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Spoil stability considering progressive failure
Mining Science and Technology, 3 (1986) 127-139
127
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
SPOIL STABILITY CONSIDERING PROGRESSIVE FAILURE R.N. Chowdhury, V.U. Nguyen Department of Civil and Mining Engineering, University of Wollongong, Wollongong, N.S.W. (Australia)
and J.A. Nemcik * ACIRIL, P.O. Box 551, Rockhampton, Queensland, (Australia) (Received July 8, 1985; accepted August 15, 1985)
ABSTRACT
In spoil piles, shear strength often decreases significantly as a consequence of moisture softening. Moreover, spoil material exhibits characteristic brittleness so that overstressing can also lead to a marked decrease in shear strength. Progressive phenomena are always important in such circumstances and in this paper an approach is outlined to include failure progression within a two-wedge limit equilibrium model. A comprehensive approach is outlined and it is suggested that the factor of safety be
obtained as a function of the residual factor which has values between 0 and 1, corresponding to no local failure on the one hand and complete softening of the slip surface on the other. It is shown that the extent of the softening zone can be obtained from simple finite element analysis. The usefulness of this approach for updating spoil stability during its life is highlighted. The significance of the direction or mode of failure progression is also discussed in the paper.
INTRODUCTION
ments. In strip mining operations, which have proved to be both feasible and economical in Australia, it is of the utmost importance to ensure the continued stability of spoil piles. Failures of spoil piles cause disruption of operations, necessitate substantial expenditure for clearing the slipped spoil masses, and cause associated delays in production. Moreover, such failures may lead to the loss of some of the coal reserves. The objective of this paper is to highlight the role of progressive phenomena in reducing
Surface mining activities for the production of coal are increasing at a rapid rate in Australia. Assessments of slope stability are required throughout the life of a surface mining operation. The success and efficiency of such an operation depend primarily on the reliability and accuracy of stability assess-
* Formerly of the University of Wollongong.
128 the stability of spoil piles. A direct consequence of progressive movements and moisture-softening within spoil materials is that the values of shear strength are reduced. Therefore, estimates of stability for a given spoil pile (e.g. in terms of a safety factor F ) which are reliable and accurate at a particular instant in time must, in due course, be revised and updated in the light of special situations and circumstances. In particular, if additional data become available about the extent to which softening of spoil has taken place, or about movements which have occurred, then the values of F would have to be recalculated. However, in this paper it is proposed that the relationship between the extent of softening along the potential slip surface on the one hand, and the factor of safety F on the other hand, be established from the very beginning. F r o m these relationships, the value of F relevant at any particular time and for any given situation can be obtained and thus, it is hoped, new analyses at short notice will be avoided. In short, the process for updating spoil-pile stability can be made efficient by supplementing any existing charts or tables, relevant to a particular project, with curves showing how the value of F decreases with progressive softening and decreasing shear strength along a potential slip surface. Stability assessments must be based on: (a) Understanding of the relevant failure mechanisms and the development of appropriate computational models; (b) Use of a suitable and accurate method of stability analysis; (c) Reliable data concerning shear strength of spoil and pit-floor materials, and other important material parameters; (d) Appropriate pore-water pressures within the spoil piles. There will always be considerable uncertainty with respect to pore-water pressures, and therefore parametric studies may be desirable in practice. Alternatively, different studies may be made for (a) spoil without water table
and (b) spoil with the water table, as it might be expected to develop on the basis of experience and judgement.
FACTORS CONTROLLING SPOIL STABILITY The factors which primarily control spoil stability during and immediately after construction are: (a) Construction procedures and construction sequence; (b) Shear strength characteristics of spoil materials and, in particular, strain-softening and related phenomena; (c) Pore-water pressure developed in spoil piles; (d) Water infiltration and wetting sequence; (e) The Susceptibility of spoil to lose shear strength during wetting, i.e. a moisturesoftening phenomenon. Investigations related to open-strip coal mining in Australia have revealed [1] that failures often occur on planar surfaces of discontinuities forming at least two wedges. The lower wedge moves outwards at the toe and the upper wedge moves downwards, so forming an exposed escarpment with an angle of the order of 60 °, i.e. a relatively steep rear failure surface OB (Fig. 1). An interwedge plane OC is part of the failure mechanism. In these flat-bedded coal measures, the basal slip
c
A
/
O
Fig. 1. Two-edge model showing softened part x of basal slip surface (progression from the toe). The residual factor R = x / ( L 1 + L z ) where L 1= AO and L 2 = OB. Arrows indicate potential direction of movement of wedges if failure develops.
129 surface has only a few degrees inclination as it follows the original floor, i.e. the base of the coal. It has been pointed out by Richards [2] that water in the spoil piles controls stability through its influence on pore-water pressure and shear strength. Moreover, tests have shown that the spoil material exhibits marked strain-softening behaviour. For example, in one test the peak shear strength parameters were Cp = 130 kPa and epp = 49 ° and the residual shear strength parameters were c r = 125 kPa and % = 15 °. Such a drastic reduction in the friction angle would have a significant influence on the mechanism of failure. Different parts of the spoil pile would suffer different degrees of relative deformation and, therefore, only localised zones of overstress and of strength decrease may develop initially. Once such failures have developed there may be a progressive increase in the size of the area within which the shear strength is reduced to the residual value. The potential for progressive failure is high because of the high brittleness indicated by the marked difference between peak and residual shear-strength parameters. The subject of progressive failure has received a great deal of attention in the recent past but primarily in relation to natural slopes and excavations. The basic concepts and recent developments have been discussed over a number of years, and the attention of readers is directed to a comprehensive review by Chowdhury [3]. It should be noted, however, that little attention has so far been given to the role of progressive failure in spoil-pile stability. An important factor in the case of spoil stability is the role of moisture softening in producing the conditions under which progressive failure may occur. Therefore the extent of water infiltration and the wetting sequence are of considerable importance. Other important factors include the development of tension failure in the spoil and the potential
for slip at the interface between old and new spoil. The long-term stability of spoil may not appear to be of immediate concern to the geotechnical engineer. Nevertheless, delayed spoil failures can be sources of disruption in rehabilitation works or coal-retrieval operations, depending on a number of different factors. It may be necessary, therefore, to monitor the stability of spoil piles over a number of years and to use observational data so obtained to update the results of stability analyses. The primary cause of delayed changes in the performance of a spoil pile is infiltration from rainfalls during the lifetime of the spoil pile. As a consequence of infiltration and moisture movement, pore pressures may increase significantly, shearstrength parameters may undergo further decrease and there may be progressive movements. Associated with these changes, there would be increased strains in some regions within the spoil pile and relative deformations along a potential slip surface. Thus progressive phenomena are of key importance to spoil stability in the short term as well as in the long term. It should be a central feature of planning and decision-making strategies to link stability assessment with evidence concerning progressive changes within spoil piles. Analyses must be updated as significant changes take place and information on these changes becomes available as part of observational procedures.
AN APPROACH TO SAFETY FACTOR
UPDATING
THE
Basic wedge model Modelling of slope-stability problems based on wedge mechanisms is a well-established procedure, and analyses for spoil dumps based on the wedge mechanism have been performed in Australia for a number of years.
