Access to this full-text is provided by EDP Sciences.
Content available from E3S Web of Conferences
This content is subject to copyright. Terms and conditions apply.
Strength of earth dams considering the elastic-plastic
properties of soils
Mirziyod Mirsaidov1,2, Takhirjon Sultanov1, Javlon Yarashоv1*, and Abduraxim Kayumov2
1“Tashkent Institute of Irrigation and Agricultural Mechanization Engineers” National Research
University, Tashkent, Uzbekistan
2Institute of Mechanics and Seismic Stability of Structures of the Academy of Sciences of the
Republic of Uzbekistan, Tashkent, Uzbekistan
Abstract. The article provides a detailed review of well-known
publications devoted to studying the stress state and dynamic behavior of
earth dams, taking into account the elastic and elastic-plastic properties of
soil. To assess the stress-strain state of earth dams, considering the elastic-
plastic properties of soil under the action of static loads, a mathematical
model was developed using the principle of virtual displacements. A
technique, algorithm, and computer programs were developed for
estimating the stress state of dams using the finite element method and the
method of variable elasticity parameters. A test problem was solved to
assess the adequacy of the developed models and the reliability of the
technique, algorithms, and computer programs. The stress-strain state of
the Pskem earth dam, 195 m high, was studied using the developed models
and calculation methods, taking into account the elastic-plastic properties
of soil under the action of body forces and various levels of filling the
reservoir with water. It was established that an account for the elastic-
plastic properties of soil leads to a sharp change in the stress state of the
dam, especially in the upper prism and in the core of the dam, and changes
the intensity of normal stresses, which can lead to a violation of the
integrity of the dam.
1 Introduction
The assessment of the stress-strain state and strength of earth dams are considered in the
article, taking into account the elastic-plastic properties of soil under various impacts, i.e.,
under the action of mass forces and different levels of filling the reservoir with water.
Today, in the Republic of Uzbekistan, special requirements are stated for the safety of
hydro-technical structures confirmed by the Law of the Republic of Uzbekistan On the
safety of hydraulic structures, dated 08.20.1999, Resolution of the President of the Republic
of Uzbekistan No. PP-4794 dated 07.30.2020 On measures on radical improvement of the
system for ensuring seismic safety of the population and the territory of the Republic of
Uzbekistan and the Law of the Republic of Uzbekistan On ensuring seismic safety of the
population and the territory of the Republic of Uzbekistan dated September 13, 2021.
*Corresponding author: zhavlon.yarashov@bk.ru
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).
Therefore, the development of design, construction, and operation of unique earth
structures requires the creation of structures that work reliably under various kinds of loads.
The existing elastic calculation, especially for high-rise structures, cannot cover the actual
operation of the structure. Therefore, the development of new mathematical models and
modern calculation methods that consider the nonlinear and plastic properties of soils, real
geometry, non-homogeneity, and design features of the structure is relevant. Classical
studies, which highlight the main theories and methods for assessing the strength
parameters of earth structures, are given in [1-12].
Along with these publications, we should mention the following studies:
in [13], natural oscillations of discrete systems were given, the difference between
elastic-plastic oscillations and elastic ones was shown; it was shown that under elastic-
plastic oscillations, the movement occurs according to an aperiodic law;
in [14], numerical studies and evaluations of the seismic behavior of earth dams
were conducted using the finite-difference method, considering the ideal plastic properties
of soil and damping. The nonlinear dynamic behavior of the dam was investigated;
the nonlinear seismic behavior of earth dams was considered in [15], using the
finite element method and Geo-Studio software. In the numerical study, a nonlinear finite
element analysis was used, taking into account the linear and elastic-plastic components of
the model to describe the soil properties;
in [16], the mitigation of the dam damage using a damping protective layer (a layer
of river sand) between the foundation and the base was studied in the model of an earth
dam under strong earthquakes;
in [17], a unified analytical solution for the analysis of elastic-plastic stresses around
a cylindrical cavity under biaxial stresses was presented. It was shown that the biaxial state
of the initial stresses has a significant effect on the stress distribution around the internal
cavity. The solutions obtained under loading and unloading were verified by comparison
with the results of numerical simulation and other analytical solutions;
in [18], the corresponding computational model and method were selected using the
ABAQUS software package, and dynamic characteristics of a complex structure under
strong dynamic impacts were analyzed. It was shown that the method of elastic-plastic
analysis is more rational and reliable in assessing the behavior of structures and in checking
calculations under strong dynamic impacts, and the calculated results are more accurate;
elastic-plastic analysis of high-rise buildings under strong ground motions was
performed in [19], using the ABAQUS software package. Anti-seismic characteristics were
assessed, the structural scheme was optimized, and weak parts of the structure were
strengthened;
in [20], a nonlinear model was considered, taking into account the interaction of the
structure with the soil base. Nonlinear effects were calculated based on an elastic-plastic
model of the soil material adjacent to the structure's base. For the artificial boundary, non-
reflective boundary conditions were used. A numerical method for solving the nonlinear
equation of motion was developed;
in [21], the method of gradual reduction of shear strength parameters was used to
analyze the static stability of the slopes of earth dams based on numerical simulation.
