Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
06&RUHSRUW
Limit states (stability, deformation, erosion…)
T.Germanov,
Professor, Department of Geotechnics, University of Architecture, Civil Engineering & Geodesy, Sofia:
germanov_fte@uacg.bg
KEYWORDS: pore pressure, liquefaction, ultimate limit state, time-depending settlement
ABSTRACT: Methods for limit states evaluation of tailings dams and other deposits containing waste
granular material are considered. The influence of the pore water pressure on the stability of saturated
deposits is evaluated. Some results from computations for liquefaction potential evaluation of tailings
dam, ultimate limit state analysis of a slime pond and time-settlement prognosis of an oxidative pond
are presented.
1 INTRODUCTION
The stability of waste deposits, such as tailings dam, landfill, waste banks and other depends on the
mechanical properties of the waste materials and the shape of the deposit’s body. The basic principles
of soil mechanics are usually used for the purpose. On the other hand, the materials included in the
waste deposits often have an unusual behavior, different from natural soils. This circumstance requires
a comprehensive program for laboratory and in situ study for determination of the real mechanical
properties of the waste materials.
The author has an unpretending experience in the field of some special problems of geotechnical
engineering related with the stress-strain behavior analysis of saturated soil massifs. On this base, a
short review of the general methods for stability analysis and some results from the design of real
projects are presented below.
Examining the proceedings of the last International conferences on environmental geotechnics,
many reports related to the subject of this paper could be found. Each one of the papers considers a
specific situation related to a separate waste deposit. Summarizing the problems, related to the stability
of waste deposits, the following limit states could be considered (Vanicec, 1998, Jessberger & Kockel,
1995):
• slope stability analysis,
• bearing capacity,
• subgrade settlement and differential surface settlement,
• erosion (internal and surface).
The slope stability analysis is very important problem, mainly for the tailings dams and landfills,
where a slope failure under gravity and filtration efforts is possible. Depending on the type of the
project, different design methods are used. If the type of the slip surface is accepted, conventional
(based on the Bishop, Jnbu or Spencer principles) methods could be applied.
Erosion is important problem in the case of tailings, ash or other dams built up of fine-grained
materials where, after raining, a surface slope failure is possible.
The most parts of the industrial waste deposits are in water-saturated conditions. By this reason, the
effect of the pore water pressure should be taken into account evaluating the deposit stability. The pore
water pressure influences the stress-strain behavior, changing the values of the effective stresses over
the time. The variation of the pore water pressure over time depends on many factors such as
permeability, geometry of the waste deposit’s body, mechanical properties of the materials and others.
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Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
In the case of tailings, slimes and other fine grained materials, the rheological properties of the
deposited materials have great effect on the pore water pressure.
The results presented in the other papers (Abadjiev, Germanov, Markov, 1987, Germanov, 2003),
showed an essential part of the creeping settlement on the tailings and slimes materials. That’s why,
the effect of the creeping properties on the stress-strain-time behavior should be determined.
The increasing of the pore water pressure under static and dynamic (seismic) excitation loads may
lead to decrease the effective stresses to zero. This phenomenon, known as liquefaction, may provoke
a loss of the bearing capacity and failure of the soil massifs.
Further, the problems of the limit state are analyzed describing some design works related to the
projects considered in the other paper presented from the author at the Conference (Germanov, 2003).
The effect of the pore water pressure on the stress-strain-time behavior of the “Liuliakovitsa” tailings
dam, “Blue Lagoon” and the oxidative pond near Burgas is analyzed
2 THE EFFECT OF THE PORE WATER PRESSURE ON THE LIMIT STATES
2.1 Basic constitutive equations for the pore water pressure evaluation
Following Germanov (2000), the massifs of saturated waste materials could be considered as multiphase medium and their stress-strain behavior being accompanied by two simultaneous, rheological
processes: filtration and creeping. It is assumed that the deformation of the soil skeleton could be
presented according to the theory of linear creep by the equation:
e0 − e(t ) =
θ (t )
1 + 2K 0
t
m v (t , t ) −
1
θ (τ )mv (t ,τ )dτ ;
1 + K 0 τ∫1
(1)
where: e0 and e(t) are the initial and variable over time void ratios;
θ(t) is the sum of normal effective stresses at a fixed point of the soil massifs;
K0 is the coefficient of the lateral pressure at rest;
mv(t,τ) is the generalized coefficient of volume strain.
mv (t ,τ ) = m0 (τ ) + ϕ (τ ){1 − exp[−η (t − τ )]};
(2)
m0(τ) is the coefficient of instantaneous strain (linear compressibility);
ϕ(τ) is the function of ageing (tixotropic strengthening) of the soil skeleton.
ϕ (τ ) = ml +
mh
τ
;
(3)
ml is the coefficient of volume creep strain (secondary compression);
η - the parameter of creeping speed;
mh - the coefficient of "ageing" strain of the soil skeleton;
τ1 - the parameter of the soil skeleton age (the previous stressed condition).
