31-10-2016, 12:52 PM
1462450188-BehaviourofDamunderSiesmicLoads.pdf (Size: 1.55 MB / Downloads: 11)
Abstract
The stability and safety are very important issues for the dam structure which are built in seismic
regions. The dam body consists of soil materials that behave nonlinearly modelled with finite
elements. The numerical investigation employs a fully nonlinear finite element analysis considering
linear and elastic-plastic constitutive model to describe the material properties of the soil. In
this paper, seismic analysis of an earthen dam is carried out using Geo-Studio software based on
finite element method. Initially, the in-situ stress state analysis has been done before the earthquake
established, and then its results are used in the seismic analysis as a parent analysis. A
complete parametric study is carried out to identify the effects of input motion characteristics, soil
behaviour and strength of the shell and core materials on the dynamic response of earthen dams.
The real earthquake record is used as input motions. The analysis gives the overall pattern of the
dam behaviour in terms of contours of displacements and stresses.
Introduction
Earthen dams are very important structure and provide renewable energy and agriculture facility to the country.
As the dams’ structure is very large and the dams store tremendous amount of water, with respect to environmental
and economic considerations, their safe performance is very important. Stability and performance are
always primary concerns for any structure such as the huge structure of dams and the failure of it which causes
disaster and loss of human being and properties in results. Despite significant development in geotechnical engineering,
earthquakes continue to cause failure of many dams and result in the destruction of life and the damage of properties, so the stability of earthen dams during earthquake is of primary concern.
Earthen dams are preferred over the concrete gravity dam due to simple construction and relative economical
advantage. Locally available materials and less skills labor reduce the construction cost thus it is still widely
used. Dams have made an important and significant contribution in development of human being and society.
The benefits derived from dams are always considerable in the field of renewable energy and agriculture and
very important to control floods.
Core dam is a type of earthen dam where a compacted central clay core is supported on the upstream and
downstream sides by compacted shell materials. The core is separated from the compacted shells by a series of
transition zones build of the well-graded material, however if well-graded materials such as sand are used in
shells, there are no requirements of such zones. Materials used in the shells are generally medium to dense sand
and due to pervious nature of sand it allows the seepage through it which is the point of concern. Laboratory and
field test of these materials are easy as compared to rock-fill materials which are large and irregular in size.
Like most engineering structures, earth dams can fail due to faulty design, inadequate construction practices
and poor maintenance, etc. Performance evaluation and the stability of earth dams during earthquakes require a
dynamic response analysis to determine acceleration, dynamic stresses and deformations induced in the dam by
the seismic forces. In current engineering practice, dynamic response of earth dams (located in valleys or narrow
canyons) undergoing high-magnitude earthquakes is generally determined by independently calculating the dynamic
response of the various sections of the dam performing a finite element analysis.
There are two important issues to be solved in the assessment of seismic behavior of earth dams under earthquakes:
1) Stability: Is dam stable during and after earthquake?
2) Deformation: How much deformation will occur in the dam?
The possible forms of failure of earth dams due to earthquakes have been recruited by Sherard. It was stated
that: a) Disruption of dam caused by major fault movement at base; b) lack of slope ground movement; c) loss
induced freeboard, due to the difference of the movements of tectonic ground; d) loss due to freeboard slope
failure or soil compaction movements induced ground failure; e) piping through cracks due to earthworks; f) the
overflow of dam due to slides or rock falls in the tank; g) slip of dams on weak foundation materials; and h)
failure spillway or outlet works [1].
Using a traditional approach, the stability of large earthen dam in static condition is studied with the limit
equilibrium method [2], while the dynamic response of such a structure is analyzed by a pseudo-static analysis,
the displacement method derived from Newmark’s rigid block method [3]. Slopes become unsafe when shear
stresses of potential surface are more than shearing resistance of the soil [4]. “Slides can occur in practically
all possible manner, gradually or rapidly and by or short of several superficial hassle” [5]. IITK-GSDMA
recommended an equivalent static method for the dynamic analysis using the seismic coefficient of earthquake
[6]. Newmark presented the ideas of dynamic stability for dam in terms of deformation rather than the
factor of safety. [3] engaged dynamic stress deformation finite element analysis to yield the time variable horizontal
resulting force acting on failure surface [7]. Finite element method is a modern computer oriented
approach to analysis for complex structure of arbitrary shapes [8]. There are two methods of the finite element
analysis [9] [10]:
1) Flexibility or force method and
2) Stiffness or displacement method.
Finite element method is used to analyze a two-dimensional earthen dam section. To observe effects of nonlinearity
of soil, linear and nonlinear soil models are used in the analysis using software GeoStudio (2012) [11]
and results are obtained in terms of contour of stresses and displacements to observe the performance of the earthen
dam in case of earthquake loads.
