IN1ERNATIONAL CONFERENCE ON
RHEOLOGY AND SOIL MECHANICS
Edited Ьу
М. J. KEEDWELL
Coventry Polytechnic,
Coventry, UК
ELSEVIER APPLIED SCIENCE
LONDON and NEW YORK, 1988
194
CREEP AND AGEING EFFECTS ОН STRESSES AND
DEFORМATIONS OF SAТURAТED CLAYED SOILS
TRIFON GERМANOV
Dr Ph. Eng., Аssos. Professor
Secretary of the National Committee
for SMFE, University of Architecture
and Civil Engineering. 1421 Sofia,
Bulgaria
ABSTRACT
The investigations on one-dimensional time-dependent stress-strain
state of nearly saturated clayed soils are presented. Long lasting
tests are carried out with samples of different types of soils
under compression. Results from the tests in an open (drained)
system and а closed (undrained) system under constant
instantaneously applied loading are presented. А good agreement
between the experimental and theoretical results, obtained with the
use of the theory of linear creep and ageing is observed. The
following conclusions for clayed soil behavior are drawn: the
height of the soil sample (layer thickness) effects on the stressstrain state of clayed soils in an open system, change over time of
the pore pressure in а closed system, change over time of the
coefficient of earth pressure at rest.
INTRODUCTION
Clayed soils are found in almost all regions in Bulgaria.
Environment control, soil preservation, development of transport
and energetic induced the construction of important machinery and
equipment in regions with complex geological conditions, the
saturated clayed soils being among them. This is the reason why the
study and prognosis of the stress-strain state of the clayed
massifs used for foundations, medium or material for erecting
buildings and structures are of great importance for improving the
methods of designing the foundations. Unlike the other continuous
mono-phase deformable systems, the stress-strain state of the
clayed soils (as complex disperses multi-phased systems) varies
with the elapse of long periods of time. On the other hand, due to
differences in load intensity are distinguished two relative states
in clayed soils, namely sub-limited (when the existing stresses do
not exceed the shear strength), and limited, presented here are the
investigations related to the sub-limited stress state,
195
i.e., the compression phase. The behavior of nearly saturated soils
is examined, their deformations being accompanied by two
simultaneously rheological processes: filtration and creep of the
soil skeleton.
THEORETICAL CONDITIONS AND RESULTS
Multi-phased clayed soil which changes its stress-strain state over
time, subjected to vertical instantaneous loading is investigated.
It is supposed that, due to incomplete saturation, the fluid is
linearly deformable, while the deformations of the soil skeleton
are presented according to the theory of the linear creep. The
equation which describes the skeleton condition, according to [2,3]
acquires the following form:
θ (t )
t
1
e0 − e(t ) =
mv (t , t ) −
θ (τ )mv (t , t )dτ
1 + 2K 0
1 + K 0 ∫t1
(1)
where: е0 and e(t) are the initial and the variable over time voids
ratios Θ(t) is the sum of normal effective stresses at one point of
the soil massif; К0 is the coefficient of the lateral pressure at
rest; mv(t;t) is the generalized coefficient of volume deformation.
mv(t,τ) – m0(τ) + ϕ(t){1 – exp[-η(t-τ)]}
(2 )
where: m0(τ) is the coefficient of the instantaneous consolidation;
ϕ(t) is the function of ageing (tyxotropic strengthening) of the
soil skeleton.
ϕ (τ ) = ml +
mh
τ
(3)
where ml is the coefficient of creep (secondary) volume deformation;
η is the parameter of creeping speed; mh is the coefficient of the
"ageing" volume deformation of the soil skeleton; τ1 is the
parameter of the soil skeleton age (the prehistory of the stressed
condition).
Examining the pore water and air dissolved into the water as а
component which is deformed as а result of the bubbles compression
[13], the following equation is suggested:
1 ∂ρ w 1 − S r
=
= mw
pa
ρ w ∂u w
(4)
where: ρw is the water density; uw -the pore pressure (stress of the
pore liquid, or natural stress) mw - the coefficient of linear
volume deformation of the pore liquid; Sr – the degree of
saturation; pа - the atmospheric pressure.
196
Assuming that the fluid filtration in vertical direction
along axis z is in accordance with Darcy's law [13] in onedimensional stress state the equation of consolidation is, as
follows:
∂ 2u w
∂u w
∂ 3u w
∂ 2uw
+
f
(
t
)
=
β
+
χβ
v
0
0
∂t v
∂t v ∂ξ
∂t v2
∂ξ 2
(5)
where:
(1 + e0 ) K f
⎛
βh ⎞
Cv
H2
H2
z
⎜
⎟
f (t v ) = χ ⎜1 + β1 +
t
=
;
;
ν
=
;
;
χ
=
η
;
=
;
C
=
ξ
v
v
t v ⎟⎠
Cv
Cv
m0 γ w
H
H2
⎝
Ah
em
m
A1
m
1
; β1 =
; βh =
; Aw = 0 w ; A1 = 1 ; Ah = h ;
β0 =
Aw
1 + Aw
1 + Aw
m0
m0
m0
Н is the thickness of the examined layer; γw - the unit weight of
the water.
