Essentially the neutral point method
considers the ratio of the new to old factors of safety (Fs1 / Fs0)
for a potential (or existing) failure surface, as a load is placed at
different points on the ground above it.
In every slope there are forces which tend to promote downslope movement and opposing forces which tend to resist movement.
A general definition of the factor of safety (Fs) of a slope results from comparing the downslope
shear stress (t) with the shear strength (tf)
of the soil along an assumed or known rupture surface:
Fs = tf / t
back to Mechanics
Changes produced by loading or unloading are widely recognised as being mechanisms by which instability can occur. The effects of variations in loading can be considered using the concept of the 'neutral point' developed by Hutchinson in 1977.
back to Loads
Essentially the neutral point method
considers the ratio of the new to old factors of safety (Fs1 / Fs0)
for a potential (or existing) failure surface, as a load is placed at
different points on the ground above it.
If placed toward the toe of the failure surface, the load will produce an increase in the factor of safety (i.e. the loading is beneficial and Fs1 / Fs0 increases), but if placed toward the head of the failure surface, it produces a decrease in the factor of safety (i.e. loading is detrimental and Fs1 / Fs0 decreases).
There is clearly an intermediate position where the loading causes no change in the factor of safety for the failure surface and Fs1 / Fs0 = 1.0, this is termed the 'neutral point'.
back to Neutral Point Concept
It can be shown that two extreme neutral
points exist, depending upon whether the loading is applied under drained or
undrained conditions. For the undrained condition (
=1.0),
the neutral point (Nu) occurs at the point of zero inclination
of the failure surface, whilst for drained conditions (
=0 )
the neutral point (Nd) occurs where the inclination of the failure surface a is given by
Drainage conditions between these two extremes (1.0 >
> 0 ) have a corresponding intermediate neutral point (Ni).
Similar effects can be observed for the removal of loads, by for example making cuts in the slope.
Fso = factor of safety before addition or removal of load.
Fs1 = factor of safety after addition or removal of load.
a = local dip of slip surface (units: degrees).
f' = angle of friction in terms of effective stress (units: degrees).
= pore pressure coefficient.
Nu = neutral point for undrained condition.
Nd = neutral point for drained condition.
Ni = neutral point for intermediate drained conditions.
back to Neutral Point Concept
The effects due to the location of
load vary according to its position in relation to the drained and undrained
neutral points. Three zones describing the effect of adding loads can therefore,
be defined:
· Zone A : Always detrimental,
· Zone B : Detrimental in the short term; beneficial in the long term, and
· Zone C : Always beneficial.
Three zones can also be defined for the effects of reduced loading (i.e. cutting):
· Zone A : Always beneficial,
· Zone B : Beneficial in the short term; detrimental in the long term, and
· Zone C : Always detrimental.
The simple concept of the neutral point must, however, be applied with care. For example, the engineer must recognise that the addition or removal of load may cause a change in the position of the critical failure surface (and hence the neutral points). Particular care must be exercised when dealing with potential deep/shallow slips, since the addition of load may, in these cases, cause improvements in the stability condition of a shallow slip surface, whilst reducing the stability condition of a deeper slip surface.
back to Neutral Point Concept
Hutchinson, J.N., "Assessment of the effectiveness of corrective measures in relation to geological conditions and types of slope movement." General Report to Theme 3. Symposium on Landslides and other Mass Movements, Prague, September 1977. Bulletin, International Association of Engineering Geology, No. 16, 1977, pp. 131-155. Reprinted (1978) in Norwegian Geotechnical Institute Publication, No. 124, pp. 1-25.
Hutchinson, J.N. , "Engineering in a landscape." Inaugural Lecture, 9 October 1979, Imperial College of Science and Technology, University of London, London, England. 1983.