130
There are many ways of performing wedge analyses and the authors have described their own version of the model in a recent publication [4]. Essentially, it differs from other conventional approaches in that components of forces are balanced in the vertical direction (similar to the Bishop method of slices associated with slip surfaces of circular shape). At the same time, however, cohesion and friction along the interwedge boundary are taken into consideration as well as the pore-water pressure on that boundary. Few other wedge models include these features except the unpublished model of Coulthard [5]. The solution method developed for the model works very well and there are few computational problems. Comparative studies are required to investigate further the scope and reliability of the authors' model. Residual factor
Consider a potential failure mass with basal slip surface AO of length L 1 (Fig. 1) and let the shear-strength parameters be denoted as follows: peak values: cpa, %1; residual values: crl, q~r~. Let the rear slip surface OB have a length L2, and let the shear-strength parameters of the spoil material (which are generally quite different from those of the basal slip surface) be denoted as follows: peak values: %2, %2; residual value: c~2, qP~2. The total length of the two slip surfaces is L = L a + L 2. A portion x of this total length may, at any given stage in the life of the spoil pile, have reduced in shear strength so that only residual-shear-strength parameters are operative over that length. Now a residual factor R may be defined as the ratio of x to L, i.e. R = x/L
= x/(La
+
L2)
(1)
Depending upon construction method and
sequence, spoil height, spoil characteristics and other factors, the residual factor may have either a small or a significantly high value. The value of R will, however, tend to increase with time and will reflect the changes associated with moisture infiltration. Considerable uncertainty is usually associated with the actual value of R at any given time. Therefore, it is proposed to incorporate a procedure for spoil stability analysis in which R may be varied between the extreme limits of 0 and 1. Moreover, it should be noted that the overall safety factor, which decreases with increasing value of R, also depends on the mode of failure progression. A given value of R may be reached in various ways, e.g. (see Fig. 2): (a) Strength decrease progressing from the top or crest along the rear failure surface; (b) Strength decrease progressing from the bottom or toe along the basal failure surface; (c) Development of progressive failure from both the crest and the toe; (d) Development of localised failure near the intersection of the two slip surfaces and its progression outwards in the direction of the toe, or the crest, or both. For the same value of R, the value of overall safety factor will be different for different modes of failure progression. However, the bounds to the value of overall
A
D
0
Fig. 2. Wetting front DEFG in a spoil pile with a potential two-wedge failure mechanism. Arrows indicate different ways in which progr,ession of strength reduction or of softening may develop,
131 safety factor m a y be determined for all practical purposes by considering the first two modes mentioned above, i.e. progression from the crest and progression from the toe.
in which r L = L 1 / L 2 is the length ratio of the basal to rear slip surface. Note that, when R 2 = 0 , i.e. R 1 = 1, R = L 1 / L as before. The weighted average of cohesion is
Incorporation of failure progression in the wedge mode
cwl = Crl, x > L l
Modified values of cohesion and friction are required for the two parts of the slip surface for any given value of the residual factor. Failure progression may be incorporated most readily in the numerical model of wedge stability if equivalent shear strength parameters along the basal and rear failure surfaces are calculated first. For any non-zero value of the residual factor, these equivalent parameters may be obtained as weighted averages. It is useful to consider cohesion and friction separately.
Cw2=R2cr2+(1-R2)cp2, x > L l
(a) Weighted average of cohesion at a given stage of failure progression (1) Consider that progression occurs from the toe inwards and that it has reached a point within the basal slip surface AO of the potential wedge (Fig. 1). The weighted average of cohesion is
(6a)
for basal slip surface AO, and (6b)
for rear slip surface OB.
(b) Weighted average of friction angle The friction angle cannot be averaged in the same way as the cohesion, since the frictional part of the shear strength is dependent on normal stress which varies from point to point along the slip surface. The weighted averages q0wl and Cpw2 of the friction angles relevant to the two slip surfaces may be defined on the basis that the frictional part of the shearing resistance remains unaltered in the averaging process. (1) Consider failure progression from the toe but within the basal slip surface, then the weighted friction angle is given by the following equations. Along basal slip surface AO: x
Cw ' = C r l R 1 -4:- C p l ( 1 - - R 1 ) ' x ~ L 1
(2a)
tan
~9wl £L,( On - -
for basal slip surface AO, and Cw2 = Cp2 , X ~
Ll
-~-
tan qgrl£ (o n
u)dx
LI
(2b)
for rear slip surface OB, where
R 1 = X l / L l = ( L / L 1 ) R , x <~n 1
u)dx
+ t a n q)plf (On-- u)dx, x ~< LI, R 1 ~< 1,
(3)
(Note: R = L 1 / L when xl = L> i.e. R 1 = 1) (2) Consider now that failure progression has extended from the toe along the basal slip surface and beyond the point O; i.e. the value of x, the softened or strength-reduced part of the slip surface, is greater than L 1. Define
(7a)
where % and u are respectively the normal stress and pore water pressure at any given point at a distance from the toe of x (or more precisely over the length dx). Along rear slip surface OB: qOw2 = qOp2, X ~
L 1, R 1 ~< 1
(7b)
It is easy to show that R 2 is related to R as follows
(2) Consider failure progression from the toe and extending beyond the point O so that x>L v Along basal slip surface AO,
R = ( L 2 / L ) ( R 2 + rL) ,
qgwl = (/)rl, X >
R 2=(x-L1)/L
2 , x > L 1.
(4)
(5)
L 1.
(8a)
132
EXTENT ZONE
Along rear slip surface OB, L2
tan epw2L ((l n
-
-
SOFTENED
OR
FAILED
u)dx 1=
tan q%2Lx'(on - u ) d x 1 + tan epp2 I.2(On
OF
u)dxl, - -
1
x > L1
(Sb)
where Xl = x - L 1 and dxl = dx. (When Xa = 0, x = L1; when Xl = L2, x = L)
Modification of the computer program The computer program for the wedge model was modified to include the above features. It was found convenient to perform the calculations in terms of the effective weights of the wedges. The computation of effective normal stresses at every point along the slip surfaces is not necessary. The computer program includes the search for the critical wedge. Given the inclination of the basal slip surface, the spoil height and the top surface configuration of the spoil pile, the program automatically finds the critical location of points O and B (Fig. 1). This is repeated for every value of the residual factor R. Thus the critical wedge for one value of R may not be the same as the critical wedge for another value of R. Although the differences in the location of point O are generally not significant, the capability of the program to locate the critical wedge for any mode of failure progression and for any extent of progressive failure is a very desirable one. For simplicity, it may be desired to keep the critical wedge fixed as that wedge relevant to either R -- 0 or R = 1 and then to perform analyses for various values of R. Thus, one may plot the overall safety factor F against the value of R for a fixed critical wedge or for a true changing critical wedge. Moreover, in either case the program is capable of considering failure progression either from the crest or from the toe.
As stated earlier, one approach for the determination of the extent of the softened or failed zone would be to have observational procedures from which it may be possible to infer a value of the residual factor R at any given stage in the life of a spoil pile. Monitoring of spoil piles is indeed very desirable for further progress in understanding the transition from stability to failure. However, the interpretation of observational data is by no means easy, and a discretization approach to study the stress-deformation behaviour of spoil may prove to be helpful. For instance, the finite element method may be used to study the development of zones of overstress within a spoil pile and to predict a value of the residual factor R. Richards [2] used a non-linear finite element model considering sequential construction of the spoil pile and three types of material, n a m e l y : (a) unsaturated spoil above groundwater level, (b) saturated spoil below groundwater level, and (c) material below the floor. The non-linear relationships for bulk modulus K and shear modulus G were based on interpretation of the shear-strength data in terms of hyperbolic equations. Plots of stress and .strain contours and displacement contour were obtained and on the basis of these an interpretation was made of the mechanism of spoil-pile failure. One drawback of sophisticated finite element procedure is that detailed and accurate data must be made available. Another drawback of such sophisticated procedures is that the selection and interpretation of data, as well as the performance of stability analyses, are time consuming processes. Where the finite element procedures are used only to supplement limit equilibrium studies, relatively simple analyses would be desirable. Moreover, for a very brittle material it may be sufficient to perform linear elastic analysis incorporat-
133
ing an appropriate failure criterion. Simple linear elastic finite element analyses were performed to demonstrate that the extent of the failed zone and hence the value of R may be determined readily. This value of R for any stage of a spoil pile and for given pore-pressure conditions may then be used in conjunction with the available results of limit equilibrium studies to obtain the safety factor relevant to a given stage in the life of the spoil pile. Consistent with accepted geotechnical practice the following failure criterion (Mohr - C o u l o m b ) was used: Failure or overstress occurs if 1- > ~-f
(9)
in which ~-, the shear stress, is given by
(lO) and rf, the shear strength, is given by ~-f = Cp COS q~p + ½(61 + O3) s i n q0p .
