ENV-2E1Y FLUVIAL GEOMORPHOLOGY
Examples of Previous Examination Questions and notes on how to solve numeric questions for Slope Stability and Related Topics.
Exam Questions 1999 onwards
Please note that in 1999 the course code was ENV-2B07 and it was a 20 credit course with a 2 hour examination with 2 one hour questions to be answered.
From 2001, the course code became ENV-2E1y and the exam became 3 hours with three one hour questions to be answered. There will be four sections and you will be expected to answer questions from three of them.
The four sections will be
Rivers – descriptive
Rivers – numeric
Slopes – descriptive
Slopes - numeric
You may thus do 2 questions from Richards part of the course and one from mine or 2 from mine and one from Richard’s. You also have the choice of doing 2 numeric questions and one descriptive one or two descriptive ones and one numeric one.
ENV-2E1Y Fluvial Geomorphology - Previous Exam Questions. 1999 – onwards
In 1999, the Course Code was ENV-2B07 and the unit was 20 credits with a 2 hour exam in which 2 questions were to be answered. There were three questions from the Slopes Section and 3 from the Rivers Sections. The number of numeric questions in the two sections used to alternate form year to year (i.e. in 1997 there were two numeric questions in the rivers Section, in 1999 there were two numeric questions in the Slopes Section.
1999 Paper
1)Discuss the similarities and differences in potential modes of failure between river banks and normal slopes. Why do methods developed for the latter not always apply to the former?
Describe the field measurements, laboratory tests, and analyses you would make to assess the stability of of composite river banks.
2). Describe how you would determine the consolidation behaviour of a sediment, and critically review any assumptions made in classical consolidation theory.
Fig. 1 shows a simplified borehole taken in 1990 from within the site reclaimed for the new Hong Kong International Airport. The sequences identified as M1 and M2 represent the marine deposits in the Holocene and last inter-glacial periods, while T1 is the part of the M2 affected by desiccation and pedogenesis during the fall in sea level during the last glaciation. The area itself was not glaciated, and it may be assumed that during the glacial period, the local ground water level was at the base of the T1 unit, and that the unit weight and degree of saturation of the T1 unit during that period were 16.50 kN m-3 and 0.4 respectively.
Estimate:
a)the unit weight of the desciccated layer after the sea level rises,
b)the effective overall stress increment when depositiion of the holocene sediments is complete
c)the consolidation of the pre-holocene layers as a result of the recent deposition.
The consolidation in the M2 and T1 units during the Holocene if the consoldation behaviour of the two units are as shown in Table 1, while it may be assumed that the specific gravity of the sediment in all layers is 2.65..
M2 unit / T1 unitnormal stress (kPa)
/ voids ratio
/ voids ratio
20 / 1.600 / 0.805
40 / 1.450 / 0.780
80 / 1.300 / 0.754
160 / 1.150 / 0.729
320 / 1.000 / 0.703
640 / 0.850 / 0.678
1280 / 0.700 / 0.652
2560 / 0.550 / 0.550
5120 / 0.400 / 0.400
Table 1. Consolidation behaviour of M2 and T1 units
Fig. 1 Simplified borehole of sediments at Chek Lap Kok Airport site.
Part (a) - need to calculate initial voids ratio
Now calculate the unit weight of the saturated layer after it becomes saturated. Here we assume that resaturation takes place with no change in voids ratio (valid unless smectitic).
Part (b)
depth / initial unit wt(kNm-3) / total stress (kPa) / water pressure
(kPa) / effective stress (KpA) / new unit weight
(kNm-3) / Not needed / Stress decrement / net stress increment
top / T1 / 0 / 0 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 55.00
mid / T1 / 1.25 / 16.5 / 20.63 / 20.63 / 19.17 / 11.46 / 9.17 / 45.83
top / M2a / 2.5 / 16.5 / 41.25 / 0.00 / 41.25 / 19.17 / 22.92 / 18.33 / 36.67
mid / M2a / 3.75 / 16.6 / 62.00 / 12.50 / 49.50 / 16.60 / 31.17 / 18.33 / 36.67
top / M2b / 5 / 16.6 / 82.75 / 25.00 / 57.75 / 16.60 / 39.42 / 18.33 / 36.67
mid / M2b / 6.25 / 17.05 / 104.06 / 37.50 / 66.56 / 17.05 / 48.23 / 18.33 / 36.67
top / M2c / 7.5 / 17.05 / 125.38 / 50.00 / 75.38 / 17.05 / 57.04 / 18.33 / 36.67
mid / M2c / 8.75 / 17.48 / 147.23 / 62.50 / 84.73 / 17.48 / 66.39 / 18.33 / 36.67
Part (c) - using mid points of each layer as being representative.