Hutchinson, J.N.,"An influence line approach to the stabilisation of slopes by cuts and fills." Canadian Geot. J., 21, 2, 1984, pp 363-370.
back to Mechanics
In order to estimate the factor of safety Fs for a slope in terms of effective stress (i.e. in the long-term condition), the pore water pressure must be known. This is frequently the greatest source of inaccuracy in slope stability work, since the determination of the most critical conditions of pore water pressure is complex and costly. The following three sets of conditions are usually considered for constructed slopes:
· End of construction
· Steady seepage
· Rapid drawdown
In natural slopes, the distribution of pore water pressure may be highly complicated due to changes in soil type, anisotrophy etc. The pore pressures are detemined from site measurements using observation wells or piezometers. Monitoring must be continued over long periods of time in order to define the worst or most critical conditions. Methods for the in-situ measurement of pore water pressure are described by Clayton, Matthews and Simons.
Clayton, C.R.I., Matthews, M.C., and Simons, N.E.,1995. Site Investigation. Blackwell Science. 584 pp.
back Pore pressures
Analyses of the short-term condition of stability are normally performed in terms of total stress, with the assumption that any pore water pressure set up by the construction activity will not dissipate at all. In many earth dams or large embankments, however, the construction period is relatively long, and some dissipation of the excess pore water pressure is likely. Under these conditions, a total stress analysis would yield a value of Fs on the low side, possibly resulting in un-economic design.
is defined as = Du / Ds1
Ds1
The pore pressure coefficient may be determined in
the triaxial apparatus. In embankments etc., if the soil is placed at a water
content below the optimum water content, the value of uo may be close
to zero, and in this case ru = .
In order to increase the rate of dissipation of pore water pressure (and hence
reduce the value of ru), drainage layers may be incorporated in the
embankment.
uo = initial pore water pressure
Du = change in pore water pressure due to a change in the major principal stress Ds1
g = unit weight of soil
h = depth of element
ru = pore pressure ratio
hw = head of water
gw = unit weight of water
back to Pore pressures
Under conditions of steady seepage, the pore water pressure can be obtained from the flow net. The pore water pressure at a point on the actual or assumed slip surface is obtained from the value of the equipotential passing through the point.
Referring to the figure, the pore water pressure at point P is obtained by constructing the equipotential line through P and is then equal to the head given by hw.
u = gw . hw
Then,
In homogeneous conditions, ru may attain values approaching 0.45. Internal drainage layers will produce lower values.
back to Pore pressures
In earth dams, rapid reductions in the water level produce significant and potentially dangerous changes in pore water pressure. This occurs because the water in the soil tends to flow back into the reservoir through the upstream face. In this scenario, even a period of some weeks may bring about a 'rapid' change in the pore water pressure distribution.
The pore water pressures under conditions of rapid drawdown are determined using the following procedure.
In the figure, consider
the point P on a trial slip surface. Under conditions of steady seepage, the
pore water pressure at P is obtained from the flow net, giving:
uo = g (h + hw - h' )
It is assumed that the total major stress at P is given by the overburden pressure,
s1 = g h
If under drawdown, the phreatic surface falls to a level below hw, then the change in total major principal stress is given by
Ds1 = - gw hw
The corresponding change in pore water pressure is
Du = -
gw hw
Therefore, immediately following drawdown, the pore water pressure at P is
u = uo + Dh
= gw [ h + hw - h' ] -
gw hw
= gw [ h + hw (1 -
) - h' ]
And, if
ru = u / gh
Then,
back to Pore pressures
Bromhead, E.N. 1992. The Stability of Slopes. Blackie. 411 pp.
Clayton, C.R.I., Matthews, M.C., and Simons, N.E., 1995. Site Investigation. Blackwell Science. 584 pp.
Whitlow, R. 1995. Basic Soil Mechanics. Longman. Scientific and Technical. 559 pp.
back to Mechanics
Earthquakes result from the sudden release of elastic strain energy stored in the Earth's crust. Stress accumulates locally from various causes until it exceeds the strength of the rocks, when slip occurs by brittle failure on dislocations or fractures known as faults. Earthquakes give rise to two types of surface displacement: permanent offsets on the fault itself, and transient displacement resulting from the propagation of seismic waves away from the source. A small movement on a fault may produce a considerable shock because of the energy involved. Earthquakes range from slight tremors which do little damage, to severe shocks which can cause widespread damage including the initiation of landslides, collapse of buildings and fracturing of supply mains and lines of transport.
