numerical analyses of rockfill dams, cut slopes and road embankments

317 Pages·2008·13.07 MB·English

5.4.1 Analysis During Construction . 86
5.4.2 Analysis During Impounding ..........................88
5.4.3 'Improved' Predictions ..............................89
5.5 CONCLUSIONS ......................................... 92
CHAPTER 6 NUMERICAL ANALYSIS OF WINSCAR DAM
6.1 INTRODUCTION ........................................ 134
6.2 DETERMINATION OF MODEL PARAMETERS ....................135
6.3 FINITE ELEMENT ANALYSIS ...............................135
6.4 CONCLUSIONS ........................................ 138
CHAPTER 7 FIRST-TIME SLIDES IN STIFF PLASTIC CLAYS
7.1 INTRODUCTION ........................................ 150
7.2 DELAYED SLIDES AND PROCESSES INVOLVED .................. 151
7.2.1 Swelling ......................................151
7.2.2 Softening .....................................1 53
7.2.3 Progressive Failure ...............................1 55
7.3 METHODS OF ANALYSIS .................................157
7.3.1 Available Methods of Analysis .......................157
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7.3.1.1 Limit Equilibrium Analysis ................... 158
7.3.1.2 Purpose Built Model .......................158
7.3.1 .3 Finite Element Analysis ..................... 158
7.3.2 Soil Model Used in the Thesis .......................1 60
7.4 RELEVANT AND ASSUMED SOIL PROPERTIES .................. 163
7.4.1 Cut Slopes .....................................164
7.4.1.1 Peak Strength ............................ 164
7.4.1.2 Residual Strength .........................165
7.4.1.3 Brittleness ..............................165
7.4.1.4 Pre-peak Stiffness .........................166
7.4.1.5 Coefficient of Earth Pressure at Rest ............ 166
7.4.1.6 Undrained Strength Profile ................... 167
7.4.1.7 Coefficient of Permeability ...................167
7.4.2 Fill Slopes ..................................... 169
7.4.2.1 Peak Strength ............................ 169
7.4.2.2 Residual Strength .........................170
7.4.2.3 Brittleness .............................. 170
7.4.2.4 Pro-peak Stiffness .........................170
7.4.2.5 Undrained Behaviour .......................171
7.4.2.6 Initial stresses due to Compaction ..............172
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7.4.2.7 Coefficient of Permeability ...................172
7.5 HYDRAULIC BOUNDARY CONDITIONS AND SURFACE EFFECTS ......173
CHAPTER 8 ANALYSIS OF CUT SLOPES
8.1 INTRODUCTION ........................................187
8.2 TYPICAL ANALYSIS .....................................188
8.3 PARAMETRIC STUDIES ..................................192
8.3.1 Effect of Residual Strength .........................192
8.3.2 Effect of Angle of Dilation ..........................193
8.3.3 Effect of Coefficient of Earth Pressure at Rest ............194
8.3.4 Effect of Rate of Softening ..........................197
8.3.5 Effect of Surface Boundary Suction ....................197
8.3.6 Effect of Slope Geometry ...........................199
8.3.6.1 Flatter and Deeper Slopes ...................199
8.3.6.2 Steeper and Lower Slopes ...................200
8.3.7 Effect of Dra nage at Base Boundary ...................201
8.4 DETERIORATION OF SURFACE CLAY .........................202
8.5 FURTHER DISCUSSION AND CONCLUSIONS ....................204
CHAPTER 9 ANALYSIS OF ROAD EMBANKMENTS
9.1 INTRODUCTION ........................................254
9.2 EMBANKMENT ON CLAY FOUNDATION .......................255
9.3 EMBANKMENT ON DRAINED FOUNDATION

WITH AN IMPERMEABLE SURFACE BOUNDARY 257

9.4 EMBANKMENT ON DRAINED FOUNDATION ...... 258

9.5 DISCUSSION AND CONCLUSIONS ............. 259
CHAPTER 10 CONCLUSIONS AND RECOMMENDATIONS
10.1 INTRODUCTION .......................................283
10.2 CONCLUSIONS .......................................283
10.2.1 Rockfill Dams ..................................283
10.2.2 Cut Slopes ....................................285
10.2.3 Road Embankments .............................287
10.3 SUGGESTIONS FOR FURTHER RESEARCH ....................288
10.3.1 Rockfill Dams ..................................288
10.3.2 Cut Slopes and Road Embankments ..................288
REFERENCES..................................................290
APPENDIX....................................................309
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CHAPTER 1
INTRODUCTION
1.1 GENERAL
The origin of rockfill dams can be traced back to California in about the middle of the 1 9th
century. Since then this type of dam has had a long and turbulent history (Cooke, 1984). Two
main types of rockfill dams have emerged, according to the nature and position of the
watertight element, namely: (i) that containing a relatively impervious internal earth core,
either thick or thin, central or inclined, and (ii) that with an upstream impervious membrane,
either of concrete or asphalt. Nowadays rockfill dams are the most numerous and the most
popular choice when constructing a new dam1 (Penman, 1986). In the search for
hydroelectric power, heights and volumes of the rockfill dams have been increasing, reaching
unprecedented heights (over 300m) in recent years.