The methods for determining the coefficients of volume strains and the creep parameters are
developed by the author (see Germanov 2000).
Assuming that the fluid filtration is according to Darcy's law, the function uw(t,x,y) for twodimensional consolidation, is determined by the solution of the following differential equation:
a1
∂ 2u w
∂u w
∂
∂
∂2
+
f
(
t
)
=
C
[(
∆
u
)
−
η
∆
u
]
−
f
(
t
)
θ
(
t
)
−
a
θ 1 (t ) ,
1
v
w
w
2
1
2
∂t
∂t
∂t
∂t
∂t 2
Main Session 1 "Man-made deposits - recent and ancient"
(4)
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Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
where:
θ1(t) = σy(t) + σz(t);
σy(t) and σz(t) are the total normal stresses which would be accepted: constant, when the period of
operation is considered; variation with a constant velocity for the construction period; variation under
cyclic loads (machine foundations or earthquake motions).
The other coefficients and functions in (4) depend on the soil properties.
The author has received an exact solution of the one-dimensional consolidation, under
corresponding initials and boundaries conditions, according to equation (4) (Germanov, 1988). Using
the finite element method, the two-dimensional consolidation has been solved (Germanov, 2000).
2.2 Liquefaction potential evaluation of a tailings dam
100
80
60
40
20
0
1.000
0.100
0.010
Percent finer by weight (% )
Liquefaction is a phenomenon in which the strength and stiffness of a soil is reduced by earthquake
shaking or other rapid loading. The phenomenon is only generally considered for sandy soils and
usually for loose sands. However, the increase of the pore pressure could reduce the effective pressure,
not only in fine-grained soils and coarse-grained soils. It was established that clay or silt with low
plasticity index, such as tailings material, has been found to be as vulnerable to liquefaction (Ishihara,
1985).
One of the criteria for liquefaction potential evaluation is the grain size distribution. The results of
the laboratory investigation of the tailings materials from “Liuliakowitsa” tailings dam shows that the
investigated tailings could be classified as fine silty sand. The representative grain-size distribution
curves are shown in Figure 1. It can be seen that the grain size curves belong to the boundaries of the
most liquefable soils (Ishihara, 1985). This means that in some conditions, tailings could reach to a
state of liquefaction.
0.001
Diameter ( mm)
Figure 1. Representative grain size distribution curves for tailings taken from different depths
A great number of practical and theoretical methods for liquefaction potential evaluation of sand
deposits during earthquakes have been developed. The methods based on the in-situ and laboratories
testing as more reliable are considered.
An approximate method based on theoretical evaluation of the increase of pore water pressure in
tailings dam’s body during an earthquake is applied herein. Following Martin & Seed (1978), the basic
assumption for pore pressure generation and dissipation analysis is that the excess pore water pressure,
uw, in a soil element, could be presented as the sum of the pore water pressure under static loading,
uw,st , and pore water pressure increment generated under dynamic excitation - uw,d.
The static pore water pressure uw,st could be computed by using a computer program, developed by
the author (Germanov, 2000), based on the constitutive equations (1), (2) and (3). The dynamic pore
water pressure is computed, considering the tailings dam, under cycling loading, in undrained
conditions, by using the expression (Martin & Seed 1978):
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Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
u w, d
N
2
= σ 0' . arcsin
π
 Nl
1
 2α
 ,

(5)
where: σ'0 is the effective overburden pressure; N – the number of uniform stress cycles undergone
by the soil element; Nl – the number of cycles at the same levels required to reach initial liquefaction.
The computations are performed, applying nonlinear experimental relations of the physical and
consolidation characteristics and expressing their variation with the dam height. A cross section of the
tailings dam is presented in Figure 2 (Kalchev, 2003).
Figure 2. Cross-section of the “Liuliakovitsa” tailings dam
140
140
120
120
100
Height, m
Height, m
The number of cycles are accepted: N = 12 for an earthquake with magnitude equal to 7; Nl =50,
according to Germanov & Kostov (1994). The computations for static conditions show that there are
no differences between theoretical and in-situ measured values of the pore water pressure. The
distribution of the pore water pressure at the dam height is presented in Figure 3.
80
60
uw,st
40
100
80
60
40
20
u w, d
0
0
200
20
400
600
800
1000
Pore pressure, kPa
0
0.00
0.20
0.40
0.60
0.80
1.00
Pore pressure ratio uw/σ 'v
Figure 3. Variation of the pore water pressure with the tailings dam height
The maximum value of pore pressure ratio uw/σ'0 reaches 0.8. It is obviously, under the stress strain
conditions, that there is no area in tailings dam, which would be susceptible to liquefaction.
2.3 Evaluation of the ultimate stress strain state of the slime pond during encapsulation
One of the variants of the project for encapsulation of the slime pond “Blue Lagoon” considers
establishment of drainage wells and filling the pond with granular materials as well as construction of
embankment 8m high.
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Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
Another variant without vertical drainage is considered as well. It is supposed that after dewatering
the filling will be made approximate by constant speed.