(11)
o 1 and o 3 are respectively the major and minor principal total stresses, 8] and 63 are the corresponding effective stresses.
TYPICAL RESULTS--SAFETY FACTOR DURING FAILURE PROGRESSION A spoil pile with the geometry shown in Fig. 3 was considered for analysis. The unit weight of the spoil was assumed to be 1900 k g / m 3. The following shear-strength data was assumed for the calculations. For basal plane
iH5,~5)
(0.0)
[3~70,20) gL OOR
Fig. 3. Geometry of spoil pile considered from analyses with failure progression from crest or toe (the coordinates are in metres). One position of water table is also shown.
of weak material, cpap = 15 ° and cpl, = 8 ° , Cap = 100 kPa and c2, = 80 kPa. For spoil material (and rear slip surface), ~2p
=
32° and q02r = 29 °,
c2p = 200 kPa and C2r = 100 kPa. The first set of analyses was made without considering any water table. Moreover, the vertex O of the critical wedge was allowed to change for different values of the residual factor. The decrease of the factor of safety with increase in R is shown in Fig. 4. The upper curve is for progression, from the toe inwards and the lower curve is for progression from the crest downwards. It may be noted that, for the latter case, the curve does not pass through all the points. This is a consequence of allowing the critical wedge to change for each value of the residual factor. It may be noted that, for any given value of residual factor, progression from the crest is more critical than progression from the toe, i.e. lower safety factors are obtained if progressive failure develops from the crest. Similar results have been noted in respect of soil slopes with cylindrical slip surface (e.g. [6]). Another set of analyses was made considering the water table to be located as shown in Fig. 3. As expected, the presence of the water table reduced the factor of safety at any given value of R and for a given mode of progression. However, the trend of the results was the same as for the case with no water table. The shaded area in Fig. 5 shows the bounds within which the rear slip surface and the inter-wedge plane may lie for all values of R. Analyses were also made considering a fixed critical wedge relevant to the first analysis, i.e. for the case when residual factor R = 0. As R increases, the same critical wedge is considered to be relevant for all analyses. Thus, the vertex O remains fixed for all analyses and for both modes of failure progression. The results
134 1.8
1.7 e
1.6
1.5
(a)0
nO
<~
•
1.4
U-
>FUJ M-
1.3
U3 1.2
1.1
1.O
0.O
r
I
r
l
t
0.2
0.4
0.6
0.8
1,O
RESIDUAL
FACTOR
R
Fig. 4. Factor of safety F as a function of residual factor R for problem geometry in Fig. 3 considering failure progression from the toe (curve a) and failure progression from the crest (curve b).
with and without water table are shown in Fig. 6. In general, it was found that the curves are relatively smooth and the results consistent when a fixed, critical wedge is considered. There are few, if any, odd results of
(300,20) (0,0)
FLOOR
Fig. 5. Shaded area shows the boundaries of the region in which the rear slip surface and the inter-wedge plane may lie for any value of the residual factor R.
computation, and no interference or overlap between curves for toe and crest progression. The use of a fixed critical wedge can be justified if one assumes that the potential failure mechanism is already in place before progression becomes evident. Once a continuous slip surface has been developed, one may disregard the possibility that slip will then take place along a different surface with further development of failure progression. A designer may however wish to prepare two sets of curves from the computations, one set with a variable critical wedge and the other set with a fixed critical wedge. If there are any significant differences or anomalies, these can then be detected at the very outseL
135 1.8
1.7
1.6
1,5
j(b)
or
© i.r.)
1.4
(d)
ii >.-
I...-
1.3
uJ u_
<:
CO
1.2
1.1
1,O O.O
0.2
0.4 RESIDUAL
0.6 FACTOR
0.8
1,O
R
Fig. 6. Variation of safety factor R with fixed position of critical wedge corresponding to R = 0; with no water-table progression from toe (curve a), and from crest (curve b); with water-table progression from toe (curve c), and from crest (curve d).
TYPICAL ZONE
RESULTS
THE
SOFTENED
To investigate the feasibility of using simple finite element analyses for predicting the extent of the softened or overstressed zone, several studies with different deformation and strength parameters were made. For each study, three sets of geotechnical parameters are required, one each for (a) main b o d y of spoil, (b) a weak layer of softened material at the interface between spoil and floor, and (c) the floor itself. Considering a cohesion value Cp = 0.1 M P a for the spoil and cp = 0.015 M P a for the weak layers, a high friction angle q0p = 36 ° for the
spoil and a relatively low friction angle q0p = 15 ° for the weak layer, overstressing was found to occur only in the weak layer. The influence of the values of elastic modulus E on the number of failed elements was found to be negligible. For instance, the value of E was varied from 5 M P a to 500 M P a for the spoil, from 5 M P a to 500 M P a for the weak layer and from 1000 M P a to 100,000 M P a for the floor. Quite clearly, a very weak basal plane relative to spoil will ensure that the value of R l = 1, and that the value of the residual factor R = L1/L. It should be noted, however, that the deformations and strains which may determine the conditions for progression of failure are very much dependent on the
136
relative values of E. Detailed analysis to investigate relative deformations and strains is, however, outside the scope of this paper. Table 1 shows the data and summary of results concerning failed elements with the first set of analyses. With considerably lower values of shear strength parameters for the spoil, overstressing spreads over a very large area of the pile. For instance with Cp = 0.05 MPa and epp = 15 ° for the:spoil, and Cp = 0.05 MPa and q~p = 3 ° for the weak layer, almost all the elements are overstressed except a few at the top. Thus, such a weak material would be very unstable. This refers to a residual factor close to unity, i.e. R - - 1 . U s u a l l y the geotechnical engineer would be concerned with a situation which is not so extreme. In fact very interesting results were obtained for values: Cp = 0.05-0.1 MPa, epp = 30 ° (spoil), Cp=0.05 MPa, efp= 5 ° (weak layer). The residual factor in such cases was found to be greater than the first set, i.e. R 1 > 1 and L1/L
Fig. 7. Overstressed zone indicated by finite element analysis for the following parameters: (a) spoil: E = 5 MPa, ~ = 0 . 3 , C p = 8 0 kPa, epp=30 ° , (b) Weak basal plane E = 5 MPa, ~ = 0 . 3 , c p = 5 0 kPa, % = 5 ° , (c) Floor: E = 100,000 kPa, ~ = 0.3, Cp = 900 kPa, q% = 35 °.
approaches a value of about 0.9 for Cp = 0.05. It is interesting to find that the calculated results are sensitive to the value of Cp for spoil given that other parameters are realistic. These results were found to be very much in accord with previous finite element studies of spoil piles using somewhat similar shear strength parameters [2,7]. This qualitative agreement confirms the view of the writers that, for the purposes of assessing the approximate size of the overstressed zone, simple finite element analyses may suffice. Figure 7 shows the size of the overstressed or failed
TABLE 1 D a t a for analyses in which failures were identified mainly in the weak layer at the base of spoil Parameters Cp ( M P a )
% (degrees)
Spoil 0.1
36
Weak layer 0.015
15
Poisson's ratio, u
0.3
0.3
R a n g e of values of modulus, E ( M P a )
5-500
5-500
Floor 0.9
35 0.3 1000-100,000
Comments Overstressing of failure limited to whole of weak layer Same as above Same as a b o v e Same as above
Notes: (1) The above results indicate that for the given shear strength p a r a m e t e r s a residual factor R = L1/L (i.e. R 1 = 1) would be operative over a wide range of modulus values. (2) This conclusion was f o u n d to b e u n c h a n g e d even with considerable variations of the values of spoil parameters. For instance, with Cp = 0.1 MPa, % = 50 ° (floor), Cp = 0.1 MPa, q% = 30 ° (spoil) a n d cp = 0.1, q% = 10 ° (weak layer), there was overstressing of 40 out of a total of 46 elements of the basal weak p l a n e a n d again n o failures in the spoil above or floor below.