Strains in the body of the dam and base after the end of construction and the corresponding
safety factor were modeled;
the finite element method was used in [22] for the numerical calculation of earth
dams; it considers the moisture content and plastic properties of soils and the nonlinear
strain of the structure. Calculations were performed for three earth dams using the model
proposed in the study;
in [23], an improved elastic-plastic soil model was used to simulate the subsidence
of high dams (182 m high) built from hard soils. The results showed a good agreement
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
2
between the calculated subsidence and the monitoring data. The stress-strain dependences
were shown, and the results for volumetric strain were in better agreement compared to the
results obtained using other models;
in [24], the stability of slopes of earth dams was studied using an elastic-plastic
model;
the stability and displacement of an earth dam during construction were studied in
[25] by mathematical modeling and experimental studies. The simulation results were
compared with experimental data;
in [26], the strain in the bodies was considered taking into account the elastic-plastic
properties of the material and finite deformations. As an example, the tension of a rod of a
circular cross-section was considered under elastic-plastic deformation;
in [27], a technique for solving problems for a soil mass was presented, taking into
account the elastic-plastic deformation of soil. As an example, the subsidence of an earth
embankment was studied considering the elastic-plastic properties of soil;
in [28], the pattern of strains and displacements of the body of the structure was
studied by computer modeling;
in [29], a two-dimensional problem of assessing the stress-strain state of a slope in
an elastic-plastic formulation was solved using a numerical method;
the strain state of water-saturated clay soils under triaxial cyclic loading was
considered in [30], considering elastic-plastic deformation. It was shown that the calculated
diagrams agree with the experimental strain diagrams of real soils.
Along with this, the stress-strain state and dynamic behavior of various structures
were studied in [31-43], taking into account the nonlinear, inelastic properties of the
material and the features of their deformation.
The above review of known publications shows that studying the stress-strain state
of earth structures, considering the elastic-plastic properties of soil, is an urgent task.
2 Methods
2.1 Mathematical model of the problem
A non-homogeneous deformable system under the action of various static loads is
considered (Fig. 1). It occupies volume V=V1+V2+V3. Some elements of system V have
elastic-plastic properties, and the other elements are elastic. It is necessary to determine the
stress-strain state (SSS) of a non-homogeneous system (Fig. 1) under the action of body
forces
f
&
and the hydrostatic pressure of water
p
&
. The problem is considered for the
plane-strain state of the system (Fig. 1).
When setting the problem, it is assumed that the surface of the dam base
о
is rigidly
fixed, the areas of the crest and downstream slope
2
,
3
are stress-free on the surface,
and the hydrostatic water pressure
p
&
acts on Sp , i.e., on the part of the surface
1
.
It is necessary to determine the displacement and stress fields arising in the body of the
dam (Fig.1) under the action of body forces
f
&
and the hydrostatic pressure of water
p
&
at
various levels of reservoir fillings with water.