In the beginning their design and construction was largely empirical and based on past
experience rather than on theory. With no intention of diminishing the important role of
experience, the advances made in the theory of soil mechanics started to change their
conception during the 1940's. In the past 30 years the major breakthrough in understanding
stress-strain-strength relations, particularly for rockfills, together with the development of
advanced numerical analyses has made it feasible to compute stresses, strains and
displacements in dams during construction, first impounding and subsequent operation. Today
finite element analysis using adequate constitutive laws is an essential tool to attain a good
and safe design of a rockfill dam.
Simulation of the rockfill behaviour in the field by laboratory tests is difficult and sometimes
impossible. This arises due to the coarse nature of rockfill materials. Laboratory tests require
large samples if representative behaviour is to be reproduced. The associated testing facilities
needed to incorporate such samples must also be large, and consequently such tests are
expansive and their number is usually limited. Because of this and the fact that a significant
factor of safety usually operates in rockfill dams, the stress-strn behaviour of rockfill
materials pre-peak has generally been modelled by a form of so-called the 'variable elasticity'
'If foundations allow and rockfill is available.
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constitutive model in which elastic moduli change according to the magnitudes of the stresses
(and strains). Problems have been experienced with this approach, both in deriving model
parameters from available test data and predicting displacement patterns which agree with
field measurements. It has been suspected that part of the problem lies in the failure to model
the plastic behaviour of rockfiU materials pre-peak. Alternative constitutive models
incorporating pre-peak plasticity are available in the literature, but only those based on the
critical state concept have so far been used for the finite element analysis of rockfill dams.
The first objective of this thesis was to see how good these alternative elasto-plastic models
are at predicting the displacement patterns of existing rockfill dams using parameters derived
from available laboratory test data. Bearing in mind that modelling of an earth core can create
a source of uncertainty in an analysis, only rockfill dams with upstream asphaltic membrane2
have been considered. For comparison purposes analyses using the models based on elasticity
theory are also included.
The delayed sliding of slopes cut in stiff plastic clays has been a subject of considerable soil
mechanics interest for a number of years. In Britain, studies of the problem have focused on
London Clay for which there is a well established history of delayed deep-seated sliding in
railway cuttings formed in 19th and early 20th centuries (see e.g. Skempton, 1977). More
recently a major survey conducted by the Transport and Road Research Laboratory (Perry,
1989) revealed that both motorway embankments and cuttings in similar clay strata have
suffered delayed superficial sliding.
Deep-seated slips in cutting slopes have been studied extensively. It was recognised that the
very slow rate of equilibration of depressed pore pressures following excavation played an
important part in the explanation of delayed sliding (Vaughan and Walbancke, 1973).
