UNIVERSITY OF CINCINNATI
Date:______
I, ______, hereby submit this work as part of the requirements for the degree of: in:
It is entitled:
This work and its defense approved by:
Chair: ______
BANK INSTABILITY RESULTING FROM RAPID FLOOD
RECESSION ALONG THE LICKING RIVER, KENTUCKY
A thesis submitted to the
Division of Research and Advanced Studies
of the University of Cincinnati
in partial fulfillment of the
Requirements for the degree of
MASTER OF SCIENCE
In the Department of Geology
Of the College of Arts and Sciences
2004
by
Ana Cristina Londono G.
B.S., Universidad Nacional de Colombia, 1995
Committee Chair: Dr. David B. Nash ABSTRACT River bank instability has been linked with changing land use,
deforestation and channel meandering. Fluctuations in water level, either seasonal or more frequent, have also been related to instability. Increased pore water pressure has been correlated with flooding. When, the level of water decreases rapidly, the pore water pressure within the soil remains high, thereby decreasing the soil’s effective shear strength. This reduction in shear strength
may result in bank failure.
The banks of the Licking River near Wilder, Kentucky were selected as a
study site because they exhibit instability features: tension cracks, circular and
wedge failures, slumps and piping, some of which developed after a major
flooding event in 1997. Tensiometers were installed at depth from 4 ft to 10 ft
and a piezometer was installed at a depth of 12 ft. The bank material is clay with
low plasticity (CL) with total cohesion and friction angle of 27 kPa and 13o respectively.
Although soil suction was found to respond rapidly to wetting and drying, the results demonstrate the importance of antecedent events in the saturation of the slope and in the reduction of matric suction.
High values of the factor of safety for slope failure were found when modeling the slope under steady-state conditions but lower values were found for rapid drawdown cases. Modeling of the slope indicates that cohesion and hydrostatic confining pressure are critical parameters in evaluating the bank stability.
i Thus, riverbanks are sensitive to the history of water elevation changes.
soil suction fluctuates greatly due to rainfall and flooding episodes. Because this
parameter is so variable, including it in the calculation of the stability of the slope may lead to overestimation of the factor of safety. Therefore, assumption of saturated conditions is more conservative.
Prolonged periods of flooding or flood events with significant antecedent rainfall or other flood events cause saturation of the slope. This increases the likelihood of failure when water stage lowers rapidly. The critical water elevation was found to be below 140 m for rapid drawdown conditions after flood recession on to the Licking River.
Key words: Matric suction, bank instability, Licking River, cohesion, floods
ii ACKNOWLEDGMENTS I would like to extend my gratitude to the Geology Department for electing
me to be the recipient of the Wycoff Scholarship that allowed me to conduct this
research and for the summer research grant to complete the fieldwork. The
members of my committee, Drs. David B. Nash, Thomas V. Lowell, Barry J.
Maynard in the Geology Department and Mark T. Bowers from the Civil and
Environmental Engineering Department for their advice, for sharing their wisdom
with me and for the discussions to improve the results of this work.
Great appreciation to my friends, Rick Bullard for introducing me to the
Frederick’s Landing Park and its instability problems and help in the field; Ji-Yeon
Shin for being an awesome field assistant; Alejandra Bonilla for her help in the
field and Alexander Stewart for his hard work in the equipment installation and
critical revisions of this manuscript.
Thanks to Terry Vance, City of Wilder Administrator for letting me
installing the equipment at Frederick’s Landing Park. Rich Pohana for lent me
the current transducers. Mike Menard for putting together the datalogger-
tensiometer set up; Ken for finding an awesome protecting box for the
datalogger.
This work would have not been possible to complete without the
generosity of HC Nutting Co.: George Webb for providing me of free drilling and sampling, for facilitating the Soil’s laboratory for testing, Steven Xao for his supervision and advice during testing and for his observations of test results and the help of both Lab technicians, Fred and Steve for actually running the tests.
iii My Gratitude to Howard Meisner and Tom Dryer at the Cincinnati rowing team for taking me on a boat ride along the Licking River. Swaminathan
Srinivasan and Olusegun Akomolede for their recommendations in the data analysis.
Finally, special thanks to my family and friends at home for their constant support, for cheering me up in the low times and for encouraging me to pursue my dreams.
iv DISCLAIMER
Mentioning of company names and commercial products does not imply endorsement or recommendation by the University of Cincinnati.
v NOTE TO READER
The complete laboratory analysis and failure surface files can be obtained on PDF format contacting the author at the Geology Department, University of
Cincinnati.
vi TABLE OF CONTENTS
BANK STABILITY RESULTING FROM RAPID FLOOD RECESSION ALONG THE LICKING RIVER, KENTUCKY...... i ABSTRACT ...... i ACKNOWLEDGMENTS ...... iii DISCLAIMER...... v NOTE TO READER...... vi TABLE OF CONTENTS ...... vii LIST OF FIGURES ...... ix LIST OF TABLES ...... xiii CHAPTER 1 ...... 1 INTRODUCTION ...... 1 1.1. STATEMENT OF PROBLEM...... 2 1.2. LOCATION...... 2 1.3. HYDROLOGY ...... 4 1.4. PREVIOUS WORKS...... 6 1.5. LOCAL FAILURE CONDITIONS...... 14 CHAPTER 2 ...... 18 SETTING...... 18 2.1. NORTHERN KENTUCKY EROSIONAL HISTORY ...... 21 2.2. GEOLOGY...... 23 2.2.1. BEDROCK...... 27 2.2.2. UNCONSOLIDATED DEPOSITS...... 29 2.2.2.1. PLEISTOCENE DEPOSITS...... 29 2.2.2.1.1. Outwash Deposits ...... 29 2.2.2.1.2. Terraces ...... 30 2.2.2.2. HOLOCENE...... 30 2.3. Soils ...... 35 CHAPTER 3 ...... 38 METHODS AND MATERIALS ...... 38 3.1. TENSIOMETERS AND PIEZOMETER INSTALLATION...... 38 3.2. SAMPLING ...... 41 3.3. SOIL TESTING ...... 42 3.3.1. MOISTURE CONTENT ...... 42 3.3.2. SPECIFIC GRAVITY ...... 45 3.3.3. GRAIN SIZE ANALYSIS...... 45 3.3.4. ATTERBERG LIMITS...... 47 3.3.5. CONSOLIDATION TEST...... 49 3.3.6. UNCONFINED COMPRESSION TESTING ...... 49 3.3.7. TRIAXIAL TESTING...... 52 CHAPTER 4 ...... 56 THEORETICAL BACKGROUND ...... 56 4.1. DEFINITIONS ...... 57 4.1.1. AIR PHASE ...... 57
vii 4.1.2. WATER PHASE ...... 58 4.1.3. AIR-WATER INTERFACE OR CONTRACTILE SKIN ...... 60 4.2. MECHANICAL BEHAVIOR OF UNSATURATED SOILS...... 61 4.3. STABILITY ANALYSIS...... 66 4.4. INFLUENCE OF WATER ON THE MECHANICAL BEHAVIOR OF UNSATURATED SOILS ...... 72 CHAPTER 5 ...... 79 ANALYSIS AND RESULTS...... 79 CHAPTER 6...... 86 STABILITY ANALYSIS RESULTS...... 86 6.1. CIRCULAR FAILURE ANALYSIS RESULTS...... 90 6.2. WEDGE FAILURE ANALYSIS RESULTS ...... 103 CHAPTER 7...... 110 CONCLUSIONS AND RECOMMENDATIONS...... 110 REFERENCES ...... 113 APPENDIX ...... 121 Output files for fixed failure surface and free failure surface search trials ...... 121
viii LIST OF FIGURES
Figure No. Page No
1. Frederick’s Landing Park, city of Wilder, Kentucky 3
2. Ohio River stage during 1997 flood 5
3. Gage height for Ohio and Licking Rivers 7
4. Street collapse, end of 7th street, Covington, Kentucky 9
5. Rotational slide on 6th street, Covington, Kentucky 10
6. Circular slide showing development of tension cracks at Frederick’s Landing, Wilder, Kentucky 15
7. Wedge failure on high banks of western margin of Licking River 15
8. Slump failure on western margin of Licking River after flood recession, March 18, 2004 16
9. Seepage developed on banks in the western margin of the Licking River. April 3, 2003 17
10. Schematic map of physiographic units along the Licking River Basin 19
11. Digital elevation model of Licking River Basin 20
12. Glaciation history in Indiana, Ohio and Northern Kentucky 22
13. Digital elevation model Newport and Covington quadrangles, Kentucky Red dot indicates the location of Frederick’s Landing Park 24
14. Geologic map of Licking River basin 25
15. Geologic map of study area. Point X indicates location of deep borings to bedrock 26
16. Bedrock outcrop on western margin of the Licking River 28
17. Soil profile at Frederick’s Landing 32
18. XRD Pattern for Olive brown silty clay. Quartz (Q), kaolinite (K), illite (I), chlorite (Ch). 33
ix 19. XRD Pattern for greenish gray silty clay. Quartz (Q), kaolinite (K), illite (I), chlorite (Ch). 34
20. Soil survey for parts of Campbell and Kenton counties. Red dot indicates location of Frederick’s Landing Park 36
21. Pressure transducer installed on tensiometer 39
22. The lower 0.6 meters (2 feet) of the piezometer are perforated 40
23. Drilling procedure using an all terrain vehicle with hollow stem auger 41
24. Moisture content versus depth at Frederick’s Landing soil profile 43
25. Hydrometer analysis assemblage used for determining grain size distribution 45
26. Grain size analysis for silty clays at Frederick’s Landing 46
27. Plasticity chart for Unified Soil Classification System 47
28. Unified Soil Classification System 48
29. Consolidation test result. Preconsolidation pressure, σc’=235 kPa (2.45 TSF) 50
30. Unconfined compression test, Borehole 5, 3.5-3.7 meters (11’4” – 12’) 51
31. Triaxial test assembly for backpressure saturation and consolidation processes 53
32. Triaxial test after application of deviator stress and failed sample 54
33. Results of Consolidated Undrained Triaxial testing 55
34. Air – water meniscus between two solid spheres 59
35. Soil-water characteristic curves showing drying and wetting of the sandy soil 59
36. Effect of suction on the increment of normal stress 61
37. Modified Mohr – Coulomb failure envelope for unsaturated soils 63
38. Component of cohesion due to matric suction for different φb values 65
x 39. Influence on variation of φb values on the factor of safety of a slope 65
40. Forces acting on a soil slice 68
41. Forces acting on a riverbank under wedge failure type 71
42. Advance of wetting front through a soil derived from colluvium at different times (readings every five minutes) 73
43. Moisture increase within the soil 74
44. Initial and final conditions for specific resistance within a soil after a five – day raining period 75
45. Influence of rainfall intensity on the factor of safety of a slope 77
46. Influence of rainfall duration on the factor of safety of a slope 77
47. Matric suction measurements along the eastern bank of the Licking River at the city of Wilder, Kentucky. 81
48. Changes in water table and river elevations during September 2003 – July 2004. Dark blue-red dots indicate flooding. 83
49. Flood occurred in November 15th, river elevation 144 m masl 84
50. Seepage developed after two consecutive flood events 84
51. Slope profile at Frederick’s Landing 87
52. Steady-state conditions with a deep water table 88
53. Rapid drawdown conditions with seepage developed along the slope 88
54. Circular failure analysis with fixed surface, undrained analysis 91
55. Factor of safety vs. river elevation with groundwater below and at the surface (φ=17o), undrained analysis 94
56. Factor of safety vs. river elevation with groundwater at ground surface 96
57. Undrained vs. drained approach for stability analysis with groundwater below the ground surface (φ =17o) 98
58. Critical pool ratio for slope at Frederick’s Landing 100
xi 59. Circular failure analysis with free surface search, undrained analysis 102
60. Wedge failure modeling with rapid drawdown conditions 104
xii LIST OF TABLES Table No Page No
1. Historical peak streamflow in the Ohio River 8
2. Measured soil properties at Frederick’s Landing 43
3. Consolidation test results on gray lean silty clay, Borehole 3 48 (2 – 2.23 meters; 6’ 8” – 7’ 4”)
4. Consistency and unconfined compressive strength (qu) of clayey materials 50
5. Classification of sensitive clays 51
6. Results of triaxial tests under saturated and unsaturated conditions on compacted Dhanauri clay 62
7. Experimental values of φb 63
8. Static equilibrium conditions satisfied by limit equilibrium methods 67
9. Comparison of strength parameters for Licking and Missouri rivers 79
10. Factor of safety calculations for circular failure using Modified Bishop Method and fixed failure surface 91
11. Critical pool ratio with assumed base level 138.5 m masl, slope height 9.5 m for slope at Frederick’s Landing 98
12. Factor of safety calculation using Modified Bishop Method with free failure surface search 100
13. Values of factors of safety for wedge failure analysis 104
xiii CHAPTER 1 INTRODUCTION Floodplains have been centers of human occupation since the dawn of
civilization because of their fertility and the accessibility to water for agriculture
and industry. There are, however, problems with floodplains: they flood and their
banks are often unstable and prone to erosion.
