N. K. ToveyENV-2E1Y: Fluvial Geomorphology 2004– 2005 Section 5
ENV-2E1Y Fluvial Geomorphology
2004 - 2005
Multiple Landlsides at Yuen Mo Village, Kowloon East during the rain storm of 29 - 31st May 1982 when over 530 mm of rain fell. The collapse occurred in the late morning of 30th May and most of the huts in the village were destroyed or severely damaged. Three people were killed. At 16:15, the site was inspected by Emergency Duty Officer, N. K. Tovey who had previously inspected 4 other landslides in neighbouring villages, each one of which involved deaths. All remaining huts were condemed by Dr N.K. Tovey and a permanent evacuation order on all 120 inhabitants of Yuen Mo was issued. From that time Yuen Mo Village ceased to exist.
Slopes and related topics
Section 5 Slope Stability
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N. K. ToveyENV-2E1Y: Fluvial Geomorphology 2004– 2005 Section 5
Slope Stability and Related Topics
5. Slope Stability
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N. K. ToveyENV-2E1Y: Fluvial Geomorphology 2004– 2005 Section 5
5.1. Introduction
The stability of slopes and whether or not massive failure in the form of landslides occurs is dependent on several factors as were described in the introduction to this course. These may be summarised as:-
the geometry of the slope including the geometric configuration of the varying strata - determined by surveying methods,
water flow within the slope - analysed using techniques covered in section (2) of this course,
the material properties of the differing strata, including the unit weight angle of friction and cohesion, which are in turn dependent on the previous consolidation history of the soil,
additional loading by man.
There are several methods by which the stability of a slope may be analysed, many are valid only under certain conditions. There is also a group of more general solutions which can be applicable in all cases, but sometimes it is difficult to find a solution even with the aid of a computer.
Assuming we know the geometry of the slope and the underlying strata, the relevant material properties, and we also understand the water flow, then all methods of analysis begin with postulating a failure mechanism.
It is essential that we correctly identify the most critical mechanism, and this usually is a matter of experience. In the past, some slopes have been analysed and given a clean bill of health, but as a less than critical failure mechanism was identified failures have occurred on "theoretically" stable slopes sometimes with potentially disastrous consequences (e.g. the Tsing Yi, Hong Kong failures above the PEPCO oil storage depot following the rainstorm of 29th - 31st May 1982).
5.2. Types of failure
Failures in slopes may:-
1)be straight lines (particularly so in granular media)
2)approximate to arcs of circles
3)approximate to logarithmic spirals
4)be a combination of straight lines, arcs of circles, and/or logarithmic spirals.
Examples are shown in Fig. 5.1
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N. K. ToveyENV-2E1Y: Fluvial Geomorphology 2004– 2005 Section 5
Fig. 5.1 Examples of different methods for analysing stability of slopes.
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N. K. ToveyENV-2E1Y: Fluvial Geomorphology 2004– 2005 Section 5
a)example applicable for a purely cohesive soil where slip surface is a circle;
b)example applicable for soil with both cohesion and friction, but water flow must be absent. Failure is a straight line;
c)Infinite slope where slope is of approximately constant slope over a significant distance which is much greater than depth to bedrock. The failure surface is also parallel to this slope. Water flow can be included if it is parallel to slope as can changes in strata;
d)general case for slope of general shape. Slip surface may be of any form and may be composite including arcs or circles and straight line portions. In the example shown, there is a straight line section which is along the bedrock plane. Water flow can be incorporated as can variation in strata and the presence of tension cracks.
5.3. Progressive failure.
Most slope failures occur during or immediately after periods of heavy rain when the water table is high. Thus slope failures on the North Norfolk Coast are more common in winter during times of high water table. Equally, movement of the Mam Tor Landslide in Derbyshire occurs during the winter months and usually only if more than 400 mm of rain falls in the critical period. In Hong Kong, landslides are rare in the winter months from November to March, and are very common in the summer months (May - August) and over 500 landslides occurring in a single day have been reported.
Slopes may be triggered by rainfall, and may catastrophically fail if the rainstorm is prolonged (e.g. Po Shan Road, Hong Kong, 1972), but not infrequently, the failure is progressive with small amounts of movement until eventually the failure is catastrophic in a particular event (e.g. Aberfan, Tsing Yi). After massive and catastrophic failure, continued movement may take place (e.g. Mam Tor).
Fig. 5.2 Region of high stress in a slope prior to failure.
The stress-strain diagram indicates the approximate states of stress at points along the potential failure zone. Slight bulging of the toe would be discernible with accurate survey measurements.
Unlike materials such as steel which show relatively little deformation before failure, soils deform by a considerable amount before the peak shear strength is achieve in the case of dense sand or over consolidated clays. For loose sands and normally consolidated clays, the deformation before the ultimate strength is reached is large.