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
3
Fig. 1. Design scheme of a non-homogeneous system
To simulate the process of deformation in the body of the dam (Fig. 1), the principle of
virtual displacements is used:
.0
321
dSupdSufdSdSdS
P
SV
ij
V
ijij
V
ijij
V
ij
&&&
&
(1)
Along with (1), the following values are used:
- kinematic boundary conditions
0: ux
o
&&
(2)
- to describe the physical properties of the material in each area of the dam body (V1,
V2, V3), the generalized Hooke's law [44] is used:
ijnijkknij
~
2
~
(3)
- to describe the relationship between the components of the strain tensor and
displacement vector, the linear Cauchy relations are used [44]:
2,1,,
2
1
ji
x
u
x
u
i
j
j
i
ij
(4)
The hydrostatic pressure of water on the upstream face of the dam is determined by the
following formula [45]:
)(
oyhgp
&
(5)
Here
&
u
are the components of the displacement vector,
ij
,
ij
are the components
of the strain and stress tensors;
p
&
is the hydrostatic water pressure;
f
&
is the vector of
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
4
body forces;
ij
is the Kronecker symbol;
o
is the density of water; (h-y) is the depth of
a point on the upstream face of the dam;
v,,
21
uuuu
&
are the components of
displacement vectors,
yxxxx ,,
21
&
are the components of the coordinate system.
In the case of considering the law of elastic-plastic deformation of the materials of the
dam, values
n
~
and
n
~
are variables determined from the experiment for each section of
diagram
ii
f
, and in the case of elastic deformations, they are the Lame constants
(index nshows the correspondence of the characteristic of the material to the part of the
body - V1, V2, V3);
When considering the elastic-plastic properties of the material, if at certain points of the
dam body the stress intensity
iexceeds the yield strength
т (
т is determined from
experiments for specific materials), then it is assumed that plastic deformations begin to
develop in them due to a change in the shape of the body.
Now the problem under consideration can be formulated as follows: it is necessary to
find the components of displacements
xu &&
, strains
x
ij
&
, and stresses
x
ij
&
under the
action of body forces
)( f
&
and hydrostatic water pressure
p
&
, satisfying equations (1),
(3), (4) and conditions (2) at all points of the dam body (Fig. 1) for any virtual displacement
u
&
.
2.2 Model implementation method
When implementing this approach, the virtual work of elastic forces must be rewritten in
terms of the spherical and ninefold parts of stresses and strains [44]. Then the integrand in
(1) can be represented as:
2
0
2
9
niiijij
K
(6)
Here
n
n
n
E
K
213
is the volume modulus of elasticity, En is the modulus of
elasticity, n is the shear modulus of elasticity, n is Poisson's ratio.
The first term in (6) is the virtual work produced by changing the shape, and the second
term is due to the volume change.
The intensity of normal stresses
i
and strains
i
are determined by the following
formulas:
2
12
2
1133
2
3322
2
2211 6
2
1
i
(7)
2
12
2
22
2
11
2
2211 2
3
12
2
n
i
In the case of plastic strains increment, the ninefold and spherical parts of the strains of
corresponding stress components have the following form
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
5
ij
i
i
ij
Se
2
3
(8)
n
K
0
0
3
The relationship between the components of the strain tensor and the stress tensors can
be written as [44, 48]:
1212
112222
221111
1
1
1
n
n
n
n
n
E
E
(9)
Here, Sij,eij are the ninefold and
00
,
are the spherical parts of stress and strain
tensors;
i,
i are the stress and strain intensities;
***
,,
nnn
Е
are the variable elasticity
parameters [46-48], determined through elastic parameters
nnn
Е
,,
, and intensities of
normal stresses
iand strains
I, i.e.:
i
i
n
n
i
i
n
E
E
3
21
1
*
;
i
i
n
3
*
;
i
i
n
n
i
i
n
n
n
E
E
3
21
1
3
21
2
1
*
(10)
As seen from expression (10), the changing physical and mechanical parameters
***
,,
nnn
Е
at each structure point are determined based on the achieved strain state
i
and
the corresponding
*
i
(according to the selected strain diagram (Fig. 2), i.e.,
*
i
=
*
i
(
i
).
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
6
Fig. 2. Strain diagram and implementation scheme of the method of variable elasticity parameters
2.3 Problem solution methods
The considered variational problem is solved by the finite element method (FEM) [49]. The
FEM procedure allows us to reduce the problem under consideration to a nonlinear system
of algebraic equations of the N-th order:
PuK
ii
,
(11)
Here kij are the coefficients of the equation, which are elements of the stiffness matrix of
the structure
ii
K
,
and depend not only on the elastic parameters but also on the
stress-strain state of the structure;
u
is the sought-for vector of nodal displacements;
P
is the vector of acting loads (i.e., body forces
f
&
and water pressure
p
&
).