137 zone for one of m a n y sets of parameters used as part of the present investigation.
DISCUSSION OF THE APPROACH AND RESULTS A n important aim of this paper was to present a comprehensive but simple approach for stability assessment of spoil piles, taking into consideration the zones of overstress or softening. It is important to understand that the factor of safety of a spoil pile is not a fixed or constant quantity. Once sets of data have been prepared for use in stability studies, there is a tendency to consider that the results have significance beyond the stage or situation to which the data and analysis are relevant. This tendency is due to a neglect of strain-softening and moisture-softening phen o m e n a and due to a lack of emphasis on progressive failure. In published studies of field and laboratory investigations (e.g. [2,5,7]), the importance of progressive p h e n o m e n a has been brought out very clearly. However no effort has so far been made to modify conventional limit equilibrium approaches for spoil piles to include the progression of failure. In particular, the two-wedge model has been used as if it relates to a perfectly plastic material under well-defined and relatively unchanging environmental conditions. In this paper emphasis has been given to the fact that the factor of safety is a variable, the value of which changes with time as environmental factors influence the spoil pile during its life. The value of safety factor F is influenced significantly by the extent to which softening has occurred within a spoil pile. Typical curves showing the variation of F with the residual factor R have been plotted. One might have expected a sharp break in any such curve where R = L1/L (i.e. R 1 = 1) because of the biplanar nature of the slip surface. However, it is interesting to note that
there is a relatively smooth transition and that the curves do not exhibit a break or knee at any stage. This is consistent with analysis made strictly within the framework of limit equilibrium. It is shown in this paper that the mode or direction of failure progression also has an important influence on the numerical value of the safety factor F. In other words, the safety factor has a value for one mode of progression (say from the crest) which is different from its value for another mode of progression (say from the toe), even if the value of R is the same in the two cases. It has been shown that an existing twowedge model can be adapted for progressive failure studies w h i l e retaining desirable features in the original computer program, e.g. the ability to search for the critical locations of the rear slip surface and the inter-wedge plane. The zone can be identified within which these surfaces m a y lie for a wide range of values of the residual factor R. For design purposes, the factor of safety can be plotted as a function of the residual factor R, considering any n u m b e r of positions of the water table and two significant modes of failure progression (i.e. initiation from the toe and initiation from the crest). It is interesting to note that the actual value of residual factor R depends significantly on the relative values of the shear-strength parameters of the spoil material and of the weak layer forming the basal slip surface. Attention was drawn to simple finite element studies (linear elastic with inclusion of failure criterion in terms of effective stress) which demonstrate the importance of the relative values of the strength parameters and the relative unimportance of the elastic modulus values. The residual factor R will often be close to R 1 (i.e. R = R 1 L1/L ) in all cases where the spoil is much stronger than the basal layer. For cases where the spoil is quite weak, the residual factor R may approach 1. Such a situation may also arise after several =
138
heavy rainfalls when softening has taken place throughout the spoil. Considering a range of values of strength parameters of the same order as the actual published values in Queensland, Australia (e.g. [2]), residual factors over the whole of the significant range R 1 (= L1/L ) < R < 1 may be operative within spoil piles. The studies show clearly that simple finite element analyses would be sufficient for the purpose of getting an approximate value of R. A decision on the value of R at any given stage in the life of a spoil pile should not necessarily be made only on the basis of finite element studies. Observational procedures are often considered to be of key importance, and monitoring of spoil piles should provide useful data to facilitate the decision-making process. Given that new data become available from field measurements to supplement existing information, the factor of Safety of a spoil pile can be updated for the new conditions by simply referring to the available curves which relate factor of safety F to residual factor R. For design and planning throughout the life of a mine, such curves would be obtained economically at the very beginning and their validity would remain unchanged. Attention would simply need to be focussed on observations and measurements of shear strength which would be needed to learn more about the development of zones of overstressing and the progression of failure.
CONCLUSIONS Planning and design studies concerned with spoil piles at an open-cut mining project should take into consideration the changes that may occur with time, e.g. strain softening and moisture softening of spoil. Specifically, the following steps are recommended. (1) Perform limit equilibrium studies with
available data on shear-strength parameters. (2) Plot curves of factor of safety as a function of the residual factor, considering (a) at least two modes of failure progression, i.e. progression from the crest or progression from the toe, and (b) several positions of the water table. (3) Investigate the influence of residual factor on the zone within which the real failure surface may lie. (4) Monitor spoil piles to obtain significant observational data and interpret this data for observing the size of the softened zone. (5) Perform simple finite, element studies to predict the size of the "failed" or softened zone. (6) Use steps (4) and (5) to interpret the value of residual factor R. (7) From the value of R, the value of the safety factor F at any stage in the life of the spoil piles may be obtained from curves (2). (8) Study spoil-pile failures and perform careful back-analyses. (9) On the basis of these, calibrate the curves in step (2) to the extent possible and modify interpretations of the value of residual factor R based on (4) and (5). Considering that the life of a mine may be several decades and that spoil dumping is a continuous process, these procedures would not only be feasible but would prove to be economical in the long-term. The approach outlined in this paper would also lead to an improved understanding of failure mechanisms and of the transition from stability to failure.
ACKNOWLEDGEMENTS The writers would like to acknowledge The University of Wollongong, and in particular the Mining Research Centre, and the Depart-
139 m e n t of Civil a n d M i n i n g s u p p o r t i n g this project.
E n g i n e e r i n g for
REFERENCES 1 L.P. Gonano, An Integrated Report on Slope Failure Mechanisms at Goonyella, CSIRO, Div. Applied Geomechanics, Australia, Project Report No. 17, 1976 (Technical Report No. 114, 1980). 2 B.G. Richards, Finite Element Analyses of Spoil Pile Failures at the Goonyella Mine, CSIRO, Div. Applied Geomechanics, Australia, Technical Report No. 96, 1980. 3 R.N. Chowdhury, Slope Analysis. Elsevier, Amsterdam, 1978, 424 pp.
4 V.U. Nguyen, J.A. Nemcik and R.N. Chowdhury, Some practical aspects of spoil pile stability by the two-wedge model. Mining Science and Technology, 2 (1) (1984): 57-68. 5 M.A. Coulthard, Work in relation to two-wedge model of slope stability (unpublished), 1979. 6 R.N. Chowdhury and E. Derooy, Progressive reliability of a strain-softening slope. Trans. (Civ. Eng.), Inst. Eng., Australia, CE27 (1) (February, 1985): 79-95. 7 B.G. Richards, M.A. Coulthard and C.T. Toh, Analysis of slope stability at Goonyella Mine, Can. Geotech. J., 18 (2) (May, 1981): 179-194. 8 R.N. Chowdhury, Probabilistic Approaches to Progressive Failure. Two Reports, University of Wollongong, 1981.