2. Problem Statement
A case study of Nara earth dam is taken which is a low dam of height 40 m. This dam is located on Kandi canal
in Kandi area of district Hoshiarpur, Punjab. It is a medium size zoned dam near Barrian Wala village along
Shivalik hill providing irrigation facilities and flood control. The Kandi canal area is situated 16 km from the
Hoshiarpur. The dam lies in seismic zone IV as per seismic zoning map of India mention in I.S code for earthquake
resistant design of structures
2.1. Cross Section of Dam and Material Properties
Nara dam is a zoned dam and divided in core and shell. The cross section of the dam is shown in Figure 1. The
height and length of the dam are considered as 40 m and 270.5 m respectively. The crest length of the dam is 15
m. The water freeboard in upstream is about 4 m and in downstream side has a tail water of 4 m. The core
started from 12 m below from the point where shell started and the height of the core is just 1 m short of the dam
height and top crest of the core is about 10 m. The material properties of the shell and core are given in Table 2.
For calculation of shear modulus, an average shear wave velocity of 235 m/s is taken for both materials.
2.2. Modelling of the Dam
The 2D finite element model of Nara dam with all boundary conditions is shown in Figure 2. The meshing is
done using quadrilateral and triangular elements of 5 m element size with secondary nodes of element size of 1
m for core and shell regions. A total number of 814 nodes and 243 elements have been used for the modeling of
the dam. The bottom of the dam is modeled fix in both x and y directions. The model is analyzed for full reservoir
conditions with upstream water level at 36 m and having 4 m tail water. To compute stresses correctly, it is
necessary to apply the weight of the reservoir as boundary condition. The soil in the core and shell region is assigned
by the linear and elastic plastic soil model to observe effect of nonlinearity.
2.3. Formulation
In finite element analysis of dam, the problem is treated as two dimensional and the dam cross-section is
represented an assemblage of constant strain triangular and quadrilateral elements. The element used in the
present investigation is a plain strain quadrilateral element composed of two four nodal point triangles.
The element stiffness matrix is a function of the matrix is a function of the geometric and constitutive properties
of element. The stiffness [K] of the complete structural assemblage may be obtained from the individual
from the individual element stiffness matrices by direct stiffness assembly procedures.
3.2. Seismic Analysis
The seismic analysis is carried out for linear elastic and nonlinear(elastic-plastic) model soil models. The results
of static analysis are used as initial conditions for seismic analysis using QUAKE/W. The material properties of
soil required for dynamic analysis are total unit weight, Poisson’s ratio, elastic modulus, c-phi and damping ratio.
For the seismic analysis, damping ratio value is considered as 0.1 (10%). The time history of Kashmir earthquake
(2005) of magnitude 7.6 is used as the horizontal ground motion whose initial peak is 0.12 g and modified
to 0.24g as the site is located in seismic zone IV. The actual and modified time history is shown in Figure 4(a)
and Figure 4(b). The results of seismic analysis for each soil model are presented in the form of contours of
vertical stresses, horizontal stresses, vertical displacement and horizontal displacement.
3.3. Effects of Nonlinearity
The contours of vertical stresses of linear, and nonlinear soil model are shown in Figure 5(a) and Figure 5(b)
respectively. It is observed that in both cases the vertical stresses are increases from top to bottom of the dam
which is expected. The maximum vertical stresses for linear soil model is 958.2 kPa and for nonlinear (elasticplastic)
soil model it is 1031.5 kPa which shows, as the nonlinearity increases stresses increases while minimum
vertical stresses for these cases are found to be in the toe of dam which are −25.741 kPa and −23.701 kPa respectively
shows that effect of tensioning decreases with nonlinearity of the soil.
The contours horizontal stresses of linear and nonlinear soil models are shown in Figure 6(a) and Figure 6(b)
respectively.
It is observed that in all three cases the horizontal stresses are increases from top to bottom of the dam which
is expected. The maximum horizontal stresses for linear soil model is 753.69 kPa and for nonlinear soil model it
is 808.94 kPa which shows, as the nonlinearity increases stresses increases while minimum vertical stresses for
these cases are found to be in the toe of dam which are −14.355 kPa and −8.3208 kPa respectively shows that
effect of tensioning decreases with nonlinearity of the soil.
Conclusion
After the static and dynamic analysis of the Nara dam, it is found that the contours of horizontal and vertical
stresses increase from top to bottom of the dam which is expected. It is observed that the soil behaves linearly
during the static analysis. But after the seismic analysis due to effect of nonlinearity of the soil stresses and displacements,
it increases from linear elastic to nonlinear (elastic plastic) soil model. The contours of horizontal
and vertical displacements decrease from top to bottom of the dam. The value of maximum horizontal as well as
vertical settlements is within permissible limit as per I.S codeis 1% - 2% of the earthen dam height [14]. In case
of horizontal displacement, effect of nonlinearity is very high almost double of the linear soil model.