The surface displacement associated with earthquakes may range from a few centimetres up to several meters. For example in the disastrous earthquake which affected San Francisco in 1906, the motion of the ground was mainly horizontal along the San Andreas fault with one side moving approximately 4.6m relative to the other.
back to Earthquakes
Earthquakes can affect slope stability in three ways:
Earthquakes produce horizontal and vertical accelerations in soil masses. The horizontal accelerations may reach as much as 0.5g (where g is gravitational acceleration), altering the distribution of forces in hillslopes in a manner equivalent to a temporary steepening of the slope.
Rapid repeated stress fluctuations (due to cyclic loading and unloading) can induce changes in the pore fluid pressures which may lead to liquefaction.
Earthquake shaking may change the applicable shear strength properties.
The detailed discussion of the effects of earthquakes on slope stability is outside the scope of this section. It is clear however that earthquakes do influence slope stability and can lead to slope failures on a catastrophic scale (see, for example, Seed).
Most of the analytical work concerned with the stability of slopes subjected to earthquakes has been performed in connection with earth and rock-fill dams where there is great potential for damage and loss of life if failure occurs. Much of this work is also applicable to natural slopes; an excellent review of the factors involved in determining the stability of slopes under earthquake shock is given by Seed.
Seed, H.B. 1968. Landslides during earthquakes due to soil liquefaction.
A.S.C.E., Journal of the Soil Mechanics and Foundations Division, 94, 5, 1055-1122.
Seed, H.B. 1979. Considerations in the earthquake - resistant design of earth
dams. Geotechnique, 29, 3, 215-263.
back to Earthquakes and slope stability
The simplest way of including seismic effects is to perform a limit equilibrium analysis where the forces induced by the earthquake accelerations are treated a horizontal force. Vertical forces may also be caused by the earthquake but these are ignored in this simple form of analysis. The principle of this method is illustrated opposite, where a horizontal force Fh due to the earthquake is assumed to act through the centre of gravity of the soil involved in the predicted or actual failure. It is assumed that:
Fh = kw = k mg
where m is the mass of the soil.
Thus the seismic coefficient k is a measure of the acceleration of the earthquake in terms of g.
For a purely cohesive soil, the factor of safety Fs is given by
where su is the undrained strength of the soil.
This approach may also be used in conjunction with the method of slices for soils possessing cohesion and friction. For example, Sarma presented a procedure where the earthquake induced forces are considered by applying a horizontal force kWi to the slice where Wi is the weight of slice i. The method then involves the computation of the critical horizontal acceleration (i.e. value of k) required to bring the soil above the slip surface into a state of limiting equilibrium: this critical acceleration can then be used as an index of stability.
An alternative method of analysis, using seismic coefficients has also been presented by Sarma.
Although the pseudo-static methods of analysis have many limitations, they are widely used. One of the problems occurs in estimating the value of the seismic coefficient k to be used in the analysis. This coefficient depends on the accelerations caused by the earthquake and may be difficult to define.
Recently, dynamic methods of analysis have been developed which allow for the inclusion of the full time history of the earthquake acceleration. Such methods generally allow the displacements of a potential slide mass along an assumed failure surface to be estimated. A dynamic finite element approach has been described by Seed.
Sarma, S.K., 1973. Stability analysis of embankments and slopes. Geotechnique, 23, 3, 423-433.
Sarma, S.K. 1979. Stability analysis of embankments and slopes. A.S.C.E., Journal of the Geotechynical Engineering Division, 105, 12, 1511-1524.
Seed, H.B. 1966. A method for the earthquake resistant design of earth dams. A.S.C.E., Journal of the Soil Mechanics and Foundations Division, 92, 1, 13-41.
back to Earthquakes and slope stability
Generally, in the pseudo-static methods of analysis, the shear strength parameters used are those measured in conventional shear strength tests. This assumption appears to be justified by the relatively few examples where problems have arisen.
However, in cases where seismic loading may cause movement along an existing discontinuity (such as a fault or old slip surface), significant decreases in the value of f
' have been reported by Skempton.