Riverbank instability has been linked with changing land use,
deforestation, undercutting by meander migration, and seasonal, rapid
fluctuations in river level. Recent studies (Simon et al., 2000; Darby et al., 2000;
Simon et al., 2002) have also correlated bank instability with increased pore water pressure resulting from flooding events. During periods of flooding or high- water level, soils become saturated. When the river level drops with sufficient rapidity, the soil remains saturated and significant seepage forces develop, thereby increasing lateral shear stresses, which may cause the banks to fail.
The banks of the Licking River in northern Kentucky display continued instability, making them ideally suited for analyzing the processes initiating mass movement and ways they may be mitigated.
In 1997, a major flood occurred in portions of southern Ohio, Indiana and northern Kentucky. Floodplains in these areas were covered by ten meters (30 feet) of water and remained inundated for two weeks. During this period, water percolated into the soil changing its hydraulic conditions from partially saturated to saturated conditions with positive pore pressure, decreasing the effective stress. When the flood receded, the banks were fully saturated under undrained
1 conditions without lateral confinement. Elevated pore pressures combined with
the loss of soil strength triggered several rotational slumps, causing damage to
adjacent property.
This study examines the strength characteristics and hydraulic properties
of bank material located at the northern extent of the Licking River, Kentucky
near its confluence with the Ohio River and it combines them to model the
mechanical failure of the banks.
1.1. STATEMENT OF PROBLEM River bank failure causes loss of productive land and damage to
properties located on them. The banks along the Licking River present instability
features after the water stage rises, then lowers, yet they remain stable during
lower stages of the river. After water recession, some of the slopes fail while
others remain stable even under rapid drawdown conditions considered as the
worse case scenario.
This investigation examines the processes responsible for the instability of
the banks of the lower Licking River, it establish the mechanical characteristics of the Licking River banks and reviews which soil parameters are more sensitive in the stability analysis and determines the role that pore water pressure plays in the increasing of strength of the cohesive materials.
1.2. LOCATION The study area is located in northern Kentucky in the City of Wilder, along
the banks of the lower Licking River valley, a major tributary of the Ohio River
(Figure 1). The Licking River flows northwest from Magoffin County in southeast
2
Figure 1. Frederick’s Landing Park, city of Wilder, Kentucky (Source of elevation data: Northern Kentucky Planning Commission)
3 Kentucky for about 483 kilometers (300 miles) to its confluence with the Ohio
River between Newport and Covington, Kentucky, draining an area of
approximately 9,330 square kilometers (3,600 square miles; Tonning, 1998).
Northern Kentucky has a continental climate with maximum precipitation
during winter and spring and warm and humid summers. The average high
temperature during the year is 17.5 0C (63.5 0F) and the lowest is 6.2 0C (43.2
0F); during winter time temperatures range from 5.6 0C – 0 0C (42 – 32 0F) and during summer from 29.0 – 17.0 0C (84 – 63 0F) (Bair, 1992).
1.3. HYDROLOGY Dams constructed upstream, at Cave Run Lake and to the north by the
Ohio River lock navigational system control the hydraulic behavior of the Licking
River. The lower Licking River, located at mile 471, is controlled by the Ohio
River stage maintained at a level sufficient for Navigation by the Medalh Lock at
mile 436.2 northwest of Maysville, Kentucky and the Markland Lock at mile 531.5
downstream from Warshaw, Kentucky (U.S. Army Corps of Engineers, USACE,
2002a).
The 1997 flood was one of the largest registered in the tri-state area.
After a period of heavy rain, waters in the Ohio and Licking Rivers raised above
flood stage (Figure 2) inundating productive land and near-by towns. This flood
caused significant damage to homes and infrastructure and generated unstable
banks when waters receded. During the study period from July 2003 to June
2004, changes in stage were monitored for both the Ohio and Licking Rivers
4 160 0
158 0.01
156 0.02
154 0.03
152 ) )
m 0.04 (
(m e 150 ag 0.05 pitation
148 i ver St c Ri FLOOD STAGE: 146.6 m 0.06 Pre 146
0.07 144
0.08 142
140 0.09
138 0.1 12/1/96 1/20/97 3/11/97 4/30/97 6/19/97 8/8/97 9/27/97 11/16/97 1/5/98
Figure 2. Ohio River stage during 1997 flood (Source of data: U.S. Army Corps of Engineers, personal communication; Cincinnati Metropolitan Sewer District, personal communication)
5 (Figure 3). Elevated water stage occurred in November, January, April and late
May to early June. During winter time, high waters might be related with melting
of snow whereas in the other months, especially during spring, floods are caused
by the increase of precipitation. Historically, floods for the Ohio River occur
about two times during a three-year period (Table 1).
1.4. PREVIOUS WORKS Unstable riverbanks are a concern for engineers, civil planners and
property owners. River bank failures result in accelerated sediment
accumulation in natural and constructed reservoirs and lakes, loss of productive
land, and damage to properties. Any change in a fluvial environment generates
a response from the system, either a modification in the channel morphology by
deepening or widening or by varying the hydraulic behavior of the streams.
The Licking River has had conditions conducive for bank failure during
recent history. A reconnaissance report presented by the U.S. Army Corps of
Engineers, Louisville District (USACE, 1979) indicated instability features
affecting properties in the Covington area (Kentucky) such as transverse cracks
and rotational slides which damaged roads and nearly affected proximal
structures (Figures 4, 5). One of the scarps showed the upper bank to be
comprised of fill, brick fragments, cinders and an accumulation of ash, which was
probably generated in the late 19th century. Such materials are prone to failure because of their poor strength characteristics. Also observed were problems aggravated by the high flood stages present in December 1978 when the water
6
165
160
155 GAGE ELEVATION: 152.4 m ) m (
t 150 h g i e h
e
g 145 a G
140
135 OHIO1 OHIO2 LICKING1 LICKING2 GAGE ELEVATION: 130.7 m 130 28-Jun 17-Aug 6-Oct 25-Nov 14-Jan 4-Mar 23-Apr 12-Jun 1-Aug
Figure 3. Gage height for Ohio and Licking Rivers, July 2003 to July 2004 (source of data: USGS)
7 Table 1. Historical peak streamflow in the Ohio River (Source: USGS)
Year Water height Year Water height Year Water height Year Water height Year Water height 1937 508.88 1968 485.65 1779 481.42 1816 481.42 1853 481.42 1773 504.88 1887 485.18 1780 481.42 1817 481.42 1854 481.42 1884 499.98 1865 485.18 1781 481.42 1818 481.42 1855 481.42 1913 498.78 1921 484.98 1782 481.42 1819 481.42 1856 481.42 1945 498.08 1917 484.98 1783 481.42 1820 481.42 1857 481.42 1883 495.18 1950 484.86 1784 481.42 1821 481.42 1935 481.28 1964 495.08 1915 484.78 1785 481.42 1822 481.42 1957 481.18 1907 494.08 1908 484.78 1786 481.42 1823 481.42 1919 480.88 1948 493.68 1924 484.68 1787 481.42 1824 481.42 1876 480.68 1832 493.18 1867 484.68 1788 481.42 1825 481.42 1910 480.68 1847 492.48 1886 484.68 1789 481.42 1826 481.42 1972 480.32 1933 492.48 1959 484.4 1790 481.42 1827 481.42 1902 479.78 1792 491.88 1859 484.28 1791 481.42 1828 481.42 1881 479.68 1918 490.68 1875 484.28 1794 481.42 1829 481.42 1906 479.28 1898 490.28 1961 484.22 1795 481.42 1830 481.42 1927 479.28 1962 490.18 1870 484.18 1796 481.42 1831 481.42 1932 479.28 1897 490.08 1893 483.78 1797 481.42 1833 481.42 1970 479.2 1955 489.92 1920 483.48 1798 481.42 1834 481.42 1975 478.98 1943 489.68 1909 483.48 1799 481.42 1835 481.42 1861 478.28 1936 489.48 1972 482.69 1800 481.42 1836 481.42 1860 478.08 1940 488.92 1877 482.68 1801 481.42 1837 481.42 1911 477.99 1967 488.66 1916 482.38 1802 481.42 1838 481.42 1869 477.68 1901 488.58 1974 482.33 1803 481.42 1839 481.42 1944 477.48 1963 488.29 1912 482.28 1804 481.42 1840 481.42 1895 477.28 1890 488.08 1880 482.08 1805 481.42 1841 481.42 1905 477.18 1927 487.98 1903 482.08 1806 481.42 1842 481.42 1868 477.08 1882 487.48 1956 482.06 1807 481.42 1843 481.42 1874 476.78 1950 487.45 1966 481.92 1808 481.42 1844 481.42 1896 476.58 1939 487.16 1929 481.58 1809 481.42 1845 481.42 1971 476.56 1958 486.86 1949 481.51 1810 481.42 1846 481.42 1946 476.48 1891 486.28 1774 481.42 1811 481.42 1848 481.42 1923 476.48 1899 486.28 1775 481.42 1812 481.42 1849 481.42 1914 476.08 1862 486.18 1776 481.42 1813 481.42 1850 481.42 1965 476.07 1793 485.88 1777 481.42 1814 481.42 1851 481.42 1934 475.48 1952 485.8 1778 481.42 1815 481.42 1852 481.42 1926 475.18
8
Figure 4. Street collapse, end of 7th street, Covington, Kentucky (USACE, 1979)
9
Figure 5. Rotational slide on 6th street, Covington, Kentucky (USACE, 1979).
10 stage dropped 7.6 meters (25 feet) in a period of three days, and by repeated floods in February – March 1979. These changes in flood stage were considered the main factor in the instability features of the banks. Erosion effects, moreover, were monitored during the summer of 1979 and were considered minimal or not important for instability causes.
Hagerty et al. (1981) mapped erosion and instability problems along the banks of the Ohio River. They compared the changes of the channel with historical data to determine the causes of instability and the post construction effects of the navigation dams. They concluded that the principal erosion mechanism seemed to correspond to particle removal by currents during flood and through piping after flood recession and that the construction of the navigational dams did not accelerate or increase the erosion problem.
Springer (1981) evaluated the effects of rapid drawdown on wedge failure along a sand seam within the cohesive and sandy-silty materials along the banks of the Ohio River. Springer considered wedge-failure analysis better reflected the field conditions present near the river. He concluded that soils are particularly sensitive to changes in friction, unit weight and are also greatly influenced by the presence of tension cracks, either dry or filled with water. His model assumes that no excess pore pressure is developed along the sand seam and failure occurred after changes in surface water level and rapid drawdown conditions.
Hagerty et al. (1983) monitored five sites on the sandy and clayey riverbanks in the Ohio River near Louisville in order to study erosion problems.
As a result of the study, they indicate that the severity of erosion depends on the
11 grain size of the bank materials, being more susceptible the banks composed of
sands. They concluded that bank material was lost during high waters and that
was accentuated when antecedent precipitation was present before flooding;
water seepage through pervious layers was indicated to be one of the major
mechanisms for bank failure.
Other published studies on river bank failure have been done in Missouri
and Montana and in Italy, which evaluate the influence of matric suction (e.g.
cohesion due to capillary tension) on the stability of river banks and in adding
resistance to erosion and particle detachment (Rinaldi & Casagli, 1999; Casagli
et al., 1999; Simon et al., 2000; Darby et al., 2000; Dapporto et al., 2001).
Rinaldi & Casagli (1999) studied the effects of negative pore water pressure on the stability of silty, sandy and gravelly streambanks in the Sieve
River, Italy. These banks are comprised of gravel in the lower section and sandy silt in the upper part. The authors suggest that part of the banks’ profiles remains unsaturated a majority of the time. Hence, the importance of introducing an unsaturated approach for this section of the profile. Under these conditions, the negative pore pressure increases the strength of the material, and the banks are stable at steeper angles than the effective friction angle of the soil during that time. After either rainfall or high flow events, however, the banks can be destabilized due to the reduction in or loss of matric suction. Stability analyses indicate that the factor of safety is higher when river stage increases due to a increase in the hydrostatic confining pressure; after drawdown, matric suction
12 increases but the confining pressure decreases, lowering the value of the factor
of safety (Rinaldi & Casagli, 1999).