However, analyses of the slips by conventional limit equilibrium methods have shown that the
average operational drained strength is significantly less than the peak strength as measured
in the laboratory (Skempton, 1964). Two explanations have often been offered for this
behaviour. The first is a reduction of the strength of stiff plastic clays to a 'fully softened'
value (Skempton, 1970), sometimes attributed to softening on fissures (Terzaghi, 1936). The
fully softened strength is often assumed to be that at critical state (Schofield and Wroth,
1968). This has lead to an empirical method of design in which the drained strength envelope
measured in the laboratory is adjusted by reducing the cohesion intercept to a nearly zero
value (Chandler and Skempton, 1974).
2An upstream membrane of asphaltic concrete is thin and flexble, and has a little bearing
on rockfill deformation during first reservoir impounding and subsequent operation.
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The second explanation involves progressive failure. When loaded, brittle soils generally reach
a peak strength which reduces to a residual strength with further straining. At rupture
involving progressive failure, strains along the f nal rupture surface are such that peak
strength is not mobilised uniformly. At collapse, some of the soil has already 'failed' and its
strength has dropped towards the residual strength, some of the soil has not yet reached peak
strength, and only a small part of the soil along the rupture surface is at peak strength. Thus,
the average operational strength mobilised along the eventual rupture surface at collapse is
less than peak strength, although it must be greater than residual strength.
Progressive failure has been suspected to play a part in slope failure for 25 years (Bjerrum,
1967; Turnbull and Hvorstev, 1967; Peck, 1967; Bishop 1967). The mechanism is complex
and analysis is difficult. It has been analyzed for simple idealised situations by the finite
element method at a surprisingly early date (Hoeg, 1972). Recent improvements in numerical
techniques arid computing power now enable such analyses to be performed in realistic
situations, as demonstrated by the analysis of the collapse of the Carsington embankment
(Potts eta!, 1990). These and other analyses (Dounias eta!, 1988, 1989) have shown that
the role of progressive failure can be significant. Thus progressive failure is the likely principal
cause of a discrepancy between the operational strength on the rupture surface of a slip in
a clay slope and the peak strength measured in the laboratory.
The stability of clay embankments has been studied less extensively. Construction of an
embankment typically generates excess pore water pressures in a saturated clay foundation,
and as these dissipate with time stability improves (Bishop and Bjerrum, 1960). However,
placement and compaction of plastic clays as fill can generate quite high pore water suctions
(Vaughan et a!, 1978), and in embankments of modest height, typical for road works, long-
term equilibrium pore water pressures are likely to be higher than those at the end of
construction. As swelling occurs there is potential for the development of deep-seated
delayed slides in road embankments of plastic clays similar to those occurring in cutting
slopes.
The behaviour of clay slopes is more complicated at shallow depth, where there are seasonal
changes in soil suction and cyclic shrinkage and swelling. This may lead to cracking, increased
permeability, softening and loss of strength in addition to that due to monotonic swelling. The
depth of the slips so far observed in motorway slopes is typically close to or within the zone
influenced by these effects.
The purpose of the research program described in the second part of this thesis was to review
the history of slides in both railway cutting and road embankment slopes formed in typical
British plastic clays, and to examine the mechanisms involved using the finite element
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techniques developed for the investigation of the Carsington collapse. However, in the present
work improved simulation of a delayed collapse was modelled using coupled consolidation
(swelling). As there is a better history of deep-seated delayed sliding for cutting slopes they
were analyzed first, in order to calibrate the method of analysis against field experience.
Particular aims were to: (i) review relevant material properties, and hydraulic boundary
conditions, (ii) quantify the role of progressive failure in reducing the average operational
strength of in-situ stiff plastic clays and clay fills, derived from them, at collapse for both
railway and motorway slopes, (iii) examine the potential for the development of deeper
seated, longer term slides in road embankment slopes, including those where shallow slides
have already occurred and been repaired, and to reconcile the conclusions drawn with the
history of failure in railway cutting slopes, (iii) indicate how the trends determined by the
analyses might be monitored and controlled in the field. Representative slopes were analyzed
on a parametric basis to examine these questions.
1.2 THESIS LAYOUT
The work presented in this thesis is divided into the following chapters:
Chapter 2 briefly describes the finite element method of analysis which has been used
throughout the thesis. Some attention is given to those aspects of the method which are of
interest to the research work presented here, and, in particular, manner in which the Imperial
College Finite Element Program (ICFEP) deals with them.