Skempton, A.W. 1985. Residual strength of clays in landslides, folded strata and the laboratory. Geotechnique, 35, 1, 3-18.
back to Earthquakes
Elastic strain energy may accumulate in rocks anywhere in the Earth's crust. Currently the plate tectonic model is used to explain that the most seismically active regions are at the 'active' margins of plates. Thus, many earthquake centres are located along two belts of the earth's surface: one belt extends around the coastal regions of the Pacific, from the East Indies through the Phillipines, Japan, the Aleution Islands and down the western coasts of North and South America; the other runs from Central Europe through the eastern Mediterranean to the Himalayas and the East Indies, where it joins the first belt (see figure opposite). Both of these belts are in places parallel to relatively young fold-mountain chains (e.g. the Andes), where much faulting is associated with the crumpled rocks. Many volcanoes are also situated along the active earthquake belts. Many shocks also occur in zones of submarine fault activity such as the mid-Atlantic ridge, and in fault-zones on continents such as the Rift Valley system of Africa.
# 
back to Earthquakes
The intensity of an earthquake is estimated from the effects produced in the affected area. The most common scale of intensity used is the Mercalli Scale, which has twelve grades as follows:
|
i) |
Detected only by instruments |
|
ii) |
Felt by persons at rest |
|
iii) |
Felt indoors; vibration like passing of a truck |
|
iv) |
Hanging objects swing; windows, door rattle |
|
v) |
Felt outdoors; some objects displaced; pendulum clocks stop |
|
vi) |
Strong: felt by all, many frightened; weak masonry cracked |
|
vii) |
Damage to some buildings; weak chimney fall; waves on ponds |
|
viii) |
Destructive: much damage to buildings, ground cracks, flow of springs affected |
|
ix) |
General damage (including reservoirs), buried pipes broken |
|
x) |
Disastrous: framed buildings destroyed, rails bent, landslides |
|
xi) |
Few structures left standing, fissures opened in ground |
|
xii) |
Catastrophic: damage nearly total, ground twisted and warped. |
A more detailed description of the Mercalli scale, and of other ways for quantifying earthquakes is given by Skipp and Emreaseys.
Skipp, B.O. and Emreaseys, N.N., 1987. Engineering seismology, in Ground Engineer's Reference Book, ed. by F.C. Bell, Butterworths, London.
back to Earthquakes
Close, U. and McCormick, D. 1922. Where the mountain walked. Nat. Geograph. Mag., 41, 445-464.
Hutchinson, J.N. and DEL PRETE, M. 1985. Landslides at Calitri, southern Apennines reactivated by the earthquake of 23rd November 1980. Geologia Applicata e Idrogeologia, 20, 9-38.
Murphy, W. 1995. The geomorphological controls on seismically triggered landslides during the 1908 Straits of Messina earthquake, Southern Italy. Quart. Journal of Eng. Geol. 28, 61-74.
Pain, C.F. 1972. Characteristics and geomorphic effects of earthquake-initiated landslides in the Adelbert Range, Papua New Guinea. Eng. Geol,. 6, 261-274
Sarma, S.K., 1973. Stability analysis of embankments and slopes. Geotechnique, 23, 3, 423-433.
Sarma, S.K., 1975. Seismic stability of earth dams and embankments. Geotechnique, 25, 4, 743-761.
Sarma, S.K. 1979. Stability analysis of embankments and slopes. A.S.C.E., Journal of the Geotechynical Engineering Division, 105, 12, 1511-1524.
Seed, H.B. 1966. A method for the earthquake resistant design of earth dams. A.S.C.E., Journal of the Soil Mechanics and Foundations Division, 92, 1, 13-41.
Seed, H.B. 1967. Slope stability during earthquakes. A.S.C.E., Journal of the Soil Mechanics and Foundations Division, 93, 4, 299-323.
Seed, H.B. 1968. Landslides during earthquakes due to soil liquefaction. A.S.C.E., Journal of the Soil Mechanics and Foundations Division, 94, 5, 1055-1122.
Seed, H.B. 1979. Considerations in the earthquake - resistant design of earth dams. Geotechnique, 29, 3, 215-263.