Equation (5) is solved in [10] according to the Fouier's
method with the help of confluent hypergeometrical functions.
The vertical deformations settlement in an one-dimensional
stress state (compression condition) can be defined by applying the
practical method cited in [13], under the condition that for each
moment the effective stresses will be defined according to the
Terzaghi’s principle, namely:
σ’(t,z) = σ – uw(t,z)
The solution of the equation (5) is given in [7].
(6)
Figure 1. Theoretical curves uw(t) in a closed system
197
Figure 2. Theoretica1 curves of the pore pre55ure coefficient
Кw(t) and for re1ative deformation ε(t) for different va1ues of
the parameter η .
The results, obtained by the theoretica1 solution of the pore
pressure coefficient Кw and the re1ative deformation e are
presented on Figure 2.
In а closed system (undrained condition) the pore pressure
function is determined from the fo11owing homogenous differentia1
equation:
⎛
ηβ ⎞
u w" (t n ) + ⎜⎜1 + β1 + h ⎟⎟.u w' (t n ) = 0
(7)
tn ⎠
⎝
where tn = η.t.
The solution of equation (7) is given in [6]. The graphics of
the function uw(t) in the closed system for different va1ues of the
"age" parameter are given on Figure 1.
With observing the princip1e of the effective pressures, the
equation for the horizonta1 stresses σx is:
σ x (t ) = u w (t ) + K 0' (σ z − u w (t ) )
In which K 0' =
σ
σ
'
x
'
z
(8)
is the coefficient of lateral pressure at
rest.
In (8), we accept that the coefficient of 1atera1 pressure of
the f1uid is of unit va1ue. Then, the coefficient of the 1atera1
pressure for near1y saturated c1ayed 50i15 wi11 change in
accordance with the fo11owing:
198
(
K 0 (t ) = K 0 + 1 − K 0' ) K w (t )
)
(9)
EXPERIMENTAL RESULTS
The one-dimensional stress state is examined by using а oedometer
with vertical deformable walls [4]. Cylindrical soil samples with
different heights (50 to 200 mm) can be tested by help of the
oedometer, simultaneously measuring the vertical deformations, the
pore pressure and the lateral pressure. The main parts of the
oedometer are shown on Figure 3. Using this apparatus continuous
compression tests may be carried out on different types of soils:
clay, loam (sandy clay), loess [9], silt [8], tailings [1] and
others.
Figure 3. Oedometer without friction along the circular area of the
sample: 1. Soil sample 2. Deformable walls (elastic gum cover and
light metal rings-meters of the lateral pressure) 3. Loading frame
4. Drainage tiles 5. Pore pressure meter 6. Vertical deformations
meters.
199
Figure 4. Experimental curves Кw(t) and
different heights of he soil samples.
ε(t) for а sandy clay with
Figure 5. Experimental curves Кw(t) and ε(t) for а clay with different
heights of he soil samples.
Figures 4 and 5 show the experimental curves of sandy clay and
clay soils with different heights of the soil sample. Similarity
can be observed in the theoretical and experimental dependences.
After а successful selection of the physical parameters according
to the method elaborated [5, 13] а good similarity between the
theoretical and experimental resu1ts has been observed.
The ana1ysis of the theoretica1 dependences and experirnenta1
200
resu1ts have confirmed the existence of an important inf1uence of
the 1ayer thickness upon the stress-strain state of saturated
c1ayed soi1s with creep and ageing characteristics. .
The ageing character [11, 13] is considered as being one of
the structura1 changes 1n the ageing materia1 (tyxotrop1c
strengthening of c1ayed soi1), which depend sole1y on some interna1
processes taking р1асе independent1y from the active pressures.
Th1s fact can exp1ain the decrease in the re1ative deformation for
d1fferen heights of the soi1 sarnp1es (layer thicknesses). The
increase in 1ayer height 1eads to an increase in the intensity of
the pore pressure and the time for its dispersa1 is consequent1y
a1so increased. This reduces the speed of the effective pressure
increase. The reduction in the effective pressure induces а
decrease in the speed of deformations. Simu1taneous1y, the soil
ske1eton is strengthened (ageing occurs) and the re1ative
deformation decreases. The greater the 1ayer height, the greater
the possibi1ity for increasing the contacts between the soi1
partic1es, which have been loosened at time of loading. This fact,
theoretica11y exp1ained [7] and [12], and confirmed experimenta11y
[7] 1s of principa1 importance for predicting the stress-strain
state of saturated soi1 massifs under natura1 conditions.