Strain is defined as a non-dimensional ratio which is the displacement during shearing over the original length of the sample. In a triaxial test, the sample is usually 75 mm long and a deformation of about 1 - 2 mm is needed to achieve peak strength in a dense test representing 1 - 3% strain. For loose samples, the deformation will be around 10 mm in a sample of comparable length.
In a slope the soil mass is large, and it is not possible for the whole slope to deform (with the associated volume change instantaneously. Near the base of the slope, the material can expand and bulge slightly and allow small strains along the potential failure plane as shown by the shaded region in Fig. 5.2.
The corresponding point on the stress - strain diagram is shown at point A on the rising part of the curve. Further around the failure zone, the points B and C have low amount of strain on the stress - strain plot, and the mobilised shear strength is thus small.
Fig. 5.3 Failure is now more advanced. The most highly stressed region has just passed peak shear strength, while at B, the strength is approaching peak. Region C is still relatively lightly stresses. Bulging at toe might noticeable in aerial photographs and might be visible to naked eye.
Once the lower part of the slope has deformed, the next part can deform (see Fig. 5.3. Here, the lowest part of the failure zone is at the peak shear strength, while moderate strengths have been mobilised further along the failure arc. The stress points corresponding to points B and C have moved further up the curve.
Finally (Fig. 5.4), after further deformation, bulging should become very evident at the base of the slope while the stress at the point A will now be less than previously as it has past the peak strength while the stress at B is now at peak and that at C is rising rapidly.
All along the failure arc, the mobilising shear stress will vary and it is the integrated value of the strength along the whole failure surface which will determine whether or not failure will occur. Such a failure which develops in this fashion is called a progressive failure.
Of importance is the fact that there will be a time delay (albeit quite short in some cases) from the start of the failure to the time of catastrophic failure. Normally, evidence of failure may be detected from bulging of the toe (early stage) and the development of tension cracks at the top (later stage), and finally a settlement of the crest immediately prior to failure.
Fig. 5.4. Whole of potential failure surface is now highly stressed with region A well beyond peak strength at the residual strength, region B at peak strength and region C approaching peak strength. Noticeable bulging at the toe which should be seen by naked eye. Failure is imminent.
Though the circumstances leading up to the Aberfan disaster on October 21st 1966 were contributory to the disaster. There were many signs in the months and years before that a potential disaster that a disaster might occur, the consequences of the disaster could have been avoided even at a late stage. Two people who were working at the top of the waste tip about 30 minutes before the disaster noted tension cracks and a settlement at the top. In vain they attempted to raise the alarm, but vandals had removed the wires of the communication telephones.
5.4. Methods of analysis
There are many methods available for studying the stability of slopes, and for some there are several variants. In this course we shall consider 4 basic methods:-
1)those methods for relatively shallow slopes in normally consolidated or lightly over consolidated materials and in which the soil material may be considered to be purely cohesive ( and undrained) situations (i.e. the failure envelope on the Mohr - Coulomb envelope is a constant irrespective of normal stress (i.e. = 0).
This method can be used for any slope profile, but is more suited to simple shapes. Water flow must be absent, i.e. excess water pressures, although the method may be use for slopes which are entirely submerged. Only single strata must be present.
2)those methods where the potential failure surface approximates to a straight line. It is valid for solids with both friction and cohesion, but there must be no water flow. The analysis is possible for irregular shaped surfaces, but it is more usually used for simple shapes. It is not really suited if there is more than one stratum.
3)those methods for the analysis of slopes which are approximately infinite in extent compared to the depth of the soil material. The angle of the slope is approximately constant over a large distance. Differing strata may be present, but only parallel to the surface.
The method can deal with water flow provided that it is parallel to the surface. Both frictional and cohesive materials may be present. This method of analysis is known as the Infinite Slope Method.
4)those methods which are applicable to the analysis of general slope stability. They are valid for varying ground water flow conditions, for various modes of failure (straight - line, arcs of circles or various combinations), for slopes with varying strata which may or may not be parallel to the failure surface or slope surface, and for slopes in which tension cracks have developed from desiccation of the surface layers.
These methods are collectively known as the Method of Slices, and there are several variants depending on the extent of approximations made. Generally speaking all assumptions are SAFE ASSUMPTIONS in that they underestimate the stability of the slope.
In the case of the Infinite slope method, the failure surface will always be parallel to the surface, and for a single stratum it can be shown (see section 5.7), that the stability is unaffected by the depth of the potential failure surface.