Chapter 3 discusses some factors of importance in the finite element analysis of embankment
dams (layered analysis, stiffness of simulated layer and compaction stresses), considers
typical stress paths occurring during dam construction and reservoir impounding, and reviews
the constitutive models that have been used to describe the behaviour of fill materials.
Chapter 4 describes two of Lade's elasto-p astic constitutive models that have been used here
to characterize the behaviour of rockfills. The way they are implemented into ICFEP is
outlined, their proper implementation is validated, and a preliminary appraisal of their
capabilities to accurately capture the observed behaviour of granular material for various
stress paths is given.
Chapter 5 presents results from analyses of Roadford dam both during its construction and
first reservoir impounding using three dfferent constitutive models. One of these was a
'simple' non-linear elastic perfectly plastic model. The others were 'complex' Lade's work-
hardening (-softening) elasto-plastic models. Large diameter oedometer and triaxial tests for
Roadford rockfill were available, and the procedures employed for determnation of the model
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parameters are presented in some detail. The models are compared in terms of their capability
of reproducing the full range of the observed rockfill behaviour in the laboratory and of
predicting displacement patterns in agreement with field observations.
Chapter 6 further checks the capabilities of both Lade's models by using them to analyze
Winscar dam. For this rockfill dam adequate laboratory test data to derive model parameters
were also available. Observed movements during dam construction and reservoir filling and
predictions of these movements based on elastic finite element analysis enabled useful
comparisons to be made.
Chapter 7 deals with the processes involved in delayed sI des of cut and embankment slopes
made in or of stiff plastic clays. It discusses the mechanism of progressive failure and the
various parameters affecting it. It briefly reviews the available methods of analysis for
progressive failure and outlines the soil model used during the course of this research. Finally,
relevant and assumed soil properties are presented together with a discussion of hydraulic
boundary conditions and surface effects.
Chapter 8 presents a parametric study of progressive failure in cut slopes. Effects of residual
strength, angle of dilation, coefficient of earth pressure at rest, rate of softening, surface
boundary pore water suction, slope geometry and drainage at the base boundary are
discussed in some detail. The chapter concludes with analyses in which a higher permeability
layer due to deterioration of the surface clay is simulated in an attempt to model superficial
sliding.
Chapter 9 analyzes road embankments built on different types of foundation. The emphasis
is on reproducing shallow slides by adopting a higher permeability zone near to the slope
surface and by invoking progressive failure. The risk of longer term deep-seated sliding, even
after a shallow slide has occurred and been repaired, is a so examined.
Chapter 10 summarises the main conclusions that are drawn from the thesis and provides
suggestions for further research.
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CHAPTER 2
FINITE ELEMENT ANALYSIS
2.1 INTRODUCTION
The finite element method (FEM) is a numerical technique which can provide approximate
solutions to a wide variety of real engineering problems including geotechnics. Its success,
when analysing any boundary value problem, is due to the satisfaction of the basic solution
requirements, namely: (i) equilibrium of forces, (ii) compatibility of displacements, (iii)
continuity of flow (coupled consolidation analyses), (iv) material constitutive laws, and (v) the
boundary conditions.
The Imperial College Finite Element Program (ICFEP) has been used for all analyses reported
in this thesis. ICFEP uses the displacement based FEM and is capable of handling two
dimensional problems, namely plane stress and strain, and problems involving axisymmetric
geometries. In the later case the material behaviour and/or boundary conditions need not be
axisymmetric. The program deals with material and geometric non-linearities and has been
developed specifically for geotechnical problems. In the current research only plane strain and
full axisymmetric problems (geometry, soil properties and boundary conditions all
axisymmetric) have been considered.
This chapter briefly describes the general principles of FEM, the basics of the technique used
in the present research for solution of the non-linear finite element equations and some
aspects of the method when applied to geotechnical problems. Finally, the chapter concludes
with the formulation and time integration of the finite element equations needed for a coupled
consolidation analysis together with the results from a validation exercise.