Continued work on the Sieve River by Casagli et al., (1999) indicates seasonal changes in matric suction with variations in rainfall and river stage.
Positive pore water pressures were registered for a short time during their monitoring period. This suggests that high positive pressures are rarely generated even during high flow events. The authors emphasize the importance of matric suction to bank stability due to its contribution to shear strength.
Studies on the clayey – silt banks of Goodwin Creek, Missouri, USA
(Simon et al., 2000) indicate that river banks change from stable to unstable after rainfall due to an increase in bulk density, a decrease or loss of matric suction, a generation of positive pore water pressure, entrainment of in situ and failed material at the bank toe, and loss of confinement after flood recession. The authors concluded that not just one large event, but prolonged wet periods weaken the bank materials generating the mass failures.
Darby et al. (2000) evaluated planar failure for steep cohesive riverbanks along the Missouri River, USA. They used computer analyses to model failure.
They found that reduced soil shear strength and increasing unit weight resulted in decreased bank stability. Rapid drawdown from high river stage also decreased stability as a result of positive pore water pressure.
Slab (wedge failure) and alcove-shaped (a block detaching of the bank leaving a niche of the face of the slope) mechanisms of bank failure have been observed and studied by Dapporto et al., (2001) on the Arno River, Italy.
13 Geotechnical data obtained from the bank material and the hydrologic conditions of the river allowed them to conduct stability analyses of the banks including the effects of seepage. These studies indicated that alcove failures are likely to occur during moderate flow events and slab failures for high, peak-river stage.
Simon et al. (2002) analyzed bank stability problems along the Missouri
River, USA, and the role of closure of the Fort Peck Dam. They modeled circular failures and planar failures in response to features observed in the field, changes in water stage and groundwater level and included the effects on matric suction in the calculation of the factor of safety. They concluded that circular and planar failures occur when high flow maintained for a period of time allowing saturation of the bank. They also suggested that failure occurred because of loss of matric suction and development of positive pore water pressures during high flows.
1.5. LOCAL FAILURE CONDITIONS Different types of failures can be distinguished along the riverbanks in the
Licking River: circular, wedge and sloughing failures. Circular failures occur in the elevated banks and are more pervasive in the slopes than any other failure type in the study area. Scarps appear about 10-15 meters upslope from the active channel. Toes are not visible (Figure 6), presumably because they form below the water surface.
Wedge failures were observed in the occasionally flooded higher banks.
They are mostly found associated with cut banks where water undercuts the toe causing loss of support and consequently their failure (Figure 7).
14 Tensiometer
Tension cracks
Figure 6. Circular slide showing development of tension cracks. Frederick’s Landing, Wilder, Kentucky.
Figure 7. Wedge failure on high banks of western margin of Licking River.
15 Slump failures are widespread along the banks; they occur close to the
edge of the bank after high flow events when the material becomes saturated
and tends to flow after water recedes. These failures are characterized by a
spoon-shaped failure surface with an arcuate crown and a pronounced scarp
(Figure 8); they are not deep-seated slides. They behave like earthflows, the
thickness of the material involved being about 0.5 – 1 meter (2-3 feet) mobilizing
together great amounts of sediments into the channel.
Figure 8. Slump failure on western margin of Licking River after flood recession, March 18, 2004
In addition to the failure types mentioned above, piping failure resulting from seepage was observed at the face of some of the banks; the seepage conduits are variable in size and in the amount of water that comes through them
(Figure 9). Seepage causes cavities to form by removal of soil particles resulting
16 in caving and collapse of the overlying material. USACE (2002b) reports on the
mechanics of piping failure along the banks of the Kentucky River.
Figure 9. Seepage developed on banks in the western margin of the Licking River, April 3, 2003
17 CHAPTER 2 SETTING The Licking River flows through several physiographic units; south at the head waters, the river drains the highlands of the Eastern Coal Field
(Cumberland Plateau), cutting through the Eastern Pennyroyal Plateau, the
Knobs, sections of the Inner Blue Grass and a vast area in the outer Blue Grass
(Figure 10, Tonning, 1998). The basin varies in elevation from 135 to 500 meters. The study area comprises the northernmost part of the Outer Blue
Grass region in Kentucky, in Kenton and Campbell counties.
The Bluegrass Region corresponds to gently rolling low land, developed in sedimentary rocks, shale and limestone of Ordovician and Silurian age. This physiographic unit has been separated into the Outer Blue Grass and Inner Blue
Grass regions (Newell, 1986). The Outer Blue Grass has a low to moderate relief (Figure 11) with exposures of limestones and shales of Ordovician and
Silurian age. The low lands have wide valleys carved by a meandering stream
(Figure 11) with the valley bottoms filled with alluvial deposits, materials prone to present erosion and failure problems. Weathering of Silurian shales generates swelling clays and consequently the development of low-angle landslides
(Newell, 1986).
The Inner Blue Grass is characterized by very low relief developed over limestones of Mississippian age; sinkholes are abundant and thick, rich phosphatic soils are present. The Knobs correspond to an upland area comprised of rounded hills of Mississippian limestones overlying Devonian
18
Figure 10. Schematic map of physiographic units along the Licking River Basin (modified from Tonning, 1998)
19 ±
Elevation (m)
High : 500
Low : 135
94.5 09182736 Kilometers
GCS North American 1983
Figure 11. Digital elevation model of Licking River Basin (Source: USGS National Elevation Database)
20 shales. It marks the limit of the Outer Blue Grass region as a narrow belt 16-24 kilometers (10-15 miles) wide, with knobs that mainly occupy alluvial floodplains.
The knobs are the product of differential erosion where resistant caprocks overlie erodible shales and limestones; they have symmetrical concave-upward slopes
(Newell, 1986).
The Pennyroyal Plateau occupies the south-central and western part of
Kentucky. Its topography is dominated by the presence of rounded low hills and depressions, dolines or sinkholes, developed on the Mississippian limestone. It is separated from the Bluegrass Region by the Knobs. The Eastern Coal Field
(Cumberland Plateau) corresponds to highly dissected Pennsylvanian shales, sandstones, conglomerates and coal-bearing rocks. The valleys are narrow, steep and sinuous, locally wide (one or more miles) and the crests of the mountains are narrow and have a knife-edge shape; topography varies in elevation from 61 to 600 meters (200 -2000 feet; Newell, 1986).
2.1. NORTHERN KENTUCKY EROSIONAL HISTORY The Licking River is part of an old drainage system affected during the
Pleistocene by several glaciations that reshaped its basin. Three major glacial advances (pre-Illinoian, Illinoian and Wisconsinan) were present in the northern
Kentucky area (Durrell, 1995). During these times, the north-flowing drainage
(Teays River system) was dammed (Figure 12). After the glaciers retreated, the existent drainage course was modified from north flowing streams to south flowing streams with the exception of the Licking River which continued flowing north debouching into the newly formed Ohio River (during the Illinoian
21
Figure12. Glaciation history in Indiana, Ohio and Northern Kentucky (Durrell, 1995). A: Teays drainage. B: North flowing tributaries (blue) of the Teays drainage system. C: Teays drainage blocked by glacier advance during pre- Illinoian glaciation. D: Deep stage Ohio. E: Ponding of Licking River during Illinoian glaciation. F: Wisconsinan glaciation.
22 glaciation). Ice advanced during the Wisconsinan glaciation and melted leaving
behind extended outwash deposits that partially filled pre-existing drainage
channels.
The influence of glaciations on the morphology of the channel and the
northern basin of the Licking River is marked by the presence of clay deposits
accumulated during the damming of the river, terraces and old channels (Figure
13).
2.2. GEOLOGY The Licking River flows through rocks of different depositional
environment and origin and different age (Figure 14). Pennsylvanian shales,
sandstones, conglomerates and coal-bearing rocks, form the headwaters.
Flowing northwest, in the middle basin, the Licking River crosses Devonian
shales and Mississippian age limestones, and towards the lower valley and its
confluence with the Ohio River, the Licking River flows through Ordovician and
Silurian shales and limestones and Pleistocene-Holocene unconsolidated
deposits.
The study area is located in the lower Licking River valley where the
predominant bedrock corresponds to rocks of Ordovician-age such as the Point
Pleasant, Kope, Fairview, and Bellevue Member of the Grant Lake Formation
and Bull Fork Formations. The unconsolidated Pleistocene-Holocene-aged
sediments are primarily alluvial sediments deposited by the Licking River and its
tributaries and colluvium derived from the valley walls (Figure 15).
23 OHIO RIVER ±
LICKING RIVER .
021 468 Elevation (m) Kilometers High : 283
Projection: 1983 State Plane, Kentucky north Low : 136
Figure 13. Digital elevation model Newport and Covington quadrangles, Kentucky. Red dot indicates the location of Frederick’s Landing Park (Source: Kentucky office of geographic information).
24
±
904.5 9182736 Kilometers
water Pm Mauzy P Lee (Rockcastle) M Fort Payne (incl Muldraugh/Renfro) O Drakes-Calloway Creek Q alluvium P Sturgis M upper Chesterian M Fort Payne (Knifley) O Drakes-Bull Fork Q glacial deposits P Monongahela-Conemaugh M lower Chesterian M Fort Payne (Ls, CaneValley) O Drakes QT continental deposits & loess P Carbondale M lower Chesterian (Mooretown) MD Borden-Bedford O Bull Fork QT continental deposits P upper Breathitt M Pennington-Monteagle MD New Albany-Boyle O Ashlock-Fairview T Jackson-Claiborne P Tradewater M Pennington-Newman MD Chattanooga-Ohio O Cumberland-Leipers T Wilcox P middle Breathitt MD Pennington-Grainger D Sellersburg-Jeffersonville O Kope-ClaysFerry T Porters Creek P lower Breathitt M Newman S Louisville-Waldron O Kope TK Clayton-McNairy P Caseyville M Ste. Genevieve - St. Louis S Bisher O Clays Ferry K Tuscaloosa P Lee M Salem-Warsaw-Harrodsburg S Laurel-Brassfield O Lexington Pm peridotite (intrusive) P Lee (Corbin) M Warsaw S Crab Orchard-Brassfield O High Bridge
Figure 14. Geologic map of Licking River basin (Source: Kentucky Geological Survey)
25
af wo Ok Ok Qt Qal af Ok ± X Ok
Qt
Qal Of R Qt
Ob CKING RIVE I L
af
Ok
Ob 0 0.35 0.7 1.4 2.1 2.8 Kilometers
DEM River area High-level fluvial deposits Elevation (m) Artificial fill Bull Fork Formation Alluvium Grant Lake Limestone High : 281 Alluvium of meander, abandoned channels Fairview Formation Terrace deposits Kope Formation Low : 137 Glacial outwash (Wisconsinan) Point Pleasant Tongue of Clays Ferry Formation
SOURCES: KENTUCKY GEOLOGICAL SURVEY DEM SEAMLESS DATABASE PROJECTION: GCS NA1983
Figure 15. Geologic map of study area. Point X indicates location of deep borings to bedrock
26 2.2.1. BEDROCK Middle to Late Ordovician-aged Point Pleasant, Kope, Fairview, Bellevue
Tongue and Bull Fork formations crop out in the walls of the Licking River Valley.
The Point Pleasant Formation is part of the Upper Lexington Group. The Kope,
Fairview, Bellevue Member of the Grant Lake Formation and Bull Fork formations
belong to the Cincinnatian Series.
These units were deposited in a subtropical epicontinental sea (Kohrs,
2003). Middle Ordovician to Early Silurian tectonism started the formation of the
Cincinnati Arch, a gently dipping arch extending from Tennessee to northern
Ohio (Potter, 1996).
The Middle Ordovician Point Pleasant Formation is the oldest unit that crops out in the Cincinnati area and it corresponds to the upper part of the
Lexington Group (Brett and Algeo, 2001). Exposures of the upper part of this
formation are encountered along the northern Licking River valley as small
patches in contact with the Kope Formation (Figure 16). In the area of interest
this formation is exposed in the western bank of the Licking River at its
confluence with Three Mile Creek (Gibbons, 1973). It consists of a 30-meter
(100 feet) thick sequence of medium to coarse-grained fossiliferous wackestones
and packstones, medium to thick bedded, interbedded with shales (Potter, 1996).