Then, at each stage of the process, the nonlinear system of algebraic equations (11) is
solved by the Gauss method.
At the first stage of the solution, an elastic calculation of an earth structure is performed;
the structure is in equilibrium under the action of applied loads. Then, the transition to the
second stage of the calculation is realized, which consists of the analysis of the SSS in all
finite elements of the system (Fig. 1). If in individual finite elements, the stress intensity
i
(Fig. 2) exceeds the yield strength
Т (
Т is determined from experiments for specific
materials), it is assumed that plastic deformations begin to develop in them due to a change
in the shape of the body.
Using (10), variable elasticity parameters are determined for these elements, stiffness
matrices and then common matrix
K
ii
,
for the entire system are compiled (Fig. 1).
The solution of the resulting new system of equations (11) is analyzed: if necessary, new
variable elasticity parameters are introduced, and then the process continues until sequence
i converges throughout the structure within the specified accuracy. The described method
(Fig. 2) is a method of variable elasticity parameters [46-48].
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
7
2. Test task 4
The reliability of the developed models, methods, algorithms, and computer programs was
verified by studying the practical convergence when solving test problems.
The solution to a plane problem under the action of body forces for a homogeneous
structure of an earth dam (Fig. 3) is considered, taking into account the elastic and elastic-
plastic properties of soil. The problem is solved for the plane-strain state of the structure.
The following values of geometric parameters of the dam and physical and mechanical
properties of the soil material were taken: height - H=86.5m; the ratio of slope =
1: 2.5, =1:2.2; modulus of elasticity and specific gravity of soil Е=3.07 104МPа;
=1.98 t/m3; Poisson's ratio - =0.36; soil yield strength σТ=5 МPа.
Fig. 3. Design scheme of a homogeneous earth dam
With the developed mathematical model and methods, the stress-strain state of the earth
dam (Fig. 3) was determined under the action of body forces, taking into account the elastic
and elastic-plastic properties of the dam material.
Vertical displacements u2, intensities of horizontal and normal stresses obtained
at various partitions of the structure into finite elements for elastic and elastic-plastic cases
are given in Table 1 for certain points (A, B, C) of the dam.
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
8
Table 1.The results obtained with various partitioning of the structure into finite elements
Points
coordinate
s
(x,y)
Displaceme
nt and stress
components
Number of finite elements
Elastic solution
N = 280 N = 336 N = 576
Point
-
А
0.44336*10
-
2
0.44392*10
-
2
0.44441*10-2
x=79.2m
i
12.7045
12.7651
12.7908
y=28.8m
11
-10.5147
-10.4173
-10.0337
Point - В
у
0.01634
0.01631
0.01606
x=208.8m
i
70.2274
70.5124
70.7116
y=46.1m
11
-20.7621 -20.7108 -20.6831
Point - С
0.01635
0.01639
0.01641
x=223.0m
i
69.8439
70.0173
70.5069
y=40.1m
11
-20.9777 -20.6428 -20.2835
Elastic-plastic solution
Point - А
0.5193*10-2
0.5204*10-2
0.5414*10-2
x=79.2m
i
16.206 16.673 16.888
y=28.8m
11
-16.868 -16.274
-16.145
Point - В
0.03152
0.03231
0.03241
x=208.8m
i
65.241 65.741 64.833
y=46.1m
11
-17.188 -16.917 -16.781
Point - С
0.03154
0.03181
0.03192
x=223.0m
i
64.281 64.301
64.254
y=40.1m
11
-13.605 -12.912 -12.524
Checking the practical convergence of the results obtained (Table 1) of the problems
under consideration for various numbers of finite elements shows good convergence of the
results. In the elastic case, the convergence of the results occurs more rapidly than in the
elastic-plastic case.