127
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
SPOIL STABILITY CONSIDERING PROGRESSIVE FAILURE R.N. Chowdhury, V.U. Nguyen Department of Civil and Mining Engineering, University of Wollongong, Wollongong, N.S.W. (Australia)
and J.A. Nemcik * ACIRIL, P.O. Box 551, Rockhampton, Queensland, (Australia) (Received July 8, 1985; accepted August 15, 1985)
ABSTRACT
In spoil piles, shear strength often decreases significantly as a consequence of moisture softening. Moreover, spoil material exhibits characteristic brittleness so that overstressing can also lead to a marked decrease in shear strength. Progressive phenomena are always important in such circumstances and in this paper an approach is outlined to include failure progression within a two-wedge limit equilibrium model. A comprehensive approach is outlined and it is suggested that the factor of safety be
obtained as a function of the residual factor which has values between 0 and 1, corresponding to no local failure on the one hand and complete softening of the slip surface on the other. It is shown that the extent of the softening zone can be obtained from simple finite element analysis. The usefulness of this approach for updating spoil stability during its life is highlighted. The significance of the direction or mode of failure progression is also discussed in the paper.
INTRODUCTION
ments. In strip mining operations, which have proved to be both feasible and economical in Australia, it is of the utmost importance to ensure the continued stability of spoil piles. Failures of spoil piles cause disruption of operations, necessitate substantial expenditure for clearing the slipped spoil masses, and cause associated delays in production. Moreover, such failures may lead to the loss of some of the coal reserves. The objective of this paper is to highlight the role of progressive phenomena in reducing
Surface mining activities for the production of coal are increasing at a rapid rate in Australia. Assessments of slope stability are required throughout the life of a surface mining operation. The success and efficiency of such an operation depend primarily on the reliability and accuracy of stability assess-
* Formerly of the University of Wollongong.
128 the stability of spoil piles. A direct consequence of progressive movements and moisture-softening within spoil materials is that the values of shear strength are reduced. Therefore, estimates of stability for a given spoil pile (e.g. in terms of a safety factor F ) which are reliable and accurate at a particular instant in time must, in due course, be revised and updated in the light of special situations and circumstances. In particular, if additional data become available about the extent to which softening of spoil has taken place, or about movements which have occurred, then the values of F would have to be recalculated. However, in this paper it is proposed that the relationship between the extent of softening along the potential slip surface on the one hand, and the factor of safety F on the other hand, be established from the very beginning. F r o m these relationships, the value of F relevant at any particular time and for any given situation can be obtained and thus, it is hoped, new analyses at short notice will be avoided. In short, the process for updating spoil-pile stability can be made efficient by supplementing any existing charts or tables, relevant to a particular project, with curves showing how the value of F decreases with progressive softening and decreasing shear strength along a potential slip surface. Stability assessments must be based on: (a) Understanding of the relevant failure mechanisms and the development of appropriate computational models; (b) Use of a suitable and accurate method of stability analysis; (c) Reliable data concerning shear strength of spoil and pit-floor materials, and other important material parameters; (d) Appropriate pore-water pressures within the spoil piles. There will always be considerable uncertainty with respect to pore-water pressures, and therefore parametric studies may be desirable in practice. Alternatively, different studies may be made for (a) spoil without water table
and (b) spoil with the water table, as it might be expected to develop on the basis of experience and judgement.
FACTORS CONTROLLING SPOIL STABILITY The factors which primarily control spoil stability during and immediately after construction are: (a) Construction procedures and construction sequence; (b) Shear strength characteristics of spoil materials and, in particular, strain-softening and related phenomena; (c) Pore-water pressure developed in spoil piles; (d) Water infiltration and wetting sequence; (e) The Susceptibility of spoil to lose shear strength during wetting, i.e. a moisturesoftening phenomenon. Investigations related to open-strip coal mining in Australia have revealed [1] that failures often occur on planar surfaces of discontinuities forming at least two wedges. The lower wedge moves outwards at the toe and the upper wedge moves downwards, so forming an exposed escarpment with an angle of the order of 60 °, i.e. a relatively steep rear failure surface OB (Fig. 1). An interwedge plane OC is part of the failure mechanism. In these flat-bedded coal measures, the basal slip
c
A
/
O
Fig. 1. Two-edge model showing softened part x of basal slip surface (progression from the toe). The residual factor R = x / ( L 1 + L z ) where L 1= AO and L 2 = OB. Arrows indicate potential direction of movement of wedges if failure develops.
129 surface has only a few degrees inclination as it follows the original floor, i.e. the base of the coal. It has been pointed out by Richards [2] that water in the spoil piles controls stability through its influence on pore-water pressure and shear strength. Moreover, tests have shown that the spoil material exhibits marked strain-softening behaviour. For example, in one test the peak shear strength parameters were Cp = 130 kPa and epp = 49 ° and the residual shear strength parameters were c r = 125 kPa and % = 15 °. Such a drastic reduction in the friction angle would have a significant influence on the mechanism of failure. Different parts of the spoil pile would suffer different degrees of relative deformation and, therefore, only localised zones of overstress and of strength decrease may develop initially. Once such failures have developed there may be a progressive increase in the size of the area within which the shear strength is reduced to the residual value. The potential for progressive failure is high because of the high brittleness indicated by the marked difference between peak and residual shear-strength parameters. The subject of progressive failure has received a great deal of attention in the recent past but primarily in relation to natural slopes and excavations. The basic concepts and recent developments have been discussed over a number of years, and the attention of readers is directed to a comprehensive review by Chowdhury [3]. It should be noted, however, that little attention has so far been given to the role of progressive failure in spoil-pile stability. An important factor in the case of spoil stability is the role of moisture softening in producing the conditions under which progressive failure may occur. Therefore the extent of water infiltration and the wetting sequence are of considerable importance. Other important factors include the development of tension failure in the spoil and the potential
for slip at the interface between old and new spoil. The long-term stability of spoil may not appear to be of immediate concern to the geotechnical engineer. Nevertheless, delayed spoil failures can be sources of disruption in rehabilitation works or coal-retrieval operations, depending on a number of different factors. It may be necessary, therefore, to monitor the stability of spoil piles over a number of years and to use observational data so obtained to update the results of stability analyses. The primary cause of delayed changes in the performance of a spoil pile is infiltration from rainfalls during the lifetime of the spoil pile. As a consequence of infiltration and moisture movement, pore pressures may increase significantly, shearstrength parameters may undergo further decrease and there may be progressive movements. Associated with these changes, there would be increased strains in some regions within the spoil pile and relative deformations along a potential slip surface. Thus progressive phenomena are of key importance to spoil stability in the short term as well as in the long term. It should be a central feature of planning and decision-making strategies to link stability assessment with evidence concerning progressive changes within spoil piles. Analyses must be updated as significant changes take place and information on these changes becomes available as part of observational procedures.
AN APPROACH TO SAFETY FACTOR
UPDATING
THE
Basic wedge model Modelling of slope-stability problems based on wedge mechanisms is a well-established procedure, and analyses for spoil dumps based on the wedge mechanism have been performed in Australia for a number of years.