Figure б. Experimental curves uw(t) in а closed system
The experimental results under the conditions of а closed
system, presented on Figure 6, show that the stress state depends
on the elapse of time also. This problem is important when
calculating the stability of soil massifs subjected to short-time
static loading. In such cases, the initial values of the pore
pressure may be relatively lower, as compared to that in а
stabilized state. This means that the soil skeleton may bear the
greater part of the loading. Therefore, the shear strength of
clayed soil and its bearing capacity will increase.
201
Figure 7. Experimental curves K0(t) and Кw(t) for sandy clay in an
open system
Figure 8. Experimental curves K0(t) and Кw(t) for sandy clay in an
closed system
Figures 7 and 8 show the experimental results for the
coefficient of pore pressure Кw and the coefficient of lateral
pressure at rest К0 in an open system and in а closed system. It
can be seen that in the open system (with the presence of drainage)
the coefficient of lateral stress changes over time and the
graphics of K0(t) function is similar to that of Кwt), depending on
the height of the layer. In а closed system, the influence of time
upon К0 is less expressed.
The experimental results, shown on Figure 9 are also important
in the sense that they display that the inter-dependence between
full pressures σx = f(σz) is non linear, while function of
σ'x=f(σ'z) is linear in the effective pressure. This fact shows that
with lack of pore pressure during the process of compression one
can use the theory of linear-deformable, media in order to evaluate
202
the stress-strain state of the clayed soils.
Figure 9. Experimental curves e=f(σz), σx=f(σz) and σ'x=f(σ'z)
in a closed system
CONCLUSION
These experimental investigations conducted show the extreme
character of function uw(t) and the change of relative deformation
ε(t) proportional at the time logarithm at uw(t)→0. This can be
theoretically explained when taking into a count the nearly
saturation and the viscosities of the soil skeleton according to
the theory of linear creep. Thus are presented possibilities for
explaining the unstable stress state in а closed system and the
change over time in the coefficient of а lateral pressure at rest.
REFERENCES
[1]
Abadjiev, С.В., T.S. Germanov, G.T.Markov. Determination of
tailings consolidation for а high spigotted upstream
tailings dam. Proc.9th ECSFE,v.4.1, Dublin, 1987, рр 335-357
[2]
Arutjunjan, N.H. Some problems on the theory of creeping М.,
1952 (in Russian)
[3]
F1orin V.A. Soi1 Mechanics, vo1.II, М.,1961 (in Russian)
[4]
Germanov Т. Oedometer without 1atera1 friction. Patishta,
Sofia, 1978, рр 18-20 (in Bu1garian)
203
[5]
Germanov Т. La determination des pararnetres du f1uage dans
1es soi1s argi1eux. Annuaire de l' institut d' arcgitecture et
de genie civi1, vo1.27, Fasc.4, Sofia, 1978,рр 23-34 (in
Bu1garian)
[6]
Germanov Т. On the problem of bearing capacities of the soi1
base under short-timed static loading. Stroite1stvo No.7,
Sofia, 1978, рр 20-22 (in Bu1garian)
[7]
Germanov Т. Inf1uence of the rheo1ogica1 properties of the
soi1 ske1eton оп the deformations of rnu1tiphase с1ау soi1.
Technica1 Ideas, Bu1garian Academy of Sciences No.3, Sofia
1979, рр 69-74 (in Bu1garian)
[8]
Germanov Т. Z.Ter-Маrtirоsуаn. The inf1uence of the thickness
of compacted 1ayer on the stress and strain state of the
mu1ti-phase с1ау soi1s. Proc. 6th Danube European CSMFE,
vo1.2, Varna, 1980, рр 89-100
[9]
Gerrnanov Т. В. Kirov. Inf1uence of waste waters on soi1
consolidation. Proc. 12th ICSMFE, 9/С/7, San Francisco, 1985,
рр 2407-2408
[10] Germanov Т. One-dirnensiona1 conso1idation at the
alternuate 1imit of the 1ayer. Annuaire de l' Inst. d'arch. et
de genie civi1, vo1.32, Fasc.4, Sofia, 1986, рр 29-36 (in
Bu1garian)
[11] Rabotnov, Yu.N. Creep structure e1ernents. Science Publishing
House, Moscow, 1966 (in Bu1garian)
[12] Tsytovich, N.A., Z.G. Ter-Martirosyan, K.R. Ku1karni.
Conso1idation of time-hardening soi1. Proc. 4th Danube
European SCMFE, B1ed, 1974,рр 247-253
[13] Tsytovich, N.A., Z.G. Ter-Martirosyan. App1ied Geomechanics,
М., 1981 (in Russian)