3 Results
The stress-strain state of the newly designed Pskem earth dam was studied; its height is
= 195 m, crest width - bcrest=12m, the ratio of slope m1=2.4, m2=2.0, the core width at
the bottom -130 m. Physical and mechanical properties of the core material are: specific
gravity γ =1.7t/m3, deformation modulus Εdef=30 MPa, Poisson's ratio
=0.32, internal
friction angle =24
, cohesion coefficient c=30 kPa, yield strength Т=3 MPa. Physical
and mechanical properties of the material of retaining prisms are specific gravity
γ=1.97t/m3, deformation modulus Εdef=95MPa, Poisson's ratio
=0.27, internal friction
angle =42
, cohesion coefficient c=70 kPa, yield strength Т=5 MPa. The data is taken
from the project.
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
9
According to [50], =
=
⋅
(!") =
(!").σТ=3 МPа(for loam material),
σТ=5 MPa (for retaining prisms).
The calculation results of the Pskem earth dam, taking into account the non-
homogeneous design features and elastic-plastic properties of soil under the action of body
forces and hydrostatic pressure of water, are the definitions of the components of the
displacement vector, the strain tensor, stress
ij
, and stress intensity
i
for all points of the
considered area - of the cross-section of the dam.
To assess the effect of hydrostatic water pressure on the SSS of the dam, various levels
of water filling in the reservoir were considered. The SSS obtained at each level of filling
was compared with the results without considering the filling of the reservoir.
Figure 4 shows the isoline of distribution of equal values of the stress tensor
components and the intensity of normal stresses obtained for the Pskem earth dam under
the action of body forces, with account for the elastic and elastic-plastic properties of soil.
Solid (_____) lines show elastic calculation, and dashed lines (--------) show the elastic-
plastic calculation.
а) ∙10
$ МPа
b) ∙10
$ МPа
c) ∙10
$ МPа
d) ∙10
$ МPа
Fig. 4. Isolines of the distribution of equal values of the stress tensor components and the intensity of
normal stresses in the Pskem earth dam under the action of body forces
f
&
, taking into account
elastic (──) and elastic-plastic (----) properties of soil
The analysis of the results obtained (Fig. 4) shows the highest stress values σi,σ11,σ22,
that occur in the middle of the lower part of the dam. Accounting for non-homogeneity, i.e.,
the presence of a core with other mechanical characteristics of soils leads to a decrease in
stresses in the body of the core. Therefore, the distribution pattern of the isolines of these
stresses in the dam's core goes down a little.
As for the isoline of distribution of tangential stressesσ, unlike other stresses, its most
minimal value is observed approximately in the middle of the dam since the value of the
ratio of both slopes is almost the same. The value of σ increases from the middle of the
dam to the middle of the surcharge wall, then there is a slight decrease near the slope.
When considering the elastic-plastic properties of soil, the distribution of the intensity
of normal stresses qualitatively differs little from the distribution in the elastic case,
while quantitatively the value of this stress in some sections of the dam decreases to 17%.
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
10
When considering the plastic properties of soil, the greatest change occurs in horizontal
stress in the middle part of the dam, it decreases to 30%.
Figure 5 shows the distribution of the isoline of equal values of the components of the
stress tensor and the intensity of normal stresses obtained for the Pskem earth dam under
the action of body forces and hydrostatic pressure of water when the reservoir is filled to a
height h= 190 m, taking into account the elastic and elastic-plastic properties of soil.
An analysis of the results obtained for the dam under body forces and hydrostatic water
pressure at various levels of reservoir filling showed a sharp change in the stress-strain state
in the upper prism of the dam. If we compare the results given in Figs. 4 and 5, we can see
a significant change in the stress-strain state of the dam. In this case, the stress is distributed
asymmetrically in the upper retaining prism up to 2/3 of the dam's height. Then,
considering the water pressure in the calculations, the intensity of normal stress in the
upper retaining prism increases to 30%, and vertical stress increases to 50% for
individual sections of the dam. The stresses , change substantially not only in the
upper prism, but they change in the core of the dam; the symmetrical distribution of stresses
throughout the body of the dam is completely broken.