130
There are many ways of performing wedge analyses and the authors have described their own version of the model in a recent publication [4]. Essentially, it differs from other conventional approaches in that components of forces are balanced in the vertical direction (similar to the Bishop method of slices associated with slip surfaces of circular shape). At the same time, however, cohesion and friction along the interwedge boundary are taken into consideration as well as the pore-water pressure on that boundary. Few other wedge models include these features except the unpublished model of Coulthard [5]. The solution method developed for the model works very well and there are few computational problems. Comparative studies are required to investigate further the scope and reliability of the authors' model. Residual factor
Consider a potential failure mass with basal slip surface AO of length L 1 (Fig. 1) and let the shear-strength parameters be denoted as follows: peak values: cpa, %1; residual values: crl, q~r~. Let the rear slip surface OB have a length L2, and let the shear-strength parameters of the spoil material (which are generally quite different from those of the basal slip surface) be denoted as follows: peak values: %2, %2; residual value: c~2, qP~2. The total length of the two slip surfaces is L = L a + L 2. A portion x of this total length may, at any given stage in the life of the spoil pile, have reduced in shear strength so that only residual-shear-strength parameters are operative over that length. Now a residual factor R may be defined as the ratio of x to L, i.e. R = x/L
= x/(La
+
L2)
(1)
Depending upon construction method and
sequence, spoil height, spoil characteristics and other factors, the residual factor may have either a small or a significantly high value. The value of R will, however, tend to increase with time and will reflect the changes associated with moisture infiltration. Considerable uncertainty is usually associated with the actual value of R at any given time. Therefore, it is proposed to incorporate a procedure for spoil stability analysis in which R may be varied between the extreme limits of 0 and 1. Moreover, it should be noted that the overall safety factor, which decreases with increasing value of R, also depends on the mode of failure progression. A given value of R may be reached in various ways, e.g. (see Fig. 2): (a) Strength decrease progressing from the top or crest along the rear failure surface; (b) Strength decrease progressing from the bottom or toe along the basal failure surface; (c) Development of progressive failure from both the crest and the toe; (d) Development of localised failure near the intersection of the two slip surfaces and its progression outwards in the direction of the toe, or the crest, or both. For the same value of R, the value of overall safety factor will be different for different modes of failure progression. However, the bounds to the value of overall
A
D
0
Fig. 2. Wetting front DEFG in a spoil pile with a potential two-wedge failure mechanism. Arrows indicate different ways in which progr,ession of strength reduction or of softening may develop,
131 safety factor m a y be determined for all practical purposes by considering the first two modes mentioned above, i.e. progression from the crest and progression from the toe.
in which r L = L 1 / L 2 is the length ratio of the basal to rear slip surface. Note that, when R 2 = 0 , i.e. R 1 = 1, R = L 1 / L as before. The weighted average of cohesion is
Incorporation of failure progression in the wedge mode
cwl = Crl, x > L l
Modified values of cohesion and friction are required for the two parts of the slip surface for any given value of the residual factor. Failure progression may be incorporated most readily in the numerical model of wedge stability if equivalent shear strength parameters along the basal and rear failure surfaces are calculated first. For any non-zero value of the residual factor, these equivalent parameters may be obtained as weighted averages. It is useful to consider cohesion and friction separately.
Cw2=R2cr2+(1-R2)cp2, x > L l
(a) Weighted average of cohesion at a given stage of failure progression (1) Consider that progression occurs from the toe inwards and that it has reached a point within the basal slip surface AO of the potential wedge (Fig. 1). The weighted average of cohesion is
(6a)
for basal slip surface AO, and (6b)
for rear slip surface OB.
(b) Weighted average of friction angle The friction angle cannot be averaged in the same way as the cohesion, since the frictional part of the shear strength is dependent on normal stress which varies from point to point along the slip surface. The weighted averages q0wl and Cpw2 of the friction angles relevant to the two slip surfaces may be defined on the basis that the frictional part of the shearing resistance remains unaltered in the averaging process. (1) Consider failure progression from the toe but within the basal slip surface, then the weighted friction angle is given by the following equations. Along basal slip surface AO: x
Cw ' = C r l R 1 -4:- C p l ( 1 - - R 1 ) ' x ~ L 1
(2a)
tan
~9wl £L,( On - -
for basal slip surface AO, and Cw2 = Cp2 , X ~
Ll
-~-
tan qgrl£ (o n
u)dx
LI
(2b)
for rear slip surface OB, where
R 1 = X l / L l = ( L / L 1 ) R , x <~n 1
u)dx
+ t a n q)plf (On-- u)dx, x ~< LI, R 1 ~< 1,
(3)
(Note: R = L 1 / L when xl = L> i.e. R 1 = 1) (2) Consider now that failure progression has extended from the toe along the basal slip surface and beyond the point O; i.e. the value of x, the softened or strength-reduced part of the slip surface, is greater than L 1. Define
(7a)
where % and u are respectively the normal stress and pore water pressure at any given point at a distance from the toe of x (or more precisely over the length dx). Along rear slip surface OB: qOw2 = qOp2, X ~
L 1, R 1 ~< 1
(7b)
It is easy to show that R 2 is related to R as follows
(2) Consider failure progression from the toe and extending beyond the point O so that x>L v Along basal slip surface AO,
R = ( L 2 / L ) ( R 2 + rL) ,
qgwl = (/)rl, X >
R 2=(x-L1)/L
2 , x > L 1.
(4)
(5)
L 1.
(8a)
132
EXTENT ZONE
Along rear slip surface OB, L2
tan epw2L ((l n
-
-
SOFTENED
OR
FAILED
u)dx 1=
tan q%2Lx'(on - u ) d x 1 + tan epp2 I.2(On
OF
u)dxl, - -
1
x > L1
(Sb)
where Xl = x - L 1 and dxl = dx. (When Xa = 0, x = L1; when Xl = L2, x = L)
Modification of the computer program The computer program for the wedge model was modified to include the above features. It was found convenient to perform the calculations in terms of the effective weights of the wedges. The computation of effective normal stresses at every point along the slip surfaces is not necessary. The computer program includes the search for the critical wedge. Given the inclination of the basal slip surface, the spoil height and the top surface configuration of the spoil pile, the program automatically finds the critical location of points O and B (Fig. 1). This is repeated for every value of the residual factor R. Thus the critical wedge for one value of R may not be the same as the critical wedge for another value of R. Although the differences in the location of point O are generally not significant, the capability of the program to locate the critical wedge for any mode of failure progression and for any extent of progressive failure is a very desirable one. For simplicity, it may be desired to keep the critical wedge fixed as that wedge relevant to either R -- 0 or R = 1 and then to perform analyses for various values of R. Thus, one may plot the overall safety factor F against the value of R for a fixed critical wedge or for a true changing critical wedge. Moreover, in either case the program is capable of considering failure progression either from the crest or from the toe.
As stated earlier, one approach for the determination of the extent of the softened or failed zone would be to have observational procedures from which it may be possible to infer a value of the residual factor R at any given stage in the life of a spoil pile. Monitoring of spoil piles is indeed very desirable for further progress in understanding the transition from stability to failure. However, the interpretation of observational data is by no means easy, and a discretization approach to study the stress-deformation behaviour of spoil may prove to be helpful. For instance, the finite element method may be used to study the development of zones of overstress within a spoil pile and to predict a value of the residual factor R. Richards [2] used a non-linear finite element model considering sequential construction of the spoil pile and three types of material, n a m e l y : (a) unsaturated spoil above groundwater level, (b) saturated spoil below groundwater level, and (c) material below the floor. The non-linear relationships for bulk modulus K and shear modulus G were based on interpretation of the shear-strength data in terms of hyperbolic equations. Plots of stress and .strain contours and displacement contour were obtained and on the basis of these an interpretation was made of the mechanism of spoil-pile failure. One drawback of sophisticated finite element procedure is that detailed and accurate data must be made available. Another drawback of such sophisticated procedures is that the selection and interpretation of data, as well as the performance of stability analyses, are time consuming processes. Where the finite element procedures are used only to supplement limit equilibrium studies, relatively simple analyses would be desirable. Moreover, for a very brittle material it may be sufficient to perform linear elastic analysis incorporat-
133
ing an appropriate failure criterion. Simple linear elastic finite element analyses were performed to demonstrate that the extent of the failed zone and hence the value of R may be determined readily. This value of R for any stage of a spoil pile and for given pore-pressure conditions may then be used in conjunction with the available results of limit equilibrium studies to obtain the safety factor relevant to a given stage in the life of the spoil pile. Consistent with accepted geotechnical practice the following failure criterion (Mohr - C o u l o m b ) was used: Failure or overstress occurs if 1- > ~-f
(9)
in which ~-, the shear stress, is given by
(lO) and rf, the shear strength, is given by ~-f = Cp COS q~p + ½(61 + O3) s i n q0p .