For all other methods of analysis, the method first assumes a failure surface of appropriate shape and analyses the stability to obtain a factor of safety (Fs)
If the computed factor of safety is less than unity, the slope is clearly unstable and likely to fail. If the factor of safety is greater than unity we cannot assume that the slope is stable as we may not have chosen the most critical mode of failure (i.e. failure surface). It is thus necessary to repeat the calculations with a different failure surface until the most critical one is found. Usually, experience will give a guidance as to what types of failure are likely to be more critical than others.
In the case of the straight line failures (other than the infinite slope cases), it is possible to assess the stability on a number of different failure planes each one at a different angle to the horizontal. A graph such as Fig. 5.5 is now plotted with the angle of the potential failure surface as the X - axis, and the computed Factor of Safety as the Y - axis. The value of Fs will be high for shallow angles, and fall as increases. After a critical angle, the value of s will rise again as continues to increase. In this example, the critical value of Fs is clearly the minimum of the curve.
A similar approach may be used for the purely cohesive failures. In this case, the it is the radius of curvature of the failure arc which is used as the independent variable on the X - axis.
Fig. 5.5. Variation of factor of safety with orientation of failure zone to horizontal in a straight line failure.
5.5 Method of Analysis - I
- purely cohesive failures.
Fig. 5.6 illustrates this type of failure. The failure surface is an arc of a circle with centre at point O. There is no frictional component in the resistance to failure and pure cohesion is developed along the failure arc. If the cohesion is c kPa, then the total cohesive force will be (the 1 comes from unit distance at right angles to the plane of the paper).
This cohesive force will be the resisting force, while the weight of the slope acting through the centre of gravity of the potential siding segment will be the mobilising force. In this case since the cohesive force and the weight do not act at a point we must also consider the moments of the forces in assessments of equilibrium, i.e. since the centre of gravity is not below the centre of the circle of failure, the weight will act as a pendulum and attempt to cause the segment to rotate. This tendency to move is counteracted by the cohesive force.
The assess the moments of the two key forces we need to determine the distances of their respective lines of action from the centre of the circle in a direction at right angles to the force. The weight acts at a distance X from the point O, while the cohesion acts along a tangent (i.e. at the radius of the slip surface).
Fig. 5.6 Failure of a slope in a purely cohesive medium. This failure surface is an arc of a circle. It is necessary to determine the distances X, R and L for analysis.
Restoring Moment
the factor of safety = ------
is given by:- Mobilising Moment
= ...... 5.1
Though this is a simple method of analysis there are some practical problems which require some ingenuity to solve. A question similar to this was set as an exam question a few years ago.
One problem is to determine the weight of the sliding mass:- this is equal to the area of the slice multiplied by the unit weight. The area could be computed by drawing the sliding mass on graph paper and counting squares, or it can be derived from geometry (rather more complex!). In the case in question, since this was a 40 minutes question (rather than the 60 minute question now set), the area of the wedge was given.
This still left the question of the position of the centre of gravity, the position of the centre of the sliding circle, and the length of the sliding arc to determine.
In the question, candidates were given a cardboard template of the exact shape of the sliding wedge, and a drawing pin on which to balance to wedge. So the solution to the question began with attempting to balance the wedge on the drawing pin. Once the approximate centre of gravity had been found, the template was pricked through so that the diagram on the question paper could be marked with the centre of gravity.
First join ends of slip circle, then through middle draw line at right angles. Point D is determined from equation 5.2, and hence the centre of the circle can be found.
Fig. 5.7 Geometric construction to find centre of circle accurately when using first method of analysis.
The centre of the sliding circle can be estimated by trial and error using a pair of compasses, or alternatively a geometric theorem can be used. The extreme ends of the slip circle are connected by a line which is then bisected at right angles (Fig. 5.7), such that AY = BY. These two distances can be measured from the diagram as can the distance CY.
Finally, the geometric theorem states that
DY x CY = AY x BY ...... 5.2
Hence it is possible to determine the distance DY and then the diameter of the circle CD. Finally, the distance CD is halved (i.e. OC = OD) to get the centre of the circle
The length of arc may be determined in one of three ways:-
a)join the lines from the extreme ends of the slip circle to the centre of the circle and measure the angle. Convert this angle to radians () and multiply by the radius of the circle.
i.e. L = R .
b)use a ruler and approximately rotate it around following the shape of the curve and read off the length.
c)adopt the method used by one candidate who pulled out a strand of her hair and laid this to follow the circle. Finally, the relevant length was measured on a ruler!.
5.6Method of Analysis - II
- Straight Line Failures
Fig. 5.8 shows this type of failure and the key forces to be considered.
To solve such a problem we need the weight of the sliding wedge. Once again this is derived from the area on a scale diagram (i.e. weight is area multiplied by unit weight). In all examples, the wedge is triangular, and the area may be obtained either from:-