а) ∙10
$ М%а
b) ∙10
$ М%а
c) ∙10
$ М%а
d) ∙10
$ М%а
Fig. 5. Distributions of equal values of the stress tensor components (σ11, σ12, σ22) and normal stress
intensity σiin the Pskem earth dam under the action of body forces
f
f
and water pressure
p
p
when
the reservoir is filled up to h=190 m, considering elastic (──) and elastic-plastic (----) properties of
soil
An account for the elastic-plastic properties of soil leads to a decrease in stress from 10
to 50% in the upper prism and the core of the dam and from 5 to 30% in the lower prism
and different parts of the dam.
4 Conclusions
1. A detailed review of the current state of the problem of assessing the stress-strain
state of various dams is given, taking into account the nonlinear and elastic-plastic
properties of the structure's material.
2. A mathematical model was developed for assessing the stress-strain of earth dams
under various static effects using the principle of virtual displacements and small elastic-
plastic strains occurring due to changes in the body's shape.
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
11
3. The methods and computer programs were developed for determining the stress state
of earth dams using the finite element method and the method of variable elasticity
parameters.
4. The effectiveness of the developed methods and algorithms for implementing the
problem is shown by solving test problems.
5. The stress-strain state of the newly designed Pskem earth dam (H=195 m high) was
studied under the action of body forces and hydrostatic pressures of water.
6. It was determined that:
when considering the elastic-plastic properties of soil, the distribution of the
intensity of normal stresses under the action of body forces qualitatively differs little
from the distribution in the elastic case, while in different parts of the dam, it leads to a
decrease in the stress state;
under the action of body forces and hydrostatic water pressure on the dam at various
levels of reservoir filling, an account for the elastic-plastic properties of soils leads to a
sharp change in the stress state, especially in the upper prism and in the core of the dam. It
changes the intensity of normal stresses up to 50%.
References
1. Yu.K.Zaretsky and V.N.Lombardo, Statics and dynamics of earth dams. M.:
Energoizdat, p. 256 (1976).
2. I. A. Konstantinov Dynamics of hydro-technical structures. Part 2. - L.: LPI Publishing
House, -196 p. (1976).
3. N.D. Krasnikov Seismic resistance of hydro-technicalulic structures made of soil
materials. - M.: Energoizdat, 230 p. (1981)
4. V.N. Lombardo Static calculation of earth dams. M. "Energy", -200 p. (1983).
5. V.M.Lyakhter and I.N.Ivashenko Seismic resistance of earth dams. M.: Nauka, - 233 p.
(1986).
6. M.M.Mirsaidov Theory and methods for calculating earth structures for strength and
seismic resistance.- Tashkent: Fan, -312 p.(2010).
7. L.N.Rasskazov and A.S.Bestuzheva Seismic resistance of earth dams. Hydrotechnical
construction. M.:- Number 3. - P.13-19. (1997).
8. M.M.Mirsaidov and T.Z.Sultanov Evaluation of the dynamic strength of earth dams
taking into account nonlinear deformation. Tashkent: "Adabiyot uchkunlari", 258 p.
(2018).
9. M. A.Akhmedov Earthquake, consequences and protection.- Tashkent: Tashkent State
Technical University, -387 p. (2016).
10. M.A.Akhmedov and K.J.Salyamova Analysis and assessment of damage to hydro-
technical structures. - Tashkent: "Fan va technology", 160 p. (2016).
11. Z.G.Ter-Martirosyan Soil mechanics. M.: Publishing House of the Association of
Construction Universities, 488 p. (2005).
12. T.Sh.Shirinkulov and Yu.K.Zaretsky Creep and consolidation of soils. Tashkent: Fan,
302s. (1986).
13. A.N.Potapov "Generalized orthogonality of natural vibration modes of elastic-plastic
discrete systems, taking into account the forces of resistance" Construction and
ecology: theory, practice, innovations. Collection of reports of the I International
Scientific and Practical Conference. P.90-94. (2015).
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
12
14. Babak Ebrahimian and Ali Noorzad. Numerical earthquake response analysis of the
earth dams. Рр.805-817, (2017). DOI:10.3217/978-3-85125-564-5-109
15. M.Raja and B.Maheshwari, Behaviour of earth dam under seismic load considering
nonlinearity of the soil. Journal of Civil Engineering, 6(2), 75-83. (2016).
doi:10.4236/ojce.2016.62007.