(11)
o 1 and o 3 are respectively the major and minor principal total stresses, 8] and 63 are the corresponding effective stresses.
TYPICAL RESULTS--SAFETY FACTOR DURING FAILURE PROGRESSION A spoil pile with the geometry shown in Fig. 3 was considered for analysis. The unit weight of the spoil was assumed to be 1900 k g / m 3. The following shear-strength data was assumed for the calculations. For basal plane
iH5,~5)
(0.0)
[3~70,20) gL OOR
Fig. 3. Geometry of spoil pile considered from analyses with failure progression from crest or toe (the coordinates are in metres). One position of water table is also shown.
of weak material, cpap = 15 ° and cpl, = 8 ° , Cap = 100 kPa and c2, = 80 kPa. For spoil material (and rear slip surface), ~2p
=
32° and q02r = 29 °,
c2p = 200 kPa and C2r = 100 kPa. The first set of analyses was made without considering any water table. Moreover, the vertex O of the critical wedge was allowed to change for different values of the residual factor. The decrease of the factor of safety with increase in R is shown in Fig. 4. The upper curve is for progression, from the toe inwards and the lower curve is for progression from the crest downwards. It may be noted that, for the latter case, the curve does not pass through all the points. This is a consequence of allowing the critical wedge to change for each value of the residual factor. It may be noted that, for any given value of residual factor, progression from the crest is more critical than progression from the toe, i.e. lower safety factors are obtained if progressive failure develops from the crest. Similar results have been noted in respect of soil slopes with cylindrical slip surface (e.g. [6]). Another set of analyses was made considering the water table to be located as shown in Fig. 3. As expected, the presence of the water table reduced the factor of safety at any given value of R and for a given mode of progression. However, the trend of the results was the same as for the case with no water table. The shaded area in Fig. 5 shows the bounds within which the rear slip surface and the inter-wedge plane may lie for all values of R. Analyses were also made considering a fixed critical wedge relevant to the first analysis, i.e. for the case when residual factor R = 0. As R increases, the same critical wedge is considered to be relevant for all analyses. Thus, the vertex O remains fixed for all analyses and for both modes of failure progression. The results
134 1.8
1.7 e
1.6
1.5
(a)0
nO
<~
•
1.4
U-
>FUJ M-
1.3
U3 1.2
1.1
1.O
0.O
r
I
r
l
t
0.2
0.4
0.6
0.8
1,O
RESIDUAL
FACTOR
R
Fig. 4. Factor of safety F as a function of residual factor R for problem geometry in Fig. 3 considering failure progression from the toe (curve a) and failure progression from the crest (curve b).
with and without water table are shown in Fig. 6. In general, it was found that the curves are relatively smooth and the results consistent when a fixed, critical wedge is considered. There are few, if any, odd results of
(300,20) (0,0)
FLOOR
Fig. 5. Shaded area shows the boundaries of the region in which the rear slip surface and the inter-wedge plane may lie for any value of the residual factor R.
computation, and no interference or overlap between curves for toe and crest progression. The use of a fixed critical wedge can be justified if one assumes that the potential failure mechanism is already in place before progression becomes evident. Once a continuous slip surface has been developed, one may disregard the possibility that slip will then take place along a different surface with further development of failure progression. A designer may however wish to prepare two sets of curves from the computations, one set with a variable critical wedge and the other set with a fixed critical wedge. If there are any significant differences or anomalies, these can then be detected at the very outseL
135 1.8
1.7
1.6
1,5
j(b)
or
© i.r.)
1.4
(d)
ii >.-
I...-
1.3
uJ u_
<:
CO
1.2
1.1
1,O O.O
0.2
0.4 RESIDUAL
0.6 FACTOR
0.8
1,O
R
Fig. 6. Variation of safety factor R with fixed position of critical wedge corresponding to R = 0; with no water-table progression from toe (curve a), and from crest (curve b); with water-table progression from toe (curve c), and from crest (curve d).
TYPICAL ZONE
RESULTS
THE
SOFTENED
To investigate the feasibility of using simple finite element analyses for predicting the extent of the softened or overstressed zone, several studies with different deformation and strength parameters were made. For each study, three sets of geotechnical parameters are required, one each for (a) main b o d y of spoil, (b) a weak layer of softened material at the interface between spoil and floor, and (c) the floor itself. Considering a cohesion value Cp = 0.1 M P a for the spoil and cp = 0.015 M P a for the weak layers, a high friction angle q0p = 36 ° for the
spoil and a relatively low friction angle q0p = 15 ° for the weak layer, overstressing was found to occur only in the weak layer. The influence of the values of elastic modulus E on the number of failed elements was found to be negligible. For instance, the value of E was varied from 5 M P a to 500 M P a for the spoil, from 5 M P a to 500 M P a for the weak layer and from 1000 M P a to 100,000 M P a for the floor. Quite clearly, a very weak basal plane relative to spoil will ensure that the value of R l = 1, and that the value of the residual factor R = L1/L. It should be noted, however, that the deformations and strains which may determine the conditions for progression of failure are very much dependent on the
136
relative values of E. Detailed analysis to investigate relative deformations and strains is, however, outside the scope of this paper. Table 1 shows the data and summary of results concerning failed elements with the first set of analyses. With considerably lower values of shear strength parameters for the spoil, overstressing spreads over a very large area of the pile. For instance with Cp = 0.05 MPa and epp = 15 ° for the:spoil, and Cp = 0.05 MPa and q~p = 3 ° for the weak layer, almost all the elements are overstressed except a few at the top. Thus, such a weak material would be very unstable. This refers to a residual factor close to unity, i.e. R - - 1 . U s u a l l y the geotechnical engineer would be concerned with a situation which is not so extreme. In fact very interesting results were obtained for values: Cp = 0.05-0.1 MPa, epp = 30 ° (spoil), Cp=0.05 MPa, efp= 5 ° (weak layer). The residual factor in such cases was found to be greater than the first set, i.e. R 1 > 1 and L1/L
Fig. 7. Overstressed zone indicated by finite element analysis for the following parameters: (a) spoil: E = 5 MPa, ~ = 0 . 3 , C p = 8 0 kPa, epp=30 ° , (b) Weak basal plane E = 5 MPa, ~ = 0 . 3 , c p = 5 0 kPa, % = 5 ° , (c) Floor: E = 100,000 kPa, ~ = 0.3, Cp = 900 kPa, q% = 35 °.
approaches a value of about 0.9 for Cp = 0.05. It is interesting to find that the calculated results are sensitive to the value of Cp for spoil given that other parameters are realistic. These results were found to be very much in accord with previous finite element studies of spoil piles using somewhat similar shear strength parameters [2,7]. This qualitative agreement confirms the view of the writers that, for the purposes of assessing the approximate size of the overstressed zone, simple finite element analyses may suffice. Figure 7 shows the size of the overstressed or failed
TABLE 1 D a t a for analyses in which failures were identified mainly in the weak layer at the base of spoil Parameters Cp ( M P a )
% (degrees)
Spoil 0.1
36
Weak layer 0.015
15
Poisson's ratio, u
0.3
0.3
R a n g e of values of modulus, E ( M P a )
5-500
5-500
Floor 0.9
35 0.3 1000-100,000
Comments Overstressing of failure limited to whole of weak layer Same as above Same as a b o v e Same as above
Notes: (1) The above results indicate that for the given shear strength p a r a m e t e r s a residual factor R = L1/L (i.e. R 1 = 1) would be operative over a wide range of modulus values. (2) This conclusion was f o u n d to b e u n c h a n g e d even with considerable variations of the values of spoil parameters. For instance, with Cp = 0.1 MPa, % = 50 ° (floor), Cp = 0.1 MPa, q% = 30 ° (spoil) a n d cp = 0.1, q% = 10 ° (weak layer), there was overstressing of 40 out of a total of 46 elements of the basal weak p l a n e a n d again n o failures in the spoil above or floor below.