The key issue here is to estimate mvcand there are several methods to estimate this. One involves working out the change in voids ratio with stress and correcting by the factor (1 + eo) followed by plotting a graph of mvc so that values of mvc can be read off appropriately. Another method involves an incemremtal approach where the change in e and change in stress are computed and explicit values of mvc are computed for each increment. All methods will give approximately the same answer for mvc. All methods use the formula
Using the latter method
Layer / Stress increment / initial voids ratio / Final Void ratio / Change in e / mvc / .mvc1 / T1 / 1.25 / 20.63 / 66.46 / 45.83 / 0.804 / 0.76 / 0.041 / 0.000501 / 0.022979
2 / M2a / 3.75 / 49.50 / 86.17 / 36.67 / 1.414 / 1.29 / 0.126 / 0.001423 / 0.052162
3 / M2b / 6.25 / 66.56 / 103.23 / 36.67 / 1.350 / 1.26 / 0.094 / 0.001090 / 0.03997
4 / M2c / 8.75 / 84.73 / 121.39 / 36.67 / 1.291 / 1.22 / 0.069 / 0.000818 / 0.030007
Summation / 0.145117
and total setllement =
All layers are 2.5m thick so total settlement will be 2.5 * 0.145117 = 0.363m
======
3). How are "Factors of Safety" used to assess the stabilioty of slopes. Discuss wht some slopes with low factors of safety are stable, while others with high factors fail.
[20%]
Fig. 2 shows a simplified cross section of the winter dyke on the south side of the Rhine opposite Wageningen in the Netherlands. The landward side is an extensive area including many hundred houses. During floods in February 1995, the river rose to within 0.5 m of the crest of the dyke.
Investigate the stability of the dyke based on the slip circle and slices shown. The meaen values of the unit weight, cohesion, and angle of friction are 17.8 kN m-3, 20 kPa, and 11o respectively.
[70%]
In the circumstances prevailing at the peak river flow, what recommendations would you have given, both in the short term and long term regarding the stability of the dyke?
[10%]
Fig 2 Section through winter dyke on south bank of Rhine near Wageningen, The Netherlands
ENV-2E1Y Fluvial Geomorphology Exam 2001:
Briefly discuss the validity of the assumptions made in Terzaghi’s Theory of consolidation.
[30%]
A study is to be made on the behaviour of a layer of marine clay 1.999m thick buried between two sandy-silty layers. Initially the layer is in equilibrium with no excess pore pressure. During two storm events exactly one year apart cause additional sedimentation leading to a stress increment of 10 kPa on both occasions. Estimate and plot the excess pore water distribution with depth immediately preceding the second increment, and also after two years.
Data from a laboratory oedometer test done on a sample 19.5 mm thick is shown in table 1.
[70%]
Table 1
Time (minutes) / Settlement (mm)0.0 / 0.000
1.0 / 0.120
3.9 / 0.240
8.9 / 0.360
15.8 / 0.480
25.0 / 0.604
35.9 / 0.720
50.0 / 0.837
70.9 / 0.960
106.0 / 1.080
141.3 / 1.140
188.8 / 1.200
247.5 / 1.236
405.0 / 1.296
- In the analysis of the stability of slopes, some assumptions lead to unsafe solutions while others lead to safe solutions. Explain why these differences occur, and the approach you would take for an initial appraisal of the stability of a slope.
[30%]
A 60o slope is 20m high. By considering potential planar failure surfaces, determine whether the slope is stable. Data from standard shear box tests done on the material of the slope are shown in Table 2. The unit weight of the material is 17 kN m-3.
You may assume that the water table is below any potential failure surface and you may ignore the effects of tension cracks.
[70%]
Normal Force (N) / Shear Force (N)100 / 134.8
200 / 161.6
300 / 188.4
400 / 215.2
500 / 242.0
600 / 268.8
The shear box is 6cm x 6cm in size
- You have been asked to investigate the causes of a major landslide in a slope approximately 100 m high and 150 wide. Describe the field and laboratory studies you would undertake to establish the causes of the failure.
In your answer you should include a discussion of the resources of manpower, time, and equipment you are likely to require to complete the survey.
- Explain why the mechanisms of failure of river banks are often very different from those of normal slopes.
[30%]
What field and/or laboratory measurements would you do to ascertain the stability of such river banks?
[70%].