Skempton, A.W. 1985. Residual strength of clays in landslides, folded strata and the laboratory. Geotechnique, 35, 1, 3-18.
Skipp, B.O. and Emreaseys, N.N., 1987. Engineering seismology, in Ground Engineer's Reference Book, ed. by F.C. Bell, Butterworths, London.
Walker, B. and Fell, R., 1987. Soil slope instability and stabilisation. Belkema, Rotterdam. 440 pp.
back to Mechanics
When a soil is subjected to shear, an increasing resistance is built up. For any given applied effective pressure, there is a limit to the resistance that the soil can offer, which is known as the peak shear strength tp. Frequently the test is stopped immediately after the peak strength has been clearly defined. The value tp has been referred to, in the past, as simply the shear strength of the clay, under the given effective pressure and under drained conditions.
If the shearing is continued beyond the point where the maximum value of the shear strength has been mobilised, it is found that the resistance of the clay decreases, until ultimately a steady value is reached, and this constant minimum value is known as the residual strength tr of the soil. The soil maintains this steady value even when subjected to very large displacements.
In the absence of pre-existing failures the choice is between the peak or critical state strength. In uncemented soils the peak strength is associated with dilation and occurs at relatively small strains or displacements of the order of 1% or 1mm. The critical state strength is the shearing resistance for constant volume straining and occurs at strains or displacements of the order of 10% or 10mm. In many slopes ground movements and strains are relatively large and exceed the small movements required to mobilise the peak state. In addition, there is evidence that the peak value reflects the nature of the laboratory test procedure and gives an unconservative result in slope stability analysis.
back to Peak and residual strength
The figure shows a typical plot for a shear test which has been taken to displacements large enough to mobilise the residual strength. The decrease in shear strength from the peak to the residual condition is associated with orientation of the clay particles along shear planes.
back to Peak and residual strength
|
Peak shear strength |
Residual shear strength |
Critical state |
|||
|
Soil |
c' |
f' |
c'r |
f'r |
f'c |
|
kN/mē |
degrees |
kN/mē |
degrees |
degrees |
|
|
London clay, brown |
35 |
20 |
0 |
13 |
20 |
|
London clay, blue |
25 |
23 |
0 |
14 |
22 |
|
Upper Lias clay |
20 |
24 |
0 |
15 |
22 |
|
Cucarasha shale |
30 |
23 |
0 |
8 |
22 |
|
Upper Siwalik, Jari |
40 |
22 |
0 |
18 |
20 |
|
Boulder clay, Selset |
10 |
32 |
0 |
30 |
32 |
back to Peak and residual strength
The residual shear strength condition is of considerable practical importance since, if the soil in situ already contains slip planes or shear surfaces, then the strength operable on these surfaces will be less than the peak strength, and if sufficient displacement has taken place, the strength may be as low as the residual strength.
There are a number of circumstances, as a result of which shearing of the soil may already have taken place, and the principal processes, summarised by Morgenstern et al., are:
landsliding,
tectonic folding,
valley rebound,
glacial shove,
periglacial phenomena and
non-uniform swelling.
The identification of the existence of shear surfaces is a problem of great importance during any site investigation, particularly where mass movements are involved.
back to Peak and residual strength
It is generally accepted that the residual shear strength of a soil is independent of stress history effects, not influenced by specimen size, and rate-dependent to only a small extent unless very rapid rates of shearing are used. The major difficulty in determining the residual shear strength lies in the fact that large displacements may be necessary to achieve the required degree of orientation of the particles.
The methods of measuring residual shear strength in the laboratory are given below. The most satisfactory methods, in many ways, are to obtain undisturbed samples which contain a natural slip surface and then test them either in the shear box or triaxial apparatus so that failure occurs by sliding along the existing slip plane. Alternatively, an artificial slip plane can be produced by cutting the specimen with a thin wire-saw. Much of the early work on determining the residual shear strength of soils in the laboratory was performed using multi-reversal type tests in the shear box on previously un-sheared material.
