Effect of Non-linearity on Dynamic Response of Earthen Dam

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ABSTRACT: The stability and safety are very important issues for the dam structure which are built in seismic regions. The dam body consist of soil materials that behave nonlinearly need to be modelled with finite elements. In present study, 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, dynamic analysis of a dam is carried out using GeoStudio software. Initially the in-situ stress state analysis has been done before the earthquake established, and then its results are used in the dynamic analysis as a parent analysis. A comprehensive 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 provide renewable energy and agriculture facility to the country. As the dams are very large structure and store tremendous amount of water, so with respect to environmental and economic considerations, their safe performance is very important. Stability and performance are always primary concern for any structure such as the dams are huge structure, failure of it 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 results in destruction of life and damage of properties, so stability of earthen dams during earthquake are of primary concern. Earthen dams are preferred over the concrete gravity dam due to simple construction and relative

Earthen dams are preferred over the concrete gravity dam due to simple construction and relative economical advantage. Locally available materials and less skills labor reduced the construction cost thus still it is 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, agriculture and most importantly 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 well graded material, however if well graded materials such as sand are used in shells, there are no requirement 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 compare 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 requires 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. a) Stability: Is dam stable during and after earthquake?
  2. b) Deformation: How much deformation will occur in the dam?

The possible forms of failure of earth dams due to earthquakes have been investigated by Sherard et al. [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 structure is analyzed by pseudostatic analysis, the displacement method derived from Newmark’s rigid block method [3]. The slopes become unsafe when shear stresses of potential surface is more than shearing resistance of the soil [4]. According to Terzaghi and Peck [5], “slides can occur in practically all possible manner, gradually or rapidly and by or short of several superficial hassle”. IITK-GSDMA [6], recommended equivalent static method for dynamic analysis using seismic coefficient of earthquake. Newmark [3] presented the ideas of dynamic stability for dam in terms of deformation rather than factor of safety. Chopra [7] engaged dynamic stress deformation finite element analysis to yield the time variable horizontal resulting force acting on failure surface. According to Chopra et.al [8], finite element method is a modern computer oriented approach to analysis for complex structure of arbitrary shapes. There are two methods of 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 a linear as well as a nonlinear soil models are used in the analysis using software GeoStudio [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.

 

PROBLEM STATEMENT

A case study of Nara earth dam is taken which is a low dam of height 40m. 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 and provide 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 according to IS: 1893-2002 Part 1[12].

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 40m and 270.5m, respectively. The crest length of the dam is 15m. The water freeboard in upstream is about 4m and in downstream side has a tail water of 4m. The core started from 12m below from the point where shell started and the height of the core is just 1m short of the dam height and top crest of the core is about 10m. The material properties of the shell and core are given in Table 1. For calculation of shear modulus, an average shear wave velocity of 235m/s is assumed for both materials.

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 5m element size with secondary nodes of element size of 1m for core and shell regions. A total number of 814 nodes and 243 elements have been used for the modelling of the dam. The bottom of the dam is modelled fix in both x and y directions. The model is analyzed for full reservoir conditions with upstream water level at 36m and having 4m 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 are assigned by the linear and elastic plastic soil model to observe effect of nonlinearity.

 

Formulation

In finite element analysis of dam, the problem is treated as two dimensional and the dam crosssection was represented as 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 geometric and constitutive properties of element. The stiffness [K] of the complete structural assemblage may be obtained from the individual element stiffness matrices by direct stiffness assembly procedures. The equation of motion for two-dimensional structure, idealized as a plane strain finite element system, subjected to dynamic loads, may be expressed in matrix form as

[M] {r̈} + [C] {ṙ} + [K] {r} = {R(t)}

In Eq. 1, [M], [C] and [K] are the mass matrix, viscous damping matrix and stiffness matrix, respectively for the finite element system. {r} is the vector of 2N nodal points in the finite element idealization: {ṙ} and { r̈ } are respectively the nodal point velocity and acceleration vectors. In the case of earthquake excitation the load vector {R(t)} is a function of the nodal point masses and accelerations.

 

STATIC ANALYSIS

The first step is to establish the in situ stress state conditions using SIGMA/W that exist before the most important soil properties required for linear elastic model are unit weights and Poisson’s ratios while for elastic-plastic model, the material properties required for this model are unit weights, Poisson’s ratios, Young’s modulus and c- of the soil as listed in Table 1. The contours of vertical and horizontal stresses are shown in Fig. 3a and Fig. 3b, respectively for elastic plastic model. It was observed that contours of horizontal as well as vertical stresses for linear elastic as well as elastic plastic model found to be same. In both case of horizontal as well as vertical stresses, it can be observed that the stress increases from top to bottom of the dam, which is as expected. Also stresses decreases towards the edges of the dams. The maximum horizontal stress and maximum vertical stress found to be 720.25 kPa and 884.50 kPa, respectively.

SEISMIC ANALYSIS

The seismic analysis is carried out for linear elastic and nonlinear (elastic-plastic) 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- and damping ratio. For the seismic analysis, damping ratio value is considered as 10%. The modified time history is shown in Fig. 4. 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.

 


Effects of Nonlinearity

The contours of vertical stresses of linear and nonlinear soil model are shown in Fig. 5(a) and Fig. 5(b), respectively. It is observed that in both cases the vertical stresses are increases from top to bottom of the dam which is as expected.

Figure: 4 Modified time history of Kashmir earthquake (2005) with peak value of 0.24g. The maximum vertical stresses for linear soil model is 958.2 kPa and for nonlinear (elastic plastic) 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 tension decreases with nonlinearity of the soil.

 

 

The contours of horizontal stresses of linear and nonlinear soil models are shown in Figure 6 (a) and (b) respectively-

It is observed that in both the cases, the horizontal stresses increase from top to bottom of the dam which is as expected. The maximum horizontal stress for linear soil model is 753.69 kPa and for nonlinear soil model it is 808.94 kPa. This indicate that as the nonlinearity increases, stresses increases while minimum vertical stresses for these cases are found to be at the toe of dam which are -14.35 kPa and -8.32 kPa, respectively. It shows that effect of tension decreases with nonlinearity of the soil. The effect of nonlinearity was investigated on vertical as well as horizontal displacements. It was observed that both displacements increases due to nonlinearity. All the results of the seismic analysis of Nara Dam is summarized in Table: 2 shown below. It can be observed that the value of stresses and displacement increase due to the effect of nonlinearity of the soil.

 

CONCLUSIONS

The static and dynamic analysis of the Nara dam was carried out. It was found that the contours of horizontal and vertical stresses increases from top to bottom of the dam which is as expected. It was observed that the soil behave linearly during static loading but for seismic loads due to effect of nonlinearity, the soil stresses and displacements increase from linear elastic to nonlinear (elastic plastic) soil model. The value of maximum horizontal as well as vertical settlements are within permissible limit of 1% of the dam height as par as per IS: 8826-1978 [14]. In case of horizontal displacement effect of nonlinearity is very high almost double of the linear soil model.

Posted by: Md Asif Raja. in Science | Date: 05/01/2016

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