16. Behrouz Gordan and Azlan Adnan. Excellent performance of earth dams under
resonance motion using isolator damping Layer. Shockandvibration. (2014).
https://doi.org/10.1155/2014/432760
17. P.Z.Zhuang and H.-S.Yu.A unified analytical solution for elastic–plastic stress analysis
of a cylindrical cavity in Mohr–Coulomb materials under biaxial in situ stresses.
Géotechnique.Vol. 69 Iss. 4. pp. 369-376. (2019).
https://doi.org/10.1680/jgeot.17.P.281
18. Jun Teng,Zuo-Hua Li, Xing-Fa Wang, Hong-Jun Liu, Xiao-Feng Wang. Comparison
of different elastic‐plastic analysis method of complex high‐rise structures under strong
earthquake excitations. 4th International Conference on Earthquake Engineering
Taiwan, Paper No.118 (2006).
19. Jiao Ke, Lai Hongli, Chen Xing, Huang Zhenkang. The Elastic-Plastic Dynamic
Analysis Software GSEPA and Its Application in Seismic Analysis of Tall Buildings.
The 14 World Conference on Earthquake Engineering China. (2008)
20. B. Wrana Nonlinear Elastic-plastic Model Of Soil-structure Interaction In Time
Domain.WIT Transactions on The Built Environment. Vol. 3. Paper 15. (1993). DOI:
10.2495/SDEE930421
21. R.Afiri and S.Gabi Finite element slope stability analysis of Souk Tleta dam by shear
strength reduction technique. Innov. Infrastruct. Solut. 3: 6. (2018)
https://doi.org/10.1007/s41062-017-0108-1
22. M.M.Mirsaidov, T.Z.Sultanov, Sh.A.Sadullaev An assessment of stress- strain state of
earth dams with account of elastic-plastic, moist properties of soil and large strains.
International Journal: "Magazine of Civil Engineering". Volume 40, Issue 5, Pp.59-68.
(2013) DOI: 10.5862/MCE.40.7
23. R.Sukkarak, P.Pramthawee, P.Jongpradist A modified elasto-plastic model with double
yield surfaces and considering particle breakage for the settlement analysis of high
rockfill dams. KSCE Journal of Civil Engineering. Vol.21. Issue 3.Pp. 734–745.
(2017). https://doi.org/10.1007/s12205-016-0867-9
24. V.V.Orekhov Stability of an earth dam with a vertical diaphragm. Vestnik MGSU.
Hydraulics. Engineering hydrology. Hydro-technical engineering. No. 1. P.143-149.
(2016). DOI: 10.22227/1997-0935.2016.1.143-149
25. S.Shahba, F.Soltani Analysis of Stress and Displacement оf Taham Earth Dam, Indian
Journal of Science and Technology. Vol. 9(45) (2016). DOI:
10.17485/ijst/2016/v9i45/104182
26. L.U.Sultanov, R.L.Davydov Numerical study of large deformations by finite element
method. Magazine of Civil Engineering. 9(44). P. 64-68. (2013). DOI:
10.5862/MCE.44.8.
27. L.U.Sultanov, D.V.Berezhnoi, A.V.Karamov FEM-based calculation of soil mass with
the impact of dilatancy. Magazine of Civil Engineering, No.4(48),Pp.3-9. (2014). DOI:
10.5862/MCE.48.1
28. N. A. Kalashnik Computer modeling of an earth-fill dam as a prototype of a tailing
dam, N. A. Kalashnik. International Scientific Research Journal. No. 4 (4). pp. 54 -55.
(2012).
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
13
29. M.B.Kusbekova, Z.M.Zhambakina, M.B.Permyakov Stress-strain state of the slope.
Scientific research. No. 5(16), pp. 15-17. (2017)
30. S.I.Panov and A.L.Goldin Deformations of clay soils under cyclic loading. News of
VNIIG named after B.E. Vedeneev. Vol. 280. P.79-86. (2016).
31. K.S.Sultanov, P.V.Loginov, S.I.Ismoilova, Z.R.Salikhova Variable moduli of soil
strain. E3S Web of Conferences. 97. Pp. 04013. (2019).
DOI:10.1051/e3sconf/20199704013.