The results of tests to measure residual shear strength in the shear box and triaxial apparatus have been reported by Skempton and Petley. There are practical difficulties with each of these tests, and they also have the major disadvantage that none of them permits the complete shear-stress-displacement relationship to be obtained.
Methods for measuring residual shear strength
Shear box
(a) Tests on natural shear surfaces
(b) Reversal-type tests
(c) Cut-plane tests
Triaxial
(a) Tests on natural shear surfaces
(b) Cut-plane tests
Ring shear
back to Measurement of residual shear strength
The large displacements required to define the complete shear-stress-displacement relationship can be obtained by using the ring-shear (or torsional shear) apparatus. The apparatus, shown diagrammatically, consists of two pairs of metal rings which hold an annular sample. The sample is subjected to a normal stress and then one pair of rings (normally the lower pair) is subjected to rotation. It is therefore a form of direct shear test, and failure occurs along a predetermined plane, as with the shear box. This type of apparatus was probably first used by Hvorslev and Tiedemann. More recent designs of the ring-shear apparatus have been described by Bishop et al. and Bromhead.
# Hvorslev, M.J. (1973). Über die Festigkeitseigenschaften gestörter bindiger Böden. Ingenior Skriftor A., Copenhagen, 45.
# Tiedemann, B. (1937). Über die Schubfestigkeit bindiger Böden. Bautechnik, 15,
# Bishop, A.W., Green, G.R., Garga, V.K., Andresen, A., and Brown, J.D. (1971). A new ring-shear apparatus and its application to the measurement of residual strength. Geotechnique, 21, 273-328.
# Bromhead, E.N. (1979). A simple ring shear apparatus. Ground Eng., 12, 40-44.
back to Peak and residual strength
Bishop, A.W., Green, G.R., Garga, V.K., Andresen, A., and Brown, J.D. (1971). A new ring-shear apparatus and its application to the measurement of residual strength. Geotechnique, 21, 273-328.
Bromhead, E.N. (1979). A simple ring shear apparatus. Ground Eng., 12, 40-44.
Hvorslev, M.J. (1973). Über die Festigkeitseigenschaften gestörter bindiger Böden. Ingenior Skriftor A., Copenhagen, 45.
Morgenstern, N.R., Blight, G.R., Janbu, N., and Resendiz, D. (1977). Slopes and excavations, 9th Int. Conf. Soil Mech. and Found. Eng., 12, 547-604.
Petley, D.J. (1984). Ground investigation, sampling and testing for studies sof slope instability. In Slope Instability, edited by D. Brunsden and D.B. Prior, John Wiley and Sons Ltd., Chichester.
Skempton, A.W. (1964). Long-term stability of clay slopes. Geotechnique, 14, 75-102.
Skempton, A.W., and Hutchinson, J.N. (1969). Stability of natural slopes and embankment foundations, State-of-the-Art Report. 7th Int. Conf. Soil Mech. Found. Eng., Mexico, 291-335.
Skempton, A.W., and Petley, D.J. (1967). The strength along structural discontinuities in stiff clay. Proc. Geot. Conf. on Shear Strength of Natural Soils and Rocks. Oslo, 2, 3-20.
Terzaghi, K. (1943). Theoretical Soil Mechanics, Wiley, New York.
Tiedemann, B. (1937). Über die Schubfestigkeit bindiger Böden. Bautechnik, 15,
back to Mechanics
Any sudden changes in loading on a slope will lead to changes in the pore pressures. Natural slopes are usually eroded very slowly and the soil is essentially drained throughout the process. This means that the pore pressures are governed by steady seepage from the ground towards the excavation and their magnitude can be obtained from a flownet. Man-made slopes are constructed relatively quickly, and in soils with low permeability, such as clay, there will be inadequate time during the construction period for the pore pressures to adjust to the new loading conditions, and the soil will then be essentially undrained.
back to Stress changes in slopes
The changes in total and effective stress during undrained slope excavation
are shown below.
In this simple example, the excavation is assumed to be kept full of water so
that the initial and final pore pressures are identical.
In (a) the total stresses on an element on a slip surface are t and s, and the pore pressure is indicated by the height of water in the standpipe. Obviously, before any excavation, the water in the standpipe is level with the phreatic surface, and the initial pore pressure can be represented by uo. This initial stress state is represented on (b) by the points A (in terms of total stress) and A' (in terms of effective stress).