137 zone for one of m a n y sets of parameters used as part of the present investigation.
DISCUSSION OF THE APPROACH AND RESULTS A n important aim of this paper was to present a comprehensive but simple approach for stability assessment of spoil piles, taking into consideration the zones of overstress or softening. It is important to understand that the factor of safety of a spoil pile is not a fixed or constant quantity. Once sets of data have been prepared for use in stability studies, there is a tendency to consider that the results have significance beyond the stage or situation to which the data and analysis are relevant. This tendency is due to a neglect of strain-softening and moisture-softening phen o m e n a and due to a lack of emphasis on progressive failure. In published studies of field and laboratory investigations (e.g. [2,5,7]), the importance of progressive p h e n o m e n a has been brought out very clearly. However no effort has so far been made to modify conventional limit equilibrium approaches for spoil piles to include the progression of failure. In particular, the two-wedge model has been used as if it relates to a perfectly plastic material under well-defined and relatively unchanging environmental conditions. In this paper emphasis has been given to the fact that the factor of safety is a variable, the value of which changes with time as environmental factors influence the spoil pile during its life. The value of safety factor F is influenced significantly by the extent to which softening has occurred within a spoil pile. Typical curves showing the variation of F with the residual factor R have been plotted. One might have expected a sharp break in any such curve where R = L1/L (i.e. R 1 = 1) because of the biplanar nature of the slip surface. However, it is interesting to note that
there is a relatively smooth transition and that the curves do not exhibit a break or knee at any stage. This is consistent with analysis made strictly within the framework of limit equilibrium. It is shown in this paper that the mode or direction of failure progression also has an important influence on the numerical value of the safety factor F. In other words, the safety factor has a value for one mode of progression (say from the crest) which is different from its value for another mode of progression (say from the toe), even if the value of R is the same in the two cases. It has been shown that an existing twowedge model can be adapted for progressive failure studies w h i l e retaining desirable features in the original computer program, e.g. the ability to search for the critical locations of the rear slip surface and the inter-wedge plane. The zone can be identified within which these surfaces m a y lie for a wide range of values of the residual factor R. For design purposes, the factor of safety can be plotted as a function of the residual factor R, considering any n u m b e r of positions of the water table and two significant modes of failure progression (i.e. initiation from the toe and initiation from the crest). It is interesting to note that the actual value of residual factor R depends significantly on the relative values of the shear-strength parameters of the spoil material and of the weak layer forming the basal slip surface. Attention was drawn to simple finite element studies (linear elastic with inclusion of failure criterion in terms of effective stress) which demonstrate the importance of the relative values of the strength parameters and the relative unimportance of the elastic modulus values. The residual factor R will often be close to R 1 (i.e. R = R 1 L1/L ) in all cases where the spoil is much stronger than the basal layer. For cases where the spoil is quite weak, the residual factor R may approach 1. Such a situation may also arise after several =
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heavy rainfalls when softening has taken place throughout the spoil. Considering a range of values of strength parameters of the same order as the actual published values in Queensland, Australia (e.g. [2]), residual factors over the whole of the significant range R 1 (= L1/L ) < R < 1 may be operative within spoil piles. The studies show clearly that simple finite element analyses would be sufficient for the purpose of getting an approximate value of R. A decision on the value of R at any given stage in the life of a spoil pile should not necessarily be made only on the basis of finite element studies. Observational procedures are often considered to be of key importance, and monitoring of spoil piles should provide useful data to facilitate the decision-making process. Given that new data become available from field measurements to supplement existing information, the factor of Safety of a spoil pile can be updated for the new conditions by simply referring to the available curves which relate factor of safety F to residual factor R. For design and planning throughout the life of a mine, such curves would be obtained economically at the very beginning and their validity would remain unchanged. Attention would simply need to be focussed on observations and measurements of shear strength which would be needed to learn more about the development of zones of overstressing and the progression of failure.
CONCLUSIONS Planning and design studies concerned with spoil piles at an open-cut mining project should take into consideration the changes that may occur with time, e.g. strain softening and moisture softening of spoil. Specifically, the following steps are recommended. (1) Perform limit equilibrium studies with
available data on shear-strength parameters. (2) Plot curves of factor of safety as a function of the residual factor, considering (a) at least two modes of failure progression, i.e. progression from the crest or progression from the toe, and (b) several positions of the water table. (3) Investigate the influence of residual factor on the zone within which the real failure surface may lie. (4) Monitor spoil piles to obtain significant observational data and interpret this data for observing the size of the softened zone. (5) Perform simple finite, element studies to predict the size of the "failed" or softened zone. (6) Use steps (4) and (5) to interpret the value of residual factor R. (7) From the value of R, the value of the safety factor F at any stage in the life of the spoil piles may be obtained from curves (2). (8) Study spoil-pile failures and perform careful back-analyses. (9) On the basis of these, calibrate the curves in step (2) to the extent possible and modify interpretations of the value of residual factor R based on (4) and (5). Considering that the life of a mine may be several decades and that spoil dumping is a continuous process, these procedures would not only be feasible but would prove to be economical in the long-term. The approach outlined in this paper would also lead to an improved understanding of failure mechanisms and of the transition from stability to failure.
ACKNOWLEDGEMENTS The writers would like to acknowledge The University of Wollongong, and in particular the Mining Research Centre, and the Depart-
139 m e n t of Civil a n d M i n i n g s u p p o r t i n g this project.
E n g i n e e r i n g for
REFERENCES 1 L.P. Gonano, An Integrated Report on Slope Failure Mechanisms at Goonyella, CSIRO, Div. Applied Geomechanics, Australia, Project Report No. 17, 1976 (Technical Report No. 114, 1980). 2 B.G. Richards, Finite Element Analyses of Spoil Pile Failures at the Goonyella Mine, CSIRO, Div. Applied Geomechanics, Australia, Technical Report No. 96, 1980. 3 R.N. Chowdhury, Slope Analysis. Elsevier, Amsterdam, 1978, 424 pp.
4 V.U. Nguyen, J.A. Nemcik and R.N. Chowdhury, Some practical aspects of spoil pile stability by the two-wedge model. Mining Science and Technology, 2 (1) (1984): 57-68. 5 M.A. Coulthard, Work in relation to two-wedge model of slope stability (unpublished), 1979. 6 R.N. Chowdhury and E. Derooy, Progressive reliability of a strain-softening slope. Trans. (Civ. Eng.), Inst. Eng., Australia, CE27 (1) (February, 1985): 79-95. 7 B.G. Richards, M.A. Coulthard and C.T. Toh, Analysis of slope stability at Goonyella Mine, Can. Geotech. J., 18 (2) (May, 1981): 179-194. 8 R.N. Chowdhury, Probabilistic Approaches to Progressive Failure. Two Reports, University of Wollongong, 1981.