======
- Model Answer
Evaluate (time) and plot settlement against (time)
Time / Time / Settlement / % Settlement(mins) / (mins)1/2 / (mm) / (worked out after construction of graph)
0.0 / 0.000 / 0.000 / 0.0
1.0 / 1.000 / 0.120 / 10.0
3.9 / 1.969 / 0.240 / 20.0
8.9 / 2.979 / 0.360 / 30.0
15.8 / 3.969 / 0.480 / 40.0
25.0 / 5.000 / 0.604 / 50.4
35.9 / 5.990 / 0.720 / 60.0
50.0 / 7.071 / 0.837 / 69.8
70.9 / 8.419 / 0.960 / 80.0
106.0 / 10.296 / 1.080 / 90.0
141.3 / 11.885 / 1.140 / 95.0
188.8 / 13.739 / 1.200 / 100.0
247.5 / 15.732 / 1.236
405.0 / 20.125 / 1.296
First part of curve is linear. (see approximate line. Plot line with gradient 1.155 times that of original line. Intersection at A defines 90% consolidation point, hence scale to find theoretical100% consolidation point in absence of secondary consolidation at point B corresponding with a settlement of 1.2 mm.
[suggest that 30 ex 70 marks are given for getting this graph and values]
So evaluate the proportions of consolidation for other values and enter them in table.
[35 marks]
Also since the material in field and lab are the same the following relationship is valid
So the equivalent of one year in field in terms of lab =
365 * 86400 * 0.01952 / 1.9992 = 3000 seconds = 50 minutes
This corresponds to one of the lab times and represents the 69.8% (~ 70%) consolidation..
[10 marks]
Representing a time factor of 0.4. So plot up values from graph corresponding to Tv=0.4. These must be multiplied by 10 as the annual increment is 10 kPa.
Further after 2 years, the corresponding value of Tv would be 0.8 and this is the relevant line for the residual pressure for the first increment after 2 years. Since there is a second increment after 12 months, at the end of 2 year from the start, this increment will have dissipated to Tv = 0.4, so the final pore pressure distribution after 2 years would be the equivalent of the curve from Tv=0.8 added to the curve for Tv=0.4. This does assumes linearity and that increments can be added which is a reasonable first approximation. A more detailed analysis would require a finite difference approach.
[10 marks for distribution at end of 1st year and 5 at end of 2nd year]
- Determine shear and normal stresses
Normal Force
(N) / Shear Force
(N) / Normal Stress (kPa) / Shear Stress (kPa)
100 / 134.8 / 27.8 / 37.4
200 / 161.6 / 55.6 / 44.9
300 / 188.4 / 83.3 / 52.3
400 / 215.2 / 111.1 / 59.8
500 / 242.0 / 138.9 / 67.2
600 / 268.8 / 166.7 / 74.7
Now plot Shear Stress against Normal Stress
This gives and intercept of 30 kPa for cohesion and 15o for angle of friction
Initially, one does not know the critical failure surface but it is likely to be around about 40o so try angles of 35, 40 and 45o and then revise when results from these are known. Analysis is best done in Tabular form.
failure surface angle / failure surface length / area of wedge / weight of wedge / cohesion x L / Normal force / Shear Force / Factor of Safety35 / 34.9 / 170.2 / 2892.7 / 1046.1 / 634.9 / 1659.2 / 1.0131
40 / 31.1 / 122.9 / 2089.0 / 933.4 / 428.8 / 1342.8 / 1.0145
45 / 28.3 / 84.5 / 1437.0 / 848.5 / 272.3 / 1016.1 / 1.1030
38 / 32.5 / 140.5 / 2388.8 / 974.6 / 504.4 / 1470.7 / 1.0056
37 / 33.2 / 149.9 / 2549.0 / 997.0 / 545.5 / 1534.0 / 1.0055
37.5 / 32.9 / 145.2 / 2468.0 / 985.6 / 524.6 / 1502.4 / 1.0052
Critical failure surface lies between 35 and 40o so refine analysis leading to critical angle at 37.5o.
At this angle factor of safety is 1.005 and so only just stable.
Note depending on precision of analysis, some students my find slope is marginally unstable - this will get full marks provided final value is within range of 0.98 to 1.02 and comment on stability is consistent. 100% of marks available if gets precision to 0.5o, 95% for precision to 1o and 90% marks for this part if precision is to nearest 5o. 80% maximum marks if only one slip surface done.
ENV-2E1Y Fluvial Geomorphology Exam 2003:
Section A
1). You have been appointed to establish a Landslide Warning and Slope Management System for a tropical country. Outline the strategy you would adopt taking due account of the problems encountered in Hong Kong in the early 1980s.
2). In 1911, a major landslide occurred near the village of Sarez in Tajikistan, the consequences of which have been causing much concern in recent years. Describe why there remains the potential of another major disaster. What steps you would take to assess this risk and what measure would to take to mitigate against such a disaster.
Section B
3) What field surveying methods would you use to assess the stability of a slope?
Fig. 1 shows the cross section of a slope which has been causing concern. Review the stability of the slope along the potential slip circle, if the material properties of the material are:-
[20%]
Bulk unit weight 18 kN m-3
Cohesion18 kPa
Angle of friction20o
Unit weight of water may be assumed to be 10 kN m-3
You should consider the stability for the predicted 10 year water table shown in Fig. 2 and also when the water table is below the potential slip circle.