For evaluation of ultimate stress-strain state the Mohr-Coulomb equation for ultimate equilibrium
could be used (Germanov, 1986, 2000). Considering the slime pond in unconsolidated conditions
under embankment’s loads, the dimensions of the so-called "plastic zones" could be evaluated by
using the expression:
θ cr = arcsin
(σ
'
z
− σ y'
)
2
+ 4τ zy2
σ z' + σ y' + 2c ' cot gϕ '
,
(6)
where, σ′z, σ′y and τzy, are effective normal and tangential stresses in a given point of the slime
pond.
The zones of ultimate equilibrium are defined by the condition θcr > ϕ' (ϕ'- effective angle of
internal friction). If these zones are relatively large, the subgrade (slime pond) will lost its overall
stability.
A computer program for ultimate stress-strain behavior evaluation of saturated soil massifs, taking
into account of the pore water pressure generation and dissipation during construction and operation
has been developed by the author (Germanov, 1986).
Some results from computations are given in Table.1. Two loading steps are considered: q=80 kPa
and q=160kPa, corresponding to 4.0 m and 8.0 m embankment fill respectively. All computations are
performed by using input data (geotechnical characteristics), according to Germanov (2003).
Table 1. θcr values for different depts.
Z
θcr (degree)
(m)
for q = 80 kPa
1.
2
15
2.
4
12
3.
6
10
4.
8
9
5.
10
8
6.
12
7
θcr (degree)
for q = 160 kPa
25
21
18
15
14
12
For this case (ϕ' = 180), the plastic zone could be formed to 6.0m depth at the final stage of loading.
Only small part of the computations are given here, which demonstrate the possibility to applying
the theory of consolidation of multi-phase soils, for ultimate stress-strain state evaluation in a nonconsolidated condition.
2.4 Determination of the time-depending settlement of the oxidative pond
The first stage of the project for encapsulation and remediation of the oxidative pond near the town of
Burgas, proposes a filling the pond by granular material over geotextile.
The results of the consolidation tests (Germanov, 2003) show some specific features of the
petroleum refuses which considerably distinguish them from natural soils. First of all, the test results
show a very low value of densities and very large porosity (ρn ≈1.0; e = 8.0 ÷10.0). Water content
reaches 500 – 600%. On the other hand, during the consolidation tests, the settlements are developing
very slowly over time under small loading. The great part of the secondary consolidation presumes the
presence of rheological processes.
In order то receive a preliminary prognosis of time-depending settlement, a computation was
performed for the subgrade (i.e. petroleum refuses) under loading from embankment 2.0m high. It is
accepted that the construction works (time of filling) will last six months. The degree of consolidation
at the end of construction period and during “operation” after one, two and five years is computed.
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Proc. XIII ECSMGE, Vaníček et al. (eds). © ČGtS, Prague, ISBN 80-86769-02-X, (Vol. 3)
The results presented in Table 2 show a low value of the degree of consolidation at the end of
filling. With respect to the homogeneous composition of the petroleum refuses, the computations
showed an approximately equal degree of consolidation at the end of the different periods. An increase
of the degree of consolidation could be reached by increasing the construction period (time of filling).
On the other hand, under this loading, in spite of the low values of the deformation modulus, the final
settlements are comparatively small – from 25cm to 78 cm. Increasing the final settlements could be
possible by means of additional loads, which, after reaching the predicted settlement, should be
removed. The great value of water content supposed compression under static loading only. The
influence of the dynamic loading (for example vibrations) on such type of refuse materials needs an
additional study.
Table 2. Final settlement and degree of consolidation
Cross sections
I-I
II-II
Maximum length, m
202
220
Maximum depth, m
2,10
1.80
Final settlement, cm
27.3
25.1
Degree of consolidation, %
At the end of filling
16
19
At the end of the first year
24
26
At the end of the second year
37
39
At the end of the fifth year
63
64
III - III
160
1.80
25.6
IV - IV
195
4.20
76.5
V-V
341
3.95
63.9
Longitudinal
550
4.95
79.8
16
24
37
63
14
22
35
62
14
24
35
63
14
22
35
61
3 CONCLUSION
The results presented in the paper underline the considerable influence of the pore water pressure on
the stress-strain behavior of waste deposits which reached a limit state. Besides the conventional
methods for stability analysis of the saturated waste deposits, additional analyse, such as liquefaction,
bearing capacity and time depending settlements should be made.
REFERENCES
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Germanov, T.(1986). Special problems in analyzing embankments). Proc.8-th Danube-European
Conference on SMFE, Bericht zu Sitzung E, Nurnberg, vol.II, pp 65-67.
Germanov, T.(1988). Creep and ageing effects on stresses and deformations of saturated clayey soils”.
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Germanov, T. & V.Kostov (1994). Determination of Tailings Properties for Seismic Response Analysis of a
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Germanov, T (2003). Geotechnical properties of industrial waste deposits in Bulgaria. Proc. 13th ECSMGE,
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