The Upper Ordovician Kope Formation corresponds to the lower part of
the Cincinnatian Series. Its thickness varies from 70 to 75 meters (230 to 260
feet; Brett and Algeo, 2001). It consists of 65 to 80% calcareous shale, medium
gray, and locally silty shale; poorly laminated; thinly-bedded with fine-grained
27
Figure 16. Bedrock outcrop on western margin of the Licking River.
limestone near the base of the formation. The top of the formation consists of
3.0 to 4.6 meters (10 to 15 feet) thick interbedded shale and limestone (Potter,
1996). The shales and limestones are barren to highly fossiliferous (Brett and
Algeo, 2001). The shales are easily weathered forming colluvium that is susceptible to landsliding (Potter, 1996).
The Fairview Formation overlies the Kope Formation and is exposed at the top of the surrounding hills at the area of interest. Its thickness varies from
15–30 meters (50 to 100 feet; Brett and Algeo, 2001); it is composed by 50 to 70 percent wackestones and packstones, interbedded with medium-gray shale
(Potter, 1996).
28 The hilltops of the Licking Basin expose the Bellevue Tongue of the Grant
Lake Formation. It comprises 80 percent limestone and 20 percent shale. The limestones are fossiliferous, thin and coarse-grained, interbedded with discontinuous thinly bedded, fissile, fossiliferous shales. The thickness of the
Formation varies from 6 meters (20 feet) to 15 meters (49 feet) (Tobin, 1982).
The Bull Fork Formation overlies the Belleview Tongue of the Grant Lake
Formation. It consists of 50 percent limestone, medium-gray, thinly, irregularly to evenly bedded, coarse-grained, argillaceous and highly fossiliferous; calcareous shales and minor siltstones are interbedded with the limestone (Gibbons, 1973).
2.2.2. UNCONSOLIDATED DEPOSITS This division comprises sediments deposited during the Pleistocene glacial events and alluvial activity during the Holocene.
2.2.2.1. PLEISTOCENE DEPOSITS These deposits were accumulated after glaciers retreated in the northern
Kentucky area during the Pleistocene. The melted waters after the glaciation carried a great load of sediments deposited along the courses of the existent drainage.
2.2.2.1.1. Outwash Deposits The oldest unconsolidated deposits are found primarily in the vicinity of
Newport and Covington, north of the area of interest, at the confluence of the
Ohio and Licking Rivers. They are sand, gravel, silt and clay that can be up to 52 meters (170 feet) thick. The sands are light gray-yellowish orange, coarse to fine, well to poorly sorted, commonly showing crossbeds. The gravels are
29 pebble to cobble sized, rounded to subangular, composed of limestone, dolostone, igneous and metamorphic rocks; silts and clays are more common at the top of the outwash deposit at the city of Newport; these deposits rest on top of bedrock (Gibbons, 1973). Water wells drilled in these deposits encounter scattered areas predominated by clay- and sandy clay-rich sediments.
2.2.2.1.2. Terraces Pre-Recent terraces are frequently encountered along the Licking River
(Figure 15). They are composed chiefly of clay (silty?) with minor content of sand and gravel. The clays vary in color from pale-yellowish brown to greenish- orange; they are thinly laminated, slightly silty and plastic with limestone and siltstone floaters, locally with pebbles and cobbles of chert, jasper, igneous and metamorphic rocks within the siltier layers (Luft, 1971). Water wells north of
Interstate 275 encounter 7 meters (23 feet) of brown silt and clay at the surface underlain by 7 meters (23 feet) of bluish gray clay interbedded with two meters (6 feet) of sand with medium to coarse gravel; below the clay, 7 meters (23 feet) of sand and medium gravel are present underlain by 2.5 meters (8 feet) of gray clay.
2.2.2.2. HOLOCENE The Holocene alluvial fill in the study area is thickest immediately adjacent to the river and thins away from the river to the west. The alluvial fill was found to be about 10 meters (30 feet) thick at point X in Figure 15 (proprietary consultant report, 2003). Within the field site at Frederick’s Landing (Figure 1), the riverbanks are composed of fill and alluvial deposits ranging from up to 12
30 meters (40 ft) thick in the eastern margin (Figure 15) of the area to being absent along the western margin.
The alluvial deposits are chiefly silty clays varying in color from olive-
brown to greenish-gray (Figure 17). X-ray diffraction patterns for both yellowish brown and greenish gray silty clay materials (Figures 18, 19) indicate the presence of quartz (Q), illite (I), chlorite (Ch), mixed-layer clays and kaolinite (K).
Treatment of clay samples with ethylene-glycol does not show content of smectite in the sediments. The presence of this clay minerals reflect the provenance of the parent materials; the presence of kaolinite indicates alteration of continental material possibly coming form the head waters of the Licking River
(Figure 14).
Martin (1978) in a study of clayey sediments in the Claryville area,
Campbell County in Northern Kentucky, reported the presence of illite and
kaolinite in clayey samples of the Claryville lake clay and indicates that the source of the parental material of these clays, at least the kaolinite fraction might be sediments coming from the south (headwaters of the Licking River) and not from the north which was proposed in earlier works. This same clay mineral
suite and clay-sized materials have been reported by Breuer (1965) in the bank
deposits of the Great Miami River, northwest of the study site, and in the shales
of the Kope Formation although the author indicated that kaolinite was found only as traces in the samples. Hosterman and Whitlow (1981), report also illite, chlorite, kaolinite and mixed-layer clays in samples of Devonian shales south in
Tennessee.
31
Figure 17. Soil profile at Frederick’s Landing. (Source: borings by HC Nutting; laboratory testing by the author)
32
Figure 18. XRD pattern for olive brown silty clay. Quartz (Q), kaolinite (K), illite (I), chlorite (Ch).
33
Figure 19. XRD pattern for greenish gray silty clay. Quartz (Q), kaolinite (K), illite (I), chlorite (Ch).
34 At an elevation of approximately 135 meters masl (442 feet), a layer of
gray laminated clay was encountered in a close by area (point X, Figure 15,
Pleistocene slack water deposits?). Bedrock shows at an elevation of about 132
meters (433 feet); seams of gravel and sand are found in contact with bedrock in
some areas and locally as thin layers in deeper olive-brown clay.
2.3. Soils The soil associations present along the outermost edge of the riverbanks
in Kenton and Campbell counties are separated by the Soil Conservation Service
(1973) into Alluvial Land, Urban Land, Nolin Series and Egam Series (Figure 20).
The Alluvial Land is located on the edges of the terraces and riverbanks; it
varies in composition and in texture from sandy loam to silty clay materials from
place to place. Due to the location of these materials, they are susceptible to
erosion, slumping and flooding (Soil Conservation Service, 1973).
A soil profile located within the Alluvial Land association was described at
Frederick’s Landing (Figure 16); it is underlain by fill in the upper part and alluvial deposits. The fill is composed of an olive brown mottled gray (2.5Y 4/3) silty clay, dull, moist and slightly plastic (threads can be molded) with arrangement in peds (subangular blocky), no odor to earthy odor, with roots and oxidized surfaces; traces of very fine sand and limestone pebbles also present.
Underlying the fill, there is a one-meter (three feet) thick layer of dark greenish-gray clay (10 GY 4/1), with some silt and coarse sand, very moist, plastic, glossy to very glossy, massive, plastic; and with presence of small pieces
35
X
R
E
IV
R
G
N
I
K
IC L
0 0.15 0.3 0.6 0.9 1.2 Kilometers
SOIL NAME Eden silty clay loam Newark silt loam Alluvial land Egam silty clay loam Nicholson silt loam Brashear silty clay Faywood silty clay loam Nolin silt loam Brashear silty clay loam Lawrence silt loam Robertsville silt loam Captina silt loam Licking silt loam Urban land Chagrin gravelly silty clay loam Licking silty clay loam Water
Projection: NAD 1927, State Plane Kentucky North Source: Northern Kentucky Planning Commission
Figure 20. Soil survey for parts of Campbell and Kenton counties. Red cross indicates location of Frederick’s Landing Park
36 of carbonized wood. At a depth from 2.5 to 4 meters (eight to twelve feet), a layer of olive-brown silty clay, stiff, with low plasticity and blocky structure is encountered. These layers vary in thickness along the bank; in a nearby area, the upper grayish clay layer is about 3 meters thick (10 feet).
The Urban land corresponds to areas where soils have been highly disturbed due to cutting and filling and used for residential development and industrial placement. The Nolin Series is located on the floodplains and it corresponds to loamy soils (mostly silt). The soil from the Nolin Series has a granular structure formed from recent alluvium materials subjected to flooding during winter and spring (Soil Conservation Service, 1973).
The Egam Series is located in the southern part of the counties, in the floodplains where agricultural development is present; these soils are subjected to flooding during winter and spring. The soils correspond to silty clay loam with granular to blocky structure, compact and plastic (Soil Conservation Service,
1973).
37 CHAPTER 3
METHODS AND MATERIALS Four tensiometers and one piezometer were installed to evaluate the influence of water level fluctuation on the stability of the eastern banks of the
Licking River. These instruments were connected to a datalogger, which monitored the changes in matric suction related to variations in moisture content.
The tensiometers were placed at depths of 1.2, 1.8, 2.4 and 3 meters (4, 6, 8, 10 feet) and a piezometer was set at a depth of 3.7 meters (12 feet).
3.1. TENSIOMETERS AND PIEZOMETER INSTALLATION A tensiometer measures soil-water tension in the vadose zone. A variety of tensiometers are available including mercury manometer tensiometers, vacuum gauges and pressure transducers (Figure 21). The tensiometer type used in this research is comprised of a porous porcelain tip, an acrylic tube and attached to the neck of the tube, a SOILMOISTURE Co, 5301 current transducer which converts the soil tension into current and transmits this information to a datalogger for continuing data collection.
The transducers used have a range of measurement from 0 to 103 kPa (0 to 2159 psf) with a maximum differential pressure of 200 kPa (close to cavitation of the equipment). Even though the lower limit is zero, the equipment can detect negative values (positive pore water pressure) and act as a piezometer for low pressures.
To investigate matric suction in detail, the datalogger was programmed to record readings every five minutes for the first four months of the research and
38 every ten minutes thereafter. The recording time change was implemented after evaluating the data obtained during the first four months of suction monitoring and realizing that no data would be lost by increasing the period between readings.
Figure 21. Pressure transducer installed on tensiometer
When assembling the tensiometers, the porous tip was placed at the end of the acrylic tube, then the tube was filled with water and left aside to allow complete saturation of the porous tip; later the tensiometers were placed in the soil, and the pressure transducers were installed (Figure 21). To ensure proper function of the tensiometer, any air remaining in the sealed acrylic tube was removed using a hand-operated vacuum pump connected to a one-way valve in the transducer assembly. The boreholes were backfilled with tamped soil and a
39 PVC enclosure was constructed over the top of the borehole to protect the
equipment.
The piezometer was constructed from a 3.7 meters (12 feet) length of
PVC pipe, of 5-centimeter (2 inches) diameter. The pipe was perforated at the
bottom 0.6 meters (2 feet) with a 1/4 “ diameter drill, with holes 2-2.5” apart; after it was sealed with an end cap (Figure 22); finally it was wrapped with fine wire mesh (2mm2) to prevent silting and placed vertically in the ground with coarse
sand surrounding it.
Figure 22. The lower 0.6 meters (2 feet) of the piezometer are perforated.
40 3.2. SAMPLING The five boreholes were sited in a line parallel to the riverbanks and drilled with an all terrain vehicle (ATV) with hollow-stem auger (Figure 23). Two types of samples were collected: disturbed split spoon at 0.5 meters (1.5 feet) intervals and undisturbed pushed Shelby tubes for the last 0.6 meters (two feet) of each of the holes (Figure 23). The disturbed samples were wrapped in aluminum foil and the Shelby tubes were sealed with wax and covered with plastic lids at the ends to prevent moisture loss.
Figure 23. Drilling procedure using an all terrain vehicle with hollow stem auger.
41 During the collection of the disturbed samples Standard Penetration Tests were conducted to determine the consistency of the penetrated material; pocket penetrometer tests for unconfined compressive strength were conducted in the laboratory on the exposed bottom end of the undisturbed Shelby tube samples.