2.2 FORMULATION OF FINITE ELEMENT METHOD
Formulation of the FEM can be found in standard finite element textbooks (e.g. Zienkiewicz,
1977; Naylor eta!, 1981; Bathe, 1982). The basic steps in the FEM can be summarised as:
Ii) element discretization, Cii) displacement approximation, (iii) formulation of element
equations, (iv) assemblage of global equilibrium equations, Cv) boundary conditions, (vi)
solution of global equilibrium equations, and (vii) interpretation of the results.
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2.2.1 Element Discretization
The first step in the analysis is the discretization of the problem domain into a number of
simple elements connected at their nodes to form a mesh. The simplest shape of an element
for plane strain or axisymmetric analyses is a triangular or quadrilateral with straight sides and
nodes located at the element corners (Zienkiewicz, 1977). For problems involving non-linear
material properties, curved boundaries and/or curved material interfaces higher order elements
with mid-side nodes should be considered. ICFEP uses quadrilateral elements with either four
or eight nodes.
2.2.2 Displacement Approximation
In the displacement based finite element method the primary unknown quantity is the
displacement field, df, which varies over the problem domain. In plane strain and full
axisymmetric analyses the displacement field is characterized by the two global displacement
components, u and v, in the x (r) and y (z) coordinate directions respectively. Over each
element these displacement components are assumed to have a simple polynomial form which
can be expressed as a function of the nodal displacements, d

d1 = Ndde (2.1)
where d =[u,v]T, de=EUi,ViIU2 V2,...UnVnJT and Nd is the element displacement interpolation
matrix consisting of the shape functions, Nd,', whose polynomial order depends on the
number of nodes, n, in the element (see e.g. Naylor eta!, 1991).
The essential feature of the element approximation described above is that the variation of
the unknown displacement field within an element, d, is expressed as a simple function of
the displacements at the nodes, d1. The problem of determining the displacement field
throughout the finite element mesh is therefore reduced to determining the displacement
components at a finite number of nodes. These nodal displacements are oftenreferred to as
the unknown degrees of freedom.
The accuracy of a finite element analysis depends on the size of the elements and the nature
of the displacement approximation. For the accuracy to increase as the elements become
'In an isoparametric finite element formulation, which is used by ICFEP, the element
displacement field and element geometries are approximated using the same shape functions.
This is achieved by using shape functions based on the natural coordinate system. A
quadrilateral element in the global coordinate system (x,y) is mapped onto a square parent
element in the natural coordinate system (,i)) of dimensions 2x2 units (see e.g. Naylor et a!,
1981).
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smaller, the displacement approximation must satisfy certain compatibility conditions. In order
to avoid gaps and overlaps occurring when the domain is loaded, the displacement
components must vary continuously within each element and across each element side. This
can be achieved by ensuring that the displacements of an element side depend only on the
displacements of the nodes situated on that side. In addition, the displacement approximation
must allow the element to undergo rigid body motions and constant straining if it so wishes.
Use of a simple polynomial approximation satisfies these requirements.
Stresses and strains are treated as secondary quantities and can be evaluated within each
element using the definition of strains (see e.g. Zienkiewicz, 1977) and applying the material
constitutive law2

e = Bd (2.2)

0 = D (2.3)
where B is the element strain-displacement matrix and 0 is the constitutive matrix relating the
stress vector, u, to the strain vector, €.
2.2.3 Element Equations
To satisfy equilibrium and the constitutive behaviour, the principle of virtual work is invoked
(see Zienkiewicz, 1977). For a single finite element of linear elastic material subjected to small
(infinitesimal) strains3 this results in the following set of equations
Kd1 = R (2.4)
where K1= J (BT DB)dV is the element stiffness matrix, d is the vector of the corresponding
nodal displacements (the primary unknown), and Re is the vector of the corresponding nodal
forces.
2.2.4 Global Equations
The next step in the formulation is the assembly of the separate element equilibrium equations
to give the global equilibrium equations for the whole body
2To illustrate the method, a linear elastic material will be considered.
3Large (finite) strain formulation is present in ICFEP (see Dounias, 1987), but it is beyond
the scope of this thesis.
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