32. A.A.Bakhodirov, S.I.Ismailova, K.S.Sultanov, Dynamic deformation of the contact
layer when there is shear interaction between a body and the soil. Journal of Applied
Mathematics and Mechanics. 79(6). Pp.587–595. (2015).
DOI:10.1016/j.jappmathmech.2016.04.005.
33. K.S.Sultanov A nonlinear law of the deformation of soft soils. Journal of Applied
Mathematics and Mechanics. 62(3). Pp. 465–472. (1998). doi:10.1016/S0021-
8928(98)00058-6.
34. M.M.Mirsaidov and E.S.Toshmatov Spatial stress state and dynamic characteristics of
earth dams. Magazine of Civil Engineering. 89(5), Pp. 3-15. (2019).
doi: 10.18720/MCE.89.1
35. M.M.Mirsaidov and T.Z.Sultanov Assessment of stress-strain state of earth dams with
allowance for nonlinear strain of material and large strains. Magazine of Civil
Engineering. 49(5), pp.136-137. (2014). doi: 10.5862/MCE.49.8
36. M.Mirsaidov An account of the foundation in assessment of earth structure dynamics.
E3S Web of Conferences. 97,04015. (2019). doi: 10.1051/e3sconf/20199704015
37. M.Usarov, A.Salokhiddinov, D.M.Usarov, I.Khazratkulov N.Dremova To the theory of
bending and oscillations of three-layered plates with a compressible filler. IOP Conf.
Series: Materials Science and Engineering 869 052037. (2020) doi:10.1088/1757-
899X/869/5/052037
38. M.Usarov, G.Mamatisaev, E.Toshmatov, J.Yarashov Forced vibrations of a box-like
structure of a multi-storey building under dynamic effect. Journal of Physics:
Conference Series, (2020). https://doi.org/10.1088/1742-6596/1425/1/012004.
39. E.Toshmatov, M.Usarov, G.Ayubov, D.Usarov Dynamic methods of spatial
calculation of structures based on a plate model. (E3S Web of Conferences 97, Form-
2019, 04072) https://doi.org/10.1051/e3sconf/20199704072
40. A.Abduvaliev and A.Abdulkhayzoda Transverse vibrations of an underground
cylindrical structure. IOP Conference Series: Materials Science and Engineering. №
012099. (2021) https://doi.org/10.1088/1757-899X/1030/1/012099
41. M.Mirsaidov. Assessment of dynamic behaviour of earth dams taking into account
large strains. E3S Web of Conferences 97, 05019 (2019)
https://doi.org/10.1051/e3sconf/20199705019
42. M.M.Mirsaidov et.al. Mathematical simulation and the methods to assess the strength
of earth dams. In International Conference on Information Science and
Communications Technologies (2019) doi:10.1109/ICISCT47635.2019.9011818
43. Z.Urazmukhamedova, D.Juraev, M.Mirsaidov Assessment of stress state and dynamic
characteristics of plane and spatial structure. Journal of Physics: Conference
Series, Volume 2070, Second International Conference on Advances in Physical
Sciences and Materials 2021(ICAPSM 2021) 12-13 August 2021, India
44. A.V.Aleksandrov and V.D.Potapov Fundamentals of the theory of elasticity and
plasticity. M.: Higher school, 400 p. (1990).
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
14
45. R.R.Chugaev Hydraulics. L.Energoizdat, 203 p. (1982).
46. I.A. Birger Some general methods for solving problems in the theory of plasticity,
Applied Mechanics. V. XV. Issue 6. pp.765-770 (1951).
47. I.A. Birger Calculation of structures taking into account plasticity and creep, News of
Academy of Sciences. Mechanics - mechanical engineering. No. 2. pp.113-119 (1965)
48. N.N.Malinin Applied theory of plasticity and creep. M.: Mashinostroenie, 400 p.
(1975).
49. K.Bate and E.Wilson Numerical methods of analysis and FEM. Moscow: Stroyizdat,
448 p. (1982)
50. D.D.Barkan Dynamics of bases and foundations. M.: Stroyvoenizdat, 411 p. (1948).
E3S Web of Conferences 365, 03001 (2023) https://doi.org/10.1051/e3sconf/202336503001
CONMECHYDRO - 2022
15
Available via license: CC BY 4.0
Content may be subject to copyright.