3.3. SOIL TESTING Because the purpose of this research is to analyze the stability of the riverbanks, it is necessary to know the strength characteristics of the bank materials. Several tests were conducted to determine these properties using the procedures described below.
3.3.1. MOISTURE CONTENT Soil moisture was measured in the Soil Mechanics Laboratory of the Civil and Environmental Engineering Department of the University of Cincinnati using the procedure described by Bowles (1992). A fraction of the sampled soil was placed in an oven overnight at 110±5 oC; the following day, the sample was taken out of the oven and weighed. The moisture content is calculated by:
M w ∗100% (1) M s
Where Mw: mass of water; Ms: mass of soil solids. 19 samples were tested from the split spoon samples evenly distributed along the thickness of the soil profile (Figure 24); Figure 24 indicated that a soil layer located between 1.7-
2.7 meters has higher moisture content than soil above or below. The test results are summarized in Table 2.
42
0
0.5
1
1.5 ) m
h ( 2 pt e D 2.5
3
3.5
4 16 18 20 22 24 26 28 30 32 34 36
Moisture content (%)
Figure 24. Moisture content versus depth at Frederick’s Landing soil profile
43 Table 2. Measured soil properties at Frederick’s Landing (φ’ via consolidated undrained triaxial test with pore pressure measurements).
3 γd, ω qu, C C’ K estim. BOREHOLE DEPTH DEPTH (m) γwet , lb/ft 3 2 2 2 ϕ’ ϕ LL PL PI US CS eo Gs Lb/ft % Lb/ft Lb/ft Lb/ft cm/sec B1S1 undisturbed 2’-2’8” 0.71 122.9 104.4 17.8 2801 1400 39.9 24.1 15.8 CL B1S1 remolded 2’-2’8” 0.71 122.9 104.3 17.8 2206 1103 B2S3 undisturbed 4’-4’8” 1.32 117.8 94.6 24.5 1551 775 3 8.2 25.4 12.8 ML B2S3 remolded 4’-4’8” 1.32 118.9 95.5 24.5 1393 697 120 B2S3 undisturbed 5’4”-5’11” 1.70 117.3 96.2 22 560 31 13 B3S3 undisturbed 6’-6’8” 1.93 118.7 90.6 31.1 1051 525 3 8.7 22.7 16.0 CL 0 .755 1.88x10-5 B3S3 remolded 6’-6’8” 1.93 118.8 90.6 31.1 1830 915 B3S3 undisturbed 6’8”-7’4” 2.1 113.5 89.2 27.3 1549 774 2 .733 B3S3 remolded 6’8”-7’4” 2.1 117.8 92.7 27.3 1181 590 B3S3 undisturbed 7’-7’10” 2.26 43 23.8 19.2 CL B4S4 undisturbed 8’5”-9’5” 2.72 118.6 92.6 28 1364 683 42 24.6 17.4 CL B4S4 remolded 8’5”-9’5” 2.72 117.5 91.8 28 1218 609 B5S4 undisturbed 11’4”-12’ 3.51 128 103.8 23.3 1084 542 3 8.5 22.2 16.3 CL B5S4 remolded 11’4”-12’ 3.51 121.9 98.9 23.3 2053 1026 B1 (SS) 0-1.5’ 0.22 26.2 4 5.3 27.6 17.7 ML B2 (SS) 1-2.5’ 0.53 21.9 B2 (SS) 2.5’-4’ 0.99 24.6 B3 (SS) 0-1.5’ 0.22 22.3 B3 (SS) 2.5’-4’ 1.25 22.1 B4 (SS) 1.5’-3’ 0.69 22.9 B4 (SS) 5’-6.5’ 1.75 39 25.8 13.2 ML B4 (SS) 5’-6’ 1.68 27.8 B5 (SS) 0-1.5’ 0.22 45 26.5 18.5 CL B5a (brown mat ) 4’-5.5’ 1.45 26.2 3 9.9 28 11.9 ML B5b (gray mat) 4’-5.5’ 1.45 34 B5 (SS) 7’-8.5’ 2.36 120 3 5.8 22.8 13 CL B5S4 (SS) 10’-10’8” 3.15 124 97.6 27 560 120 31 13 2 .722 B5S4 (SS) 10’8”-11’4” 3.35 123.1 97.7 26 560 31 13
44 3.3.2. SPECIFIC GRAVITY Specific gravities of two representative soil solids, the olive-brown silty
clay and the greenish gray silty clay, were determined at HC NUTTING Co.
facilities (a geotechnical engineering consultant in Cincinnati) following ASTM D
854. The results are presented in Table 2.
3.3.3. GRAIN SIZE ANALYSIS Both sieve and hydrometer (Figures 25, 26) analyses for the coarse and
fine-grained material respectively were conducted for the two representative soil
types using ASTM D 421 and D 422.
Figure 25. Hydrometer analysis assemblage used for determining grain size distribution
45
100
90
80
70 r ne
t fi 60 n rce 50 Pe
40
30
20
Olive-brown clay 10 Greenish-gray clay
0 10 1 0.1 0.01 0.001 0.0001 Particle size (mm)
Figure 26. Grain size analysis for silty clays at Frederick’s Landing
46 3.3.4. ATTERBERG LIMITS Plasticity of the soils (Liquid Limit and Plastic Limit) was determined in
order to classify them using the Unified Soil Classification System (Figures 27,
28). These tests were conducted in the Soil Mechanics Laboratory at the
University of Cincinnati following the procedure described by Bowles (1992) using the disturbed split spoon samples; the results are summarized in Table 2.
L , P it m li c ti s a Pl
Liquid limit, LL
Figure 27. Plasticity chart for Unified Soil Classification System (modified from Bowles, 1992)
47
Figure 28. Unified Soil Classification System (Bowles, 1992)
48 3.3.5. CONSOLIDATION TEST A consolidation test was conducted at the Soil Mechanics Laboratory at
the University of Cincinnati on an undisturbed sample from Borehole 3 following
the procedure described by Bowles (1992) with load increments of 27.8, 55.6,
111.1, 222.2, 444.4, 888.8 and 1777.6. kPa (0.29, 0.58, 1.16, 2.32, 4.64, 9.28
and 18.56 TSF). The results of the test (Table 3, Figure 29) indicate the clay to
be overconsolidated.
Table 3. Consolidation test results on gray lean silty clay, Borehole 3 (2 – 2.23 meters; 6’ 8” – 7’ 4”)
Cs (first rebound cycle) 0.008
Cs (final rebound cycle) 0.030
Cv, sq cm/min (for 55.56 kPa) 1.123
Cv, sq cm/min (for 111.12 kPa) 1.100
Cc 0.243
eo 0.755 Estimated preconsolidation pressure (kPa) 120
3.3.6. UNCONFINED COMPRESSION TESTING Six tests for unconfined compressive strength were conducted at the Soil
Mechanics Laboratory at the University of Cincinnati, following the procedure
presented by Bowles (1992), one for each borehole utilizing an undisturbed
sample (Table 2; Figure 30) and an extra sample from Borehole 3. The samples
were failed at a strain rate of 1mm/min. Table 4 shows the commonly accepted
definitions of consistency as a function of qu for clayey materials (Das, 1997).
Comparing the values of Table 2 and 4, they indicate the clays tested to have medium to stiff consistency.
49
Figure 29. Consolidation test result. Preconsolidation pressure, σc’=235 kPa (2.45 TSF)
50 Table 4. Consistency and unconfined compressive strength (qu) of clayey materials (Das, 1997)
qu Consistency kN/m2 TONS/ft2 Very soft 0-24 0-0.25 Soft 24-48 0.25-0.5 Medium 48-96 0.5-1 Stiff 96-192 1-2 Very stiff 192-383 2-4 Hard >383 >4
Figure 30. Unconfined compression test, Borehole 5, 3.5-3.7 meters (11’4” – 12’)
51 Under this same procedure, a sensitivity test was conducted with remolded samples at the same moisture content and moist unit weight. The purpose of this test was to evaluate the changes in strength of the natural material when it is remolded or disturbed. Sensitivity is defined as the ratio of the undisturbed compressive strength to the remolded compressive strength (Das,
1997). Values greater than one indicate that cohesive materials are sensitive
(Table 5) and improvement of the structures has to be implemented.
Table 5. Classification of sensitive clays (Das, 1997)
SENSITIVITY CLAY ≈ 1 Insensitive 1-2 Low sensitivity 2-4 Medium sensitivity 4-8 Sensitive 8-16 Extra sensitive >16 Quick
3.3.7. TRIAXIAL TESTING Consolidated-undrained triaxial tests with pore pressure measurements were conducted on three samples to determine the strength characteristics. The tests were conducted at the laboratory facilities of the HC NUTTING COMPANY following ASTM D 4767. Filter strips were placed along the sample to facilitate the saturation process using back-pressure saturation technique; a minimum limit of 98% saturation was decided before applying the deviator stress (Figure 31).
After the samples reached a minimum of 98% saturation, failure was induced at a chosen strain rate of 0.012% min-1 over a period of 20 hours (Figure 32). The
samples fail at about 7% strain and the failure stress was defined as ()σ '1 −σ '3 f .
The results of the tests are compiled in Table 2 and Figure 33.
52
Figure 31. Triaxial test assembly for backpressure saturation and consolidation processes
53
Figure 32. Triaxial test after application of deviator stress and failed sample
54
Figure 33. Results of Consolidated Undrained Triaxial testing
55 CHAPTER 4
THEORETICAL BACKGROUND In determining the “worst case” scenario for a hillslope stability analysis,
saturated conditions are generally used. Under these conditions, the influence of
the air phase is negligible and the water–soil particles interaction is responsible
for the mechanical behavior when the soil is exposed to a load. Studies
conducted by several authors (Rahardjo et al., 2001; Karube and Kawai, 2001;
Fredlund and Rahardjo, 1993) have demonstrated the importance of the air
phase in the soil profile, as well as the air-water phase and its implication in the
analysis of soils.
Fredlund and Rahardjo (1993) suggest that the strength of the
unsaturated soil is the result of the combination of effective cohesion (c’), the contribution of net stress (σ-ua), and matric suction (ua-uw); thus, the shear strength equation for unsaturated soils is modified by the addition of these variables to the effective strength approach for saturated soils.
The development of the soil–water characteristic curves, which relate the shear strength of the materials to water content, is considered of critical importance in the study of unsaturated soils, because for matric suction is a variable dependant on the degree of saturation of the soil. Water plays an important role in the behavior of unsaturated soils. Moisture content controls the magnitude of the matric suction and thereby, the strength of the material.
Londono (1995) has shown that the wetting front travels within the soil relatively quickly which increases the degree of saturation of the soil.
56 The intensity and duration of antecedent rainfall have been studied because of their role in causing landslides. It has been documented that matric suction drops during rainfall, lowering slope stability (Reid et al., 1988; Ng and Shi, 1998;
Chowdhury and Flentje, 2002).
4.1. DEFINITIONS Fredlund and Rahardjo (1993) describe the interaction among the four phases of unsaturated soils. These are, soil solids, liquid, gas and air–water interface or “contractile skin.” The contractile skin is sometimes included in the water phase when the degree of saturation is high because the pore spaces are filled with water and the influence of air is less important. Each of these phases has a different mechanical response to a stress, hence, varying the behavior of the soil.
4.1.1. AIR PHASE As noted by Fredlund and Rahardjo (1993), air can be present in the soil as a continuous phase where it surrounds the soil particles but also as occluded bubbles within the pore fluid. When the soils are close to saturation, S> 90%, the air contained in the soil voids is occluded and cannot flow as a separate continuous fluid. Under these conditions water and air flow through the voids as a homogeneous fluid moving under pore-water pressure gradients and the pore fluid becomes more compressible. When S<90%, however, air and water flow simultaneously as independent fluids (Ausilio & Conte, 1999).
57 4.1.2. WATER PHASE The water phase in the soil can be separated into three major parts: bulk,
adsorbed and meniscus water (Karube and Kawai, 2001). In the case of
unsaturated soils, the meniscus water is considered as an independent phase
and bulk water is treated as the water phase that flows freely through the void
spaces and is gradually expelled when a stress is applied.
Vassallo and Mancuso (2000) present a model that describes the nature
of both meniscus water and bulk water and their influence in soil behavior. They note that soils do not have a uniform distribution of water along the unsaturated part of the profile and that some of the water can be retained in the soil at the contact between the solid particles (meniscus water). Water may also be encountered filling the void spaces around the grains (bulk water). Both meniscus and bulk water may exert air (ua) or water (uw) pressure or both over the soil particles generating variations in the strength of the material.
