C sks
∆V skel
B
Balsawood cube V 0 203.2cm 3 n 0.436
200
) : u
39
l l e c σ
0
74 0
B
39
39 73 106
141
described by C sku
108
39
100
141 0
110
(
178
141
74
0 0
74 108
1.045
106
141
108
B
141
1.038
B 1.000
a P k
73 39
V 0(∆σcell ∆u )
∆V skel
0
V 0∆u
0
74
1.015
0
0 0
1
2
3 ∆V skel:
4
5
cm3
described by C gs
∆V grains
V 0(∆σcell ∆u )
200 202 . B 1 038
. B 1 000 a P k : u
described by C gu
169
239
201
203
134
236
. B 1 045 135
66 135
Values of (σcell u): kPa are 202
170 B
Balsawood cube V 0 203.2 cm3 n 0.436
203
169 100
(1 n )V 0∆u
169
135
100
∆V grains
1.015
203
235
given at discrete points
236
100 69
73
105
242
0 0
1
2 ∆V grains:
3
cm3
C (vol/vol (vol/vol
per kPa) C w
15 105
5 105 ) a P k r e p l o v / l o v (
Balsawood cube
10 105
(a)
C
Basswood cube
4 105
Max. pressure
Measured during unloading
(a)
3 105 2 105 Cgu Cgs Csku
C sks
5 10
0.048 105
Csks
1 105 0 0
C w 0.048 105
5
100
200 300 400 (σcell u ): ): kPa
500
600
B
Measured
1.1
C gu
Calculated
C sku
1.0
C gs
0.9
0 0
100 (σcell u ): ): kPa
B
1.10
(b)
200
0.8
Measured . Calculatedin(B 0 996 all cases)
(b)
0.7
1.00
a P k 10 r e p l o v / l o v : u
(a) Balsawood cube
g
C ) n
C sku(
5 105
) = (1 n )C gu(
)
1 (
u k s
C
0 a P k r e p l o v / l o v : u g
C ) n
0
u k s
100
200
(σcell u ): ): kPa Measured during unloading (b) Basswood cube Max. pressure
1 105
(1 n )C sku C sku
1 (
C
105
0 0
100
200
300
400
(σcell u ): ):
500
600
kPa
1
0. 8
e , o i t a r
d i o V
0. 6
0. 4
Quartz sand 0. 2
Gypsum sand (a) Separ Separate ate grains with contact points
Gradual transition
(b) Solid rock with interconnected pores
0
0.1
1
10
100
1,000
10,000
Vertical stress: MPa
0.98 η
.
, 0 96 r o t c . a0 94 F
Dam foundations and abutments, tunnel linings, mine shafts
0.92 0.9
Deep wells, mine pillars 0
20
40 60 Vertical stress: MPa
80
100
1
0.8
η
Quartz sand
0.6
, r o t c a F 0.4
Pile foundations, points of concentration in mine pillars Gypsum sand explosives,, Conventional and nuclear explosives deep focus earthquakes
Gypsum sand 0
0.9 ) n
Quartz sand
−
0.6
0
200
400 600 Vertical stress: MPa
800
1000
a 0.006
P k / 1 : 0.005 y t i l i b . i s 0 004 s e r p . 0 003 m o c n 0.002 o t e l e k 0.001 S
0.06
a P k / . 1 0 05 : y t i l . i b 0 04 i s s e r 0.03 p m o c . 0 02 n o t e . l e 0 01 k S
0
0 0
0
200
400 600 Vertical stress: MPa
800
1,000
1 ( 0.8 : n o i t c a r f 0.7 d i l o S
0.5
1
0.2 1
Quartz sand 200 400 600 Vertical stress: MPa
800
1,000
Gypsum sand 0
200
400 600 800 Vertical stress: MPa
1,000
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