As excavation proceeds, the value of s decreases and t increases due to the increase in slope height and/or angle. The total stress path is AB. The effective stress path is A'B', corresponding to undrained loading at constant water content, as indicated in (c).
The precise stress path A'B' in (c) will depend upon the characteristics of the soil and whether the soil is normally or over consolidated.
Since the process of excavation leads to reductions in loading, the pore pressure immediately after construction (u) is less than the initial pore pressure (uo), and so the initial excess pore pressure is negative (i.e. the level of the water in the standpipe is below the phreatic surface as shown in (d). As time passes, the total stress remains unchanged at B (because there is no change in the geometry of the slope). The negative excess pore pressures dissipate, leading to an increase in pore pressure. The normal effective stresses on the failure surface will decrease and swelling takes place as indicated in (b) and (c). The final state at C' corresponds to a steady state pore pressure after swelling has been completed. In this simple example, the excavation is kept full of water, and thus the initial and final pore pressures are equal (i.e. uo = uc).
Failure of the slope will take place if the states of all elements along the slip surface reach the failure line. If B' reaches the failure line, then the slope fails during the course of undrained excavation (i.e. during construction); whilst if C' reaches the failure line, it does so some time after construction has been completed. The distance of the points B' and C' from the failure line is a measure of the factor of safety of the slope.
These changes in the values of total
stress and pore pressure with time are shown here.
For the case considered above, the initial (uo) and final (uc) values of pore pressure are identical, but in general, this may not be the case.
For cutting slopes, the effective stress reduces with time, leading to leass shear resistance and a lower factor of safety. Consequently the critical time in the life of these slopes is likely to be in the long-term when the pore pressures have come into equilibrium with the steady seepage flownet.
back to Stress changes in slopes
It is of interest to compare the behaviour of cutting slopes with that of embankments. In the case of embankments, the construction process leads to an increase in pore pressure in the foundation soil, which then dissipates with time. Thus one of the critical stability conditions is likely to be at the end of construction, and will involve failure through the foundation. The relationship between total stress, pore pressure and time for this condition is indicated in the figure. In the embankment material itself, since the fill is unsaturated, the initial pore pressures are negative, and the initial states at B and B', are similar to the cut slopes.
back to Stress changes in slopes
The more general case is illustrated below.
Here the long-term pore pressures are controlled by the steady state flownet:
the general principles, however, remain unchanged.
back to Mechanics
The choice between the undrained strength su and the drained strength is relatively simple and straightforward. For temporary slopes and cuts in fine-grained soils with low permeability the undrained strength su should be used and a total stress analysis performed. This analysis is only valid whilst the soil is undrained. The stability will deteriorate with time as the pore pressures increase and the soil swells and softens.
For any permanent slope the critical conditions are at the end of swelling when pore pressures have reached equilibrium with a steady state seepage flownet or with hydrostatic conditions. In this case an effective stress strength is appropriate and the pore pressures are calculated separately.
back to Mechanics
The factor of safety should take account of uncertainties in the determinations of the loads (including the unit weight), the soil strengths and particularly the pore pressure or drainage conditions and the consequences of failure. The greatest uncertainty is in the determination of steady state pore pressures in drained analyses or in the assumption of constant volume (and hence constant strength) in undrained analyses. There is no single value of Fs that can be recommended for slope stability calculations. Typical values are often in the range 1.25 to 1.35, but can fall outside this range. The table below gives a range of suggested methods of analyses and typical factors of safety.
|
Typical Fs range |
|
|
Temporary cuttings and embankments: using undrained strength su and total stresses |
1.1 - 1.3 |
|
Permanent cuttings: using critical strength f'c and effective stresses |
1.2 - 1.4 |
|
Embankment foundation: undrained su or drained f' |
1.2 - 1.5 |
|
Embankment fill: drained f' for compacted soil and effective stresses |
1.2 - 1.4 |
|
Reactivated landslip: residual strength f'r |
(natural value) |
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