In the presence of bulk water the forces acting in the soil are different.
Vassallo and Mancuso (2000) observed that the air pressure (ua) acts on the
external half of the soil, exerting a constant stress, whereas on the internal half,
pore pressure is manifested. Thus normal forces on a soil particle due to suction
are a linear function of (ua–uw) being equal to (ua–uw) As (As: cross sectional area
of the soil spheres; Figure 34). Bulk water induces “bulk stress” with suction,
which is the same as the pore water pressure in saturated soils (Karube and
Kawai, 2001).
When suction increases within the soil, the bulk water is easily released
and is replaced by air in the soil, but when the suction decreases, the water does
58 not return entirely into the pore spaces, thereby, creating a hysteresis phenomenon reflected in the water retention curves for soils (Figure 35).
2 TR
r2
Ua-Uw) 2 TR r1
Matric suction
U -U ) r 2 +2 r a w 2 2
Figure 34. Air – water meniscus between two solid spheres (from: Vassallo and Mancuso, 2000)
Unsaturated Saturated
)
Tension saturated e
m
u
l
Saturated o
v
moisture y
30 b content=
Drying % porosity (
ψA θ
of soil ,
t
n
n=30% e
20 t
n
o
c
e
r
u
t
s 10 i
o
M Wetting 0 -400 -300 -200 -100 0 100 Pressure head, ψ (cm of water)
Figure 35. Soil-water characteristic curves showing drying and wetting of a sandy soil (from Freeze and Cherry, 1979)
This phenomenon has been demonstrated by Freeze and Cherry (1979) who note that changes in water content within the soil with pressure head, when passing from wet soil to a dry soil (dry path) or dry soil to wet soil (wet path), do
59 not follow the same path (Figure 35). This wetting and drying process occurs
repeatedly and it “induces” the stress history of the soil (Fredlund and Rahardjo,
1993).
Several authors (Freeze and Cherry, 1979; Fredlund and Rahardjo, 1993;
Rahardjo et al., 2001) have stressed the importance of the soil–water
characteristic curve (Figure 35). The slope of these curves indicate how the
moisture content in the soil changes with the increase or decrease in matric
suction because the amount of water within the soil structure depends on the
pore water pressure and the moisture retention characteristic of the soil structure
(Ng and Shi, 1998).
4.1.3. AIR-WATER INTERFACE OR CONTRACTILE SKIN Fredlund and Rahardjo (1993), describe the contractile skin as a layer
behaving as an elastic membrane under tension within the soil structure. It
exerts a tensile pull, “surface tension”, resulting in the water molecules within this
layer experiencing an unbalanced force towards the volume enclosed by the skin
(Figure 35) due to the difference in pressure between the air and the water
contained within the soil.
The mechanical influence of suction (ua-uw) in unsaturated soils varies when either meniscus or bulk water is present. In the case of meniscus water, the forces exerted (suction) at the contacts between grains produce normal forces between the particles, hence increasing the shear strength (“greater slippage strength”, Vassallo and Mancuso, 2000; Figure 34). As suction increases, the normal forces increase but these forces tend towards a threshold
60 value (Figure 36), above which suction does not have any further effect on the soil strength due to the reduction in the meniscus radius (Figure 36). As shown in Figure 36, the changes in ∆N with suction in the case of bulk water follows path AB (linear relationship); when a certain air entry value in the soil is achieved, the suction follows path DC (case of meniscus water).
Figure 36. Effect of suction on the increment of normal stress (from Vassallo and Mancuso, 2000)
4.2. MECHANICAL BEHAVIOR OF UNSATURATED SOILS Because soil, water, and air coexist and interact with each other, a special state of stress has to be considered in the mechanical analysis of this type of material. Fredlund and Rahardjo (1993) suggest that the strength of the unsaturated soil comes from effective cohesion, the contribution of the net stress
(σ-ua), and from the matric suction (ua-uw), the last two being considered as stress-state variables. As a result, the shear strength equation for unsaturated soils may be expressed as a modification of the effective strength approach for saturated soils. This equation would be:
61 b τ ff = c'+ (σ f − u a ) f tan ϕ '+ (u a − u w ) f tan ϕ (2)
Where, c’= effective cohesion (net normal stress and matric suction are
equal to zero)
(σf -ua)f = net normal stress on the failure plane at failure
uaf = pore air pressure at failure
φ’= friction angle associated with the net normal stress
(ua-uw)f = matric suction on the failure plane at failure
φb = angle that indicates the increase in strength relative to the matric
suction (it reflects the inclination of the line that joins the cohesion
intercepts at different matric suction values)
To interpret the results obtained from triaxial testing, it is necessary to
modify the Mohr-Coulomb failure envelope to include variables that define the
state of stress in unsaturated soils. This modification includes a three-
dimensional representation, where two abscissas correspond to the net normal
stress and the matric suction and the third axis to the shear strength (Figure 37).
If the failure envelope were to be represented in two dimensions, the influence of
matric suction is added to the effective cohesion giving what Fredlund and
b Rahardjo (1993) refer to as “total cohesion” c = c '+ (u a − u w ) f tan ϕ .
The angle φb accounts for the influence of matric suction in the shear strength at the cohesion intercept. A study conducted by Satija (1978) and presented by Fredlund and Rahardjo (1993), shows the comparison of strength parameters for two types of soils when tested under saturated and unsaturated
62 conditions (Table 6). From this it is possible to see the strong influence of matric suction in the increase of the cohesion of the soil. For unsaturated tests,
Fredlund and Rahardjo (1993) present a compilation of data for several soils tested under unsaturated conditions (Table 7) compared with the values of effective friction angle and φb and the corresponding value of cohesion.
) U w b - ϕ a (U n b Failure envelope: io ϕ ct ϕ‘ τ ff =C’+(σf-Ua)f tan ϕ’ u , s c s i b tr s +(Ua-Uw)f tan ϕ a
e M r
t ϕ’
s
r
a
e
h S ϕ‘
ff C
) f w -U a (U C’ 0 ( U ) σf- a f Net normal stress (σ-Ua)
Figure 37. Modified Mohr – Coulomb failure envelope for unsaturated soils (from Fredlund and Rahardjo, 1993).
Table 6. Results of triaxial tests under saturated and unsaturated conditions on compacted Dhanauri clay (Fredlund and Rahardjo, 1993)
CU test on Analysis of test results on
saturated unsaturated specimens (Ho and specimens Fredlund, 1982a) Initial volume- mass properties C’ (kPa) φ’ Type of test C’ (kPa) φb CD 20.3 12.6 Low density Dhanauri clay; 7.8 29 CW 11.3 16.5 w = 22.2%, ρ =1478 Kg/m3 d CD 37.3 16.2 High Dhanauri clay; w = 22.2%, 3 7.8 28.5 CW 15.5 22.6 ρd=1580 Kg/m
63 Table 7. Experimental values of φb (from Fredlund and Rahardjo, 1993)
Unsaturated tests C’ φ’ φb Test Soil type Reference (kPa) (degrees) (degrees) procedure Compacted shale; Bishop et al., 15.8 24.8 18.1 CW Tx w = 18.6% (1960) Boulder clay; Bishop et al., 9.6 27.3 21.7 CW Tx W = 11.6% (1960) Dhanauri clay;
w = 22.2%, ρd=1580 37.3 28.5 16.2 CD Tx Satija, (1978) Kg/m3 Dhanauri clay;
w = 22.2%, ρd=1478 20.3 29 12.6 CD Tx Satija, (1978) Kg/m3 Dhanauri clay;
w = 22.2%, ρd=1580 15.5 28.5 22.6 CW Tx Satija, (1978) Kg/m3 Dhanauri clay;
w = 22.2%, ρd=1478 11.3 29 16.5 CW Tx Satija, (1978) Kg/m3 Madrid grey clay, CD direct 23.7 22.5 16.1 Escario (1980) w= 29% shear Undisturbed Ho and CD multistage decomposed granite; 28.9 33.4 15.3 Fredlund triaxial Hong Kong (1982a) Undisturbed Ho and CD multistage decomposed rhyolite; 7.4 35.3 13.8 Fredlund triaxial Hong Kong (1982a) Tappen-Notch Hill silt, CD multistage Krahn et al., w = 21.5%; ρd=1590 0 35 16 triaxial (1989) Kg/m3 Compacted glacial till; CD multistage Gan et al., w = 12.2%, ρd=1810 10 25.3 7-25.5 direct shear (1988) Kg/m3
64 The value of “total cohesion” to be included in the equation of failure
envelope can be approximated using Figure 37 in which changes in “total
cohesion” due to variations in the value of φb are accounted for (Figure 38). Also, to explore the influence of this parameter in the factor of safety of a slope, these authors present the variation in factor of safety with changes in φb (Figure 39).
250
ϕb =45o 200
n 40o
o
i
t
c
u
]
s
a
P c 150
i
k
r
t
, o
a 30
b
m ϕ
o n
t
a
t
e 100
) u o
w d 20
U
n
-
o
a
i
s
U
(
e
[ h 50 10o
o
C
0 0 100 200 300 400 Matric suction (Ua-Uw), kPa
Figure 38. Component of cohesion due to matric suction for different φb values (Fredlund and Rahardjo, 1993)
1.6
Morgenstern & Price and
1.5 Bishop’s Simplified
y t
e methods f
a 1.4
s
f
o
r o
t 1.3
c Janbu’s Simplified
a F 1.2
1.1 0 5 10 15 20 25 30 φb (degrees)
Figure 39. Influence on variation of φb values on the factor of safety of a slope (Fredlund and Rahardjo, 1993)
65 4.3. STABILITY ANALYSIS To perform a slope stability analysis, it is necessary to determine the physical characteristics of the slope to be studied, that is, its geometry, the underlying material, the strength characteristics and also, the hydrologic conditions (Abramson et al., 1996).
The result of the analysis is a defined surface of failure and a corresponding “factor of safety” (ratio of resisting or stabilizing to driving or destabilizing forces). The resisting forces acting on a slope are the friction and the cohesion of the material and the driving forces are the weight and the pore pressure.
c '+ σ ' tan φ ' F = (3) W sin α
Where c’= effective cohesion; σ’= effective stress; φ'= effective friction angle; W: weight of soil mass; α: angle of failure surface (see figure 40).
A value of F = 1 indicates that the resisting forces are equal to the driving forces; hence the slope is considered to be in quasi-equilibrium or at incipient failure. This numeric value accounts for the uncertainties of the stability analysis such as analysis of forces, selection of shear strength parameters, pore water pressure and method of analysis (Sherard et al., 1963; Lowe, 1966). For embankment design, it has been recommended in the literature a minimum allowable factor of safety of 1.5, lower values are acceptable if the degree of uncertainty is low otherwise a value greater than 1.5 is recommended (Ashford et al., 1992). Terzaghi & Peck (1948) state that for earthdams, “the theoretical
66 factor of safety with respect to slope failures should never be less than 1.3 and
should preferably be 1.5”.
To better simulate the circular-type failure surface and the forces involved
in the stability of the slope, the “method of slices” was chosen for this study. This
method separates the failure mass into smaller slices and it treats each slide as a
unique sliding block. This permits modeling of complex geometry problems,
variable soil conditions, forces acting on the slice and influence of external loads
(Figure 40; Abramson et al., 1996). Although this method is similar to others in
the way it separates the soil mass, the analysis of the forces acting on the slope
varies depending on the analytical approach chosen. As mentioned above,
several analytical methods have been described in the literature to evaluate the
stability of the slope. Some of the methods are very rigorous in satisfying the
forces and momentum in the slices (Table 8) and some others make simplifying
assumptions to model the slope.
Weight is a driving force on the slope; it has a component parallel to the
shear surface that “pushes” the slice down slope. The shear strength along the
failure surface resists the shear forces and stabilizes the slope. The hydrostatic
pressure of the surface water (Uβ) acts as a passive force on the slope. The pore
water pressure within the soil (Uα) exerts an uplifting force (Figure 40) decreasing
the effective normal stress thus reducing shear strength. Part of the stress
imposed on the soil is carried by water when soils are partially or fully saturated
(total stress approach); if the soils are not saturated, the soil skeleton carries the stress and the influence of pore pressure is null (effective stress approach).