[70%]
What measures would you take to stabilise the slope.
[10%]
1
ENV-2E1Y [2003] Question 3
Fig. 9. Cross Section of Slope showing a potential failure surface.
1
4). What are the Atterberg Limits of a soil are and how may they be measured?.
[20%]
How may the shear and consolidation behaviour of the soil be estimated from a knowledge of the Atterberg Limits?.
[10%]
Fig. 2 shows a simplified profile of the marine Holocene deposits at the site of the Chek Lap Kok Airport in Hong Kong.
The Liquid Limit and Plastic Limit were measured as 91.0% and 30.6% respectively
In 2002 Tovey and Paul published the following relationship which relates e1 (the void ratio at 1 kPa) to the compression index (Cc ).
e1 = 0.866 + 2.711 Cc
In the construction of the airport, the top 5m of the Holocene deposit were replaced, and fill ( (unit weight 18.1 kN m-3) was placed over the area so that it rose to a height of 5m above sea level.
From the data above estimate the settlement of airport site.
You may assume that the settlement of the pre-Holocene layer is negligible, and that the unit weight of water can be approximated to 10 kN m-3..
ENV-2E1Y [2003] Question 4
Fig. 1 Simplified Sequence at Chek Lap Kok Airport Site
MODEL ANSWERS
Question 1.
There are several approaches that could be taken in answering this question.
A good answer will refer to the extensive experience from Hong Kong and in particular how the system there developed. A key aspect for the Landslide Warning System is the requirement for simplicity and to avoid ambiguities as happened in the early development of the Hong Kong System. For instance, two different bodies were involved and the interpretation of “24 hour” rainfall was very different between the two bodies that there were disastrous consequences when the system was first used.
Reference should be made to Lumb’s (1975) paper or equivalent Hong Kong report outlining the historical review of how and when Landslides occur. However, comment should also be made on how the antecedent conditions suggested by Lumb and others tended to deflect development of rational system.
With regards to Slope Management, the important issue to emphasize is the need for a logical and systematic approach which takes due account of the limitations of manpower and time resources in the years immediately after such a scheme has been set up.
A good answer will make reference to the Hong Kong Slope Information System Web site.
This part of the answer will also demonstrate the need for prioritising work e.g.
Stage 1 - quick overview study to catalogue slopes giving basic information of type, height, slope angle, signs of distress etc.
Stage 1b – providing a means to identify the most critical slopes from the catalogue – this might be a simple ranking system of the different attributes
Stage 2 shortlist slopes (say 20) from catalogue and ranking and do a more thorough analysis as well as checking original data was correct. This is then used to select the most critical slopes (say 6) which are then included in a Landslide Preventative Measures Program
Stage 3 will the involve detailed site investigation, full slope stability analysis, and the design of remedial measure such as provision of horizontal drains, regrading slope etc. This would be followed by construction of the remedial measures.
The above stages are cyclic so that when the most critical slopes have been upgraded, the next most sever slopes as identified at the Stage 1b level are considered.
Question2
This question can only be answered by those students who have read papers most of which are now on the WEB about the Lake Sarez incident, and in particular the UN: IDNDR report.
The original landslide occurred as a result of an earthquake which measured 9 – 10 on the Richter Scale, and created a natural dam which is 550 metre high and 4 km crest length. It is the largest dam (whether natural or man made) in the world. The landslide blocked the river Murgob with its several tributaries and water started impounding and has continued to rise.
After Lake Baikal, Lake Sarez is the largest volume of fresh water on the planet and has a particularly unique ecological environment. The level of water has continued to rise and it is now around 50m below the crest on the right bank, although the left bank crest is nearly 200 m higher. In recent years with the increased water pressure, seepage has occurred on the downstream face leading to some erosion. There are concerns that continued erosion like this could lead to a catastrophic collapse of the dam, and if this did not happen, then the increasing water level will impose additional stresses leading to failure.
Up to 5 million people live down stream of the dam, and many could be affected by a collapse.
The recent UN: IDNDR report suggest that a catastrophic failure of the dam at the present time is unlikely, and that attempts top drain the lake by widening the existing seepage channels could cause further erosion problems.
A new concern in this earthquake prone area is that a new quake of the magnitude of 1911 could trigger another landslide into the lake which could cause a tidal wave to overtop the dam in the same way that the Vaiont Dam was overtopped in Italy in 1962.
To assess the risk will require detailed analysis of the stability of the dam. A problem here might be the difficulty in obtaining samples which are representative of the whole core. Piezometers should be installed within the dam to monitor water pressures. Due the size of the dam it is unlikely that cohesion will be significant in the stability, and for estimates of soil properties it may be sufficiently accurate to assume a cohesionless material.