67 Q δ Uβ β Thrust line ZR
θR h Kh W
K θ v L hc α Z L Midpoint of slide N’ +Uα Sm
b
Figure 40. Forces acting on a soil slice (modified from Abramson et al., 1996). W: weight of slice; b: width of slice; h: average height of slice; hc: height to centroid of slice; Kh: horizontal seismic coefficient; Sm: mobilized strength; Uβ: surface water force; Uα: pore water force; N’= effective normal force; α: inclination of slice base; β: inclination of slice top; Kv: vertical seismic coefficient; Q: external surcharge; δ: inclination of surcharge application; ZR: right interslice force; ZL: left interslice force; θR: right interslice force angle; θL: left interslice force angle
Table 8. Static equilibrium conditions satisfied by limit equilibrium methods (Abramson et al., 1996)
FORCE EQUILIBRIUM MOMENT METHOD X Y EQUILIBRIUM Ordinary method of slices No No Yes Bishop’s simplified Yes No Yes Janbu’s simplified Yes Yes No Corps of engineers Yes Yes No Lowe and Karafiath Yes Yes No Janbu’s generalized Yes Yes No Bishop’s rigorous Yes Yes Yes Spencer’s Yes Yes Yes Sarma’s Yes Yes Yes Morgenstern-Price Yes Yes Yes
68 The Simplified Bishop Method was selected for the analysis of the study
site. This method assumes the interslice shear forces (ZR, ZL, Figure 40) are zero (Abramson et al., 1996) and as a result the factor of safety is underestimated yielding a conservative result. Abramson et al. (1996) find the
Simplified Bishop Method determines the factor of safety within 5 percent of the value determined by more rigorous methods such as Spencer or Morgenstern-
Price (Table 8). The Simplified Bishop Method determines the vertical forces of the slice and the momentum of each of the slices; the momentum acting on the center of the slice is defined in equation 4 (following page) and the factor of safety is then calculated replacing the equation 3 into equation 4 giving as a result equation 5 (Abramson et al., 1996)
The wed ge failure approach is us ed to analyze the behavior of the higher
banks that are more prone to this type of failure. The wedge method assumes
that failure of the slope occurs along a planar surface (Figure 41) therefore the distribution of forces differs from the circular failure model. The resisting forces
acting on the slope are the cohesion of the material and the component of the
weight perpendicular to the failure surface. The driving forces result from the
component of the weight vector acting parallel to the failure surface.
The banks of the Licking River are analyzed using the Bank-stability and
Toe Erosion Model version 4 developed by Simon et al. (2001) at the U.S.
Department of Agriculture. This model uses limit equilibrium analysis for the calculation of the factor of safety and incorporates in it the effects of matric
suction in the increase of cohesion of the material, the hydrostatic confining force
69 M nnnn ∑ o ⎛ h ⎞ ⎡ hc ⎤ = ∑∑[]W ()1 − K v + U β cos β + Q cos δ sin α − []S m − ∑[]U β sin β + Q sin δ ⎜ cos α − ⎟ + ∑⎢K hW (cos α − ⎥ R 111⎝ R ⎠ 1⎣ R ⎦ (4)
Where Mo is the overturning moment, R: radius of the failure arc, W: weight of the slice, kv: vertical seismic force, Uβ: surface water force, β: inclination of slice top, Q: external surcharge, δ: inclination of surcharge, α: inclination of slice, h: average height of slice, hc: height to the centroid of the slice.
n ∑()c + N'tanφ 1 (5) F = nnn ∑∑A5 − ∑ A6 + A7 11 1 Where:
A5 = [W (1− K v )+U β cos β + Q cosδ ]sinα (6) A = [U cos β + Q cos δ ](cos α − h ) (7) 6 β R h A = K W (cos α − c ) (8) 7 h R 1 ⎡ csinα ⎤ N'= ⎢W ()1− K v − −Uα cosα +U β cos β + Q cosδ ⎥ (9) mα ⎣ F ⎦ ⎡ tan α tan φ ⎤ m α = cos α 1 + (10) ⎣⎢ F ⎦⎥
70
s
W L
U
P
Figure 41. Forces acting on a riverbank under wedge failure type (modified from Simon et al., 2000). P: hydrostatic confining pressure; W: weight of wedge; L: length of failure plane; S: force due to matric suction; U: pore water pressure; α: angle of failure plane; β: slope angle
from the surface water (see equation, Simon et al., 2000), and the effects of
vegetation.
b C L + []S tanφ i + [W cos β −U P cos(α − β )]tanφ' F = ∑ i i i i i i i (11) ∑Wi sin β − Pi sin(α − β )
Where, i: layer of soil; Ci’: effective cohesion; Li: length of the failure plane
th along the i soil layer; Si: force due to matric suction in the unsaturated part of
the profile; Wi: weight of soil layer; Ui : pore water pressure; Pi: hydrostatic confining force; β: angle of the bank; α: angle of the failure surface.
71 4.4. INFLUENCE OF WATER ON THE MECHANICAL BEHAVIOR OF UNSATURATED SOILS As explained above, matric suction plays an important role in increasing
the shear strength of the soil. The main difference between saturated and
unsaturated soils is the presence of matric suction as an undependable variable
in the state of stress of the soil (Fredlund and Rahardjo, 1993). Because matric
suction is very sensitive to changes in moisture content within the soil, it is of
great importance to consider in the study the influence of water in the mechanical
behavior of these materials.
In natural conditions, the soil is subjected to changes in moisture content
along its profile due to seasonal variations. The uppermost layer of the profile is
greatly affected by daily evaporation and incipient infiltration during small
intensity rainfalls. As depth increases, the changes in moisture are controlled by
the rate of infiltration and by fluctuations in the position of the water table, thus
causing rapid changes in the soil from saturated to unsaturated conditions.
Different approaches can be taken to approximate the infiltration of water
into the soil. Field experiments conducted by Londono (1995) consider infiltration
as a function of rainfall intensity and slope by variation of the specific resistance.
That study found the wetting front rapidly advanced into the soil (Figures 42 and
43). Londono (1995) also found that after a simulated rainy period of five days
(about 20 minutes rain per day), it is possible to identify the cumulative changes
in moisture content in the soil (Figure 44). This increase in moisture content
reduces matric suction, sometimes eliminating it completely, thus decreasing the
strength of the soil.
72
Figure 42. Advance of wetting front through a soil derived from colluvium at different times (readings every five minutes; Londono, 1995)
73
Figure 43. Moisture increase within the soil (Londono 1995)
74
Figure 44. Initial and final conditions for specific resistance within a soil after a five – day raining period (Londono, 1995).
75 Figure 44 shows the importance of antecedent rainfall as a factor
decreasing matric suction and increasing unit weight of the materials, which may
cause slope failure. This area of study has been explored by several authors
(Reid et al., 1988; Ng & Shi, 1998; Rahardjo et al., 2001).
During dry periods, the soils are dry or partially saturated and have high shear strength, which allows them to remain stable. During wet periods however, the soil loses strength. Although many studies have correlated landsliding with high intensity rain events, several studies have found just one high intensity rain may not cause instability because soils respond differently, mechanically and hydraulically, when they are dry or wet.
Ng and Shi (1998) found that the factor of safety of a slope depends on the rainfall duration and intensity as well as the initial hydrological conditions of the site (location of the water table). If the ground water table is well below the failure surface, even after a high intensity rainfall, the slopes can remain stable
(Figure 45). During their study modeling the response of an unsaturated slope to rainfall events, Ng and Shi (1998) found that prolonged rainfall does not cause significant changes in groundwater level, instead it changes the pore pressure distribution, thereby lowering the factor of safety (Figure 46). They also found the factor of safety to decrease in short duration storms when the slopes have been subjected to antecedent rainfall equivalent to the rain of critical duration.
Chowdhury and Flentje (2002) found that landslides triggered by high intensity and short duration rainfall do not occur unless the soil antecedent moisture content is already high as a result of prior rainfall events. They also
76 2
1.8
61 mPD 62 mPD 63 mPD
y
t
e
f 1.6
a
s
f
o
r
o
t
c 1.4
a
F
1.2
1 0 100 200 300 400
Rainfall intensity (mm/day)
Figure 45. Influence of rainfall intensity on the factor of safety of a slope (Ng and Shi, 1998).
2
1.75
y
t
e Duration a 2 - hour rainstorm
f
a
s
f
o
r 1.5
o
t f
c 1
a
F
f2 1.25
1 0 5 10 15 20 25 30 35 Duration (days)
Figure 46. Influence of rainfall duration on the factor of safety of a slope (Ng and Shi, 1998)
77 found that pre-existing landslides may be reactivated after periods of intense and prolonged rainfall. Reid et al., (1988), in the study of a landslide in the Santa
Cruz Mountains of central California indicated that rainfall-induced positive pore pressures developed in the slope after a storm event may be accentuated by the presence of a perched water table changing the behavior of the soil.
Rahardjo et al. (2001) modeled a storm that triggered landslides in
Singapore and concluded that antecedent rainfall was significant in triggering the landslides. They demonstrated that isolated rainfall events of similar magnitude as the event that caused the failures did not cause failure. Their explanation is that antecedent rainfall causes the matric suction to decrease in the slope, consequently the hydraulic conductivity of the material increases making the soil more permeable to infiltration. This decreases the shear strength of the soils and thus the factor of safety. After the storm, water continues percolating within the soil, which gradually loses moisture, causing the factor of safety to begin increasing.
78 CHAPTER 5 ANALYSIS AND RESULTS Strength parameters (cohesion and friction angle) were measured for all
three silty clay layers that compose the upper 4 meters (12 feet) of the tested
slope. Undrained strength was obtained for the two uppermost layers using the unconfined compression test and drained and undrained properties from consolidated-undrained triaxial testing with pore pressure measurements for the lower silty clay. The values obtained in these analyses (Table 9) are comparable with values reported by Simon et al., (2002) for bank materials of the Missouri
River.
As demonstrated previously, matric suction is particularly sensitive to rainfall infiltration and rapid fall from flood stage. As water percolates through the soil or as the water table rises, matric suction is gradually lost (Figure 47).
During periods of scattered rain, water percolates into the ground increasing the soil moisture content; the free water remaining flows through the soil pores, moving within the soil profile and is incorporated into the groundwater flow without saturating the soil, thus matric suction is still present in the soil.
In periods of heavy or prolonged rain and flood stage, matric suction reaches low values or sometimes is lost completely, generating a build-up of positive pore pressure within the soil. This development of positive pore water pressure has been noted in other investigations as a factor triggering slope failures (Rinaldi & Casagli, 1999; Simon et al., 2000; Simon et al., 2002).
79 Table 9. Comparison of strength parameters for Licking and Missouri rivers.
M issouri R ive r (Sim on et a l ., 2002 ) Lick ing River b Dept h Ca Cu C' ϕ' ϕ γ am b γ sa t US CS ϕ kP a Dept h (f t) Cu C' φ' γ d γ we t (m ) kP a kP a kPa de g de g kN /m 3 kN/m 3 US C S kP a Lb /ft2 kP a Lb/f t2 de g kN /m 3 Lb /ft3 kN/m 3 Lb/ft3 3.7 CH 21 -- 8.5 26.1 17 16.9 21 2' - 2'8" CL 67.1 140 0 _ _ _ 16.4 104.4 19.31 122. 9 1.2 CH 6 -- 2.8 28.1 17 10.5 15.3 20.6 4' - 4'8" CL 37.2 776 _ _ _ 15 95 18.5 117.8 4.9 CH 29.7 -- 27.7 9.9 17 6.5 16.3 20.2 6' - 6'8" CL 25.16 524.3 _ _ _ 14.2 90.6 18.6 118.7 2.8 CH 7.8 2.1 33.8 11 29.5 13.5 20.2 6'8"- 7 '4" CL 37.1 774 _ _ _ 14 89.2 17.8 113.5 5.1 CH--C L 9.1 7.3 29.1 17 5.8 17 .9 22 .2 8' 5 "- 9' 5" CL 32.7 682 .8 _ _ _ 14.6 92. 7 18.6 118 .6 4.9 CH--C L 14.9 12. 9 23.3 17 6.5 16 .9 21 .1 11 '4" - 12 ' CL 26 542 .3 _ _ _ 16.3 103.8 20.1 128 2.4 CH--C L 17.3 8.7 29 .5 17 28 16 .6 21 .3 5'4" - 5'11" CL 26.8 560 5.75 120 31 15.1 96.2 18.4 117.3 5.5 C IL 1. 9 -- 0 35 17 14 .5 20 .1 10 ' - 10'8" CL 26.8 560 5.75 12 0 31 15. 34 97.6 19 .5 12 4 2.7 CL 18.2 10.6 20.2 17 25 15.4 21.2 10'8" - 11 '4" CL 26.8 560 5.75 120 31 15.35 97 .7 19.3 123. 1 3.2 CL 23.5 22.7 8.8 17 2.7 15.4 19.9 4.1 C L 31 -- 9.4 26 .9 17 15 .4 20 .6 4.9 C L 32.3 31. 5 5.5 17 16 .9 20 .8 2.2 CL 16.2 -- 12.5 28.3 17 15.8 20.7 7.5 C L -- 77.8 -- 0 17 -- 21 21 .6 3.8 CL -- 77.8 -- 0 17 6 21 21.6 3.4 C L 91 0 33 .6 17 30 14 .1 20 .9 7 C L 33 32. 2 14 17 2.5 17 .1 21 .4 2.7 CL 8.3 2. 5 27.6 17 19 16.1 21.4 6.7 C L 20.3 19. 2 14.5 17 3.5 16 .7 20 .5 2.4 CL 0 0 37.7 17 -- 14.8 21 0.9 CL 9.2 8. 1 28.8 17 15.4 20.4 4.9 C L 9.2 -- 8.1 28.8 17 3.5 15 .4 20 .4 6.1 C L 17.8 -- 15. 8 22.5 17 6.5 15 .1 19 .7 4.3 CL 1.1 -- 1. 1 28.9 11 16 14 21.2 3.8 CL- -CH 25.1 22.3 13.4 17 17.3 21.4 2.7 CL- -CH 0 0 32 17 16 21.1 1.8 C L--CH 10.2 5 33 .2 17 17 15 .2 21 .1 3.4 M L 17.8 13.2 30.1 17 15 14.2 21.4 2.1 M L 17.8 -- 10.1 30.1 17 -- 15.7 20.7 2.1 M L--C L 16 -- 8.5 20 .9 17 -- 16 .6 21 .3 4.1 S M 2.9 2. 1 37.6 17 2.5 16.9 21.4 3 S C 0.2 0 35 17 6 15 .4 21 .1 7 SM 1.9 1. 7 32.9 17 0.5 16.3 20.9 5.5 SM 1.9 -- 1. 9 32.9 17 20.3 23 1.8 SM 0 -- 0 38.1 17 -- 13.5 20 3.4 S M 2.2 0.4 26.9 17 6 14 .5 21 .4 5.5 SM 0 0 37.9 17 15.2 20.9 3.8 SM 1.9 -- 1. 9 32.9 11 14.5 20.1 8.3 SM 1.9 -- 1. 9 32.9 11 -- 14.5 20.1 0.6 SM --M L 0 -- 0 30.9 17 -- 13 15.4 1.5 SP 0 -- 0 26.4 17 -- 16.9 21.1 3.7 S P 0 0 35 17 18 21.6 2.4 SP 0 0 35 17 -- 13.5 21.1 2.7 SP 4.6 -- 0 35.4 17 -- 16.5 21.3 4 SP 0 --035170 18 21.6
80
25 Rain
20 Rain Rain Flood Flood 15 Flood Flood
10 )
Pa 5 (k n o i
t 0 c 8 6 6 3 2 6 0 3 5 2 7 9 / / / 1 3 1 27 11 2 2 20 20 1 16 30 14 28 11 25 23 u 6 7 1/ 2/ 3 / / / / / / 3 3 4 4/ 5/ 5 6 7/ 1/ 2 9/ 9/ 12/ s 10/ 10/ 11/ 11/ 12/
c -5 tri a
M 2003 2004 -10
-15
T1 (4ft) T2 (6ft) -20 T3 (8ft) T4 (10ft) 1 2 3 4 -25
Figure 47. Matric suction measurements along the eastern bank of the Licking River at the city of Wilder, Kentucky.
81 During the study period, several floods were observed and measurements of the groundwater table were taken after the flood recession (Figure 48). In the
majority of the cases, the water table was 0.5 – 1.5 meters below the ground
surface, demonstrating the lag time existing between percolation and the rise of
the water table. On the other hand, two flood events were observed in the area
separated by eight days. During the recession following the first event (144 m
masl, November 15th, Figure 49), the groundwater table was below the ground surface resulting in partial saturation of the soil in the upper meter of the profile.
After the recession of the first flood, the river stage rose again resulting in a water table elevation of 146 m masl (November 23rd, Figure 50). Following the
recession of that second flood event, the groundwater table was observed to be
at the surface of the slope (seepage conditions, Figure 50).
These seepage conditions encountered in the slope after two consecutive
flood events underscore the importance of antecedent events in the behavior of
water within the soils. After one flood event that covered the slope for a couple
of days, the soils did not reach full saturation. Therefore positive pore pressures
were not developed during that period. This first event “prepared” the slope for
saturation. Hence, after the second flood event, full saturation was achieved in
the slope causing positive pore pressures to develop.
Saturated consolidated undrained triaxial tests conducted on samples
from the bank of the Licking River on the brownish lean clay yielded values of
82
150 0
20 GW level 148 River level Precipitation 40
60 )
sl 146 mm) ma 80 m ion ( ( n at o 144 100 ipit ati c e ev l r
e 120 r e 142 Daily p Wat 140
160 140
180
138 200 5/9 6/6 7/4 8/1 8/29 9/26 10/24 11/21 12/19 1/16 2/13 3/12 4/9 5/7 6/4 7/2 2003 2004
Figure 48. Changes in water table and river elevations during September 2003 – July 2004. Dark blue-red dots indicate flooding.
83 Flood peak, November 15th, river elevation: 144 masl
Figure 49. Flood occurred in November 15th, river elevation 144 masl.
Figure 50. Seepage developed after two consecutive flood events.
84 c’= 5.8 kPa (120 psf) and φ’ = 31o. In this case if one were to consider the strength of the clay under unsaturated conditions, there is a need to include the effects of suction on the calculations, thus the values of matric suction and φb
have to be known.
Wood et al., (2001), assumed an average value of φb=17o for alluvial
materials from the banks of the Mississippi River to calculate the strength of the
unsaturated soils. Values of φb=15o have been suggested also by Fredlund and
Rahardjo (1993). In the particular case of the Licking River, using φb = 17o and the maximum and minimum values of matric suction measured in the field
(Figure 46), it is possible to quantify the increase in cohesion due to suction in the soils. For a value of (ua-uw ) = 20 kPa (417.7 psf) and c’= 5.8 kPa (120 psf),
b the “total cohesion” [c'+(ua − uw ) tanϕ ], corresponds to 11.8 kPa (247.7 psf), or an increase of 106 % in the value of cohesion. On the other hand, a drop in suction, (ua-uw) = 0.3 kPa (6.3 psf), results in total cohesion of 5.8 kPa (122 psf),
or an increase of 1.7 %.
In the case of failure along the riverbanks, it was observed that rainfall
prior to the flood events modified the degree of saturation of the materials,
increasing the hydraulic conductivity of the soil thus facilitating the percolation of
water within the soil. As the banks were flooded, the soil had enough time to
become saturated and after the water receded, an undrained condition
developed accompanied by loss of confinement of the slope. Seepage forces
may have developed under those conditions triggering the slope failures.
85 CHAPTER 6. STABILITY ANALYSIS RESULTS The study site contains a gently sloping bank with an average height of 9
meters (27 feet) above the river’s edge (Figure 51). About mid-height in the
slope, there are a series of tension cracks present (Figure 6) defining an arcuate shape as in circular failures.
Different hydrologic scenarios have to be considered due to changes caused by seasonal and flooding-induced conditions within the study area
(Figure 48). During summer and early fall, the Licking River remains at low stage
(average 139 m masl), the banks have a deep water table and the lower slope is partially submerged (steady-state; Figure 52). During winter and spring the river stage rises as a result of snow melt and heavy rainfall. At these times, the water level rises, the riverbanks become partially and occasionally totally submerged, and the water table rises (Figure 53).
Both hydrologic scenarios must be analyzed for a proper understanding of the stability of the banks. At low stage, steady-state conditions prevail and effective stress must be considered in the slope stability analysis. Following high-stage, if rapid drawdown conditions develop, undrained behavior must be examined. For the particular case of rapid drawdown, because the surface water level fluctuates, different conditions of water elevation are considered in the analysis to determine the effect pore water exerts on the stability of the slope and to determine the conditions under which the slopes are more prone to instability..
86
Figure 51. Slope profile at Frederick’s Landing.
87
Figure 52. Steady-state conditions with deep water table.
SEEPAGE ZONE
Figure 53. Rapid drawdown conditions with seepage developed along the slope
Different hydrological flow patterns have been observed during the ten
months monitoring period. Low river elevations of 140 m masl and 139 m masl
occurred during the months of June – September 2003 with consequent lowering
of the groundwater table (Figure 48). During late fall and winter, surface water
elevations increased and major floods occurred with water elevations of 144.2
and 146 m masl inundating the study area for several days and raising the
groundwater table to the ground surface.
Riverbank failures along the Licking River are chiefly circular and
sloughing type failures. Slumps and piping failures are most likely to occur in
88 areas that have been under water for a long time. Because, as mentioned
above, wedge failures are primarily restricted to the higher cut banks, this study
concentrates on the analysis in circular type failures prevalent near the river’s
banks.
The stability analysis of the study area used the XSTABL computer
program with Simplified Bishop analysis for circular failure surfaces, either
specifying a failure surface passing through the tension cracks present in the
slope or allowing the computer to find the surface with the lowest factor of safety.
To be able to model the stability of the slope, it was necessary to make
some simplifying assumptions regarding groundwater behavior and strength
properties of the materials. These assumptions were as follows:
• The groundwater level is parallel to the surface of the slope for an
insufficient number of piezometers were installed to positively
locate the piezometric surface.
• In rapid drawdown conditions the groundwater level remains high
due to the low permeability of the silty clay material
• The strength characteristics of each soil layer do not vary through
the thickness of the layer
• No failure occurs below an elevation of 132 m masl for bedrock is
located at about that depth
Analysis of wedge failures was completed utilizing the limit equilibrium method with the bank-stability and toe erosion model (Simon et al., 2001).
89 6.1. CIRCULAR FAILURE ANALYSIS RESULTS Circular failure analysis under low-stage, steady-state conditions (i.e.,
summer), indicate the slope is stable (factor of safety greater than one). When
the river elevation rises, the stability of the slope increases considerably. Initially
the stability of the slope was analyzed with a fixed failure surface and varying
river elevation to show the change in factor of safety resulting from the decrease
in the hydrostatic confining pressure in the slope (Figure 54).
The worst-case scenario, rapid drawdown, results in undrained conditions
and development of a perched water table (e.g., November 2003) with no
hydrostatic confining pressure on the lower slope. This case was modeled with
changes in surface water elevation from 144.2, 142.5, 142, 140.3 and 139 m
masl and location of the groundwater table at the surface after water recession in
the inundated slope.
Utilizing the measured unconfined compressive strength (Table 2) cu = 37
o kPa (700 psf) and ϕ = 0 for the uppermost layer of the slope, cu = 25 kPa and
o o ϕ = 0 for the middle layer and cu= 27 kPa and ϕ = 13 for the lower layer yields a high factor of safety, 6.5 for high river elevation and 3.3 for a lower river elevation
(Figure 54, Table 10) indicating a stable slope. The presence of tension cracks in the slope shows that the factor of safety should not be that high. Under rapid drawdown with river elevation between 140 and 139 m masl, the value of factor of safety would be expected to be between 1.2-1.4.
90
Figure 54. Circular failure analysis with fixed failure surface, undrained analysis.
91 Table 10. Factor of safety calculations for circular failure using Modified Bishop Method and fixed failure surface
XTABLE RUNS FOR MODIFIED BISHOP METHOD Groundwater at ground surface FS dif c, φ for each layer River elevation c=0;φ =17 c=2.4;φ =17 c=4.8;φ=17 c=5.8;φ=17 c=7.2;φ=17 6.51 144.2 1.45 1.93 2.41 2.61 2.89 4.9 142.5 1.16 1.47 1.83 1.98 2.19 4.41 142 1.01 1.34 1.66 1.8 1.99 3.49 140.3 0.82 1.08 1.33 1.44 1.59 3.32 139 0.79 1.03 1.27 1.37 1.52 c=0;φ =17; with crack River elevation c=0;φ =13 c=2.4;φ =13 c=4.8;φ =13 c=5.8;φ =13 c=7.2;φ =13 1.46 144.2 1.09 1.57 2.05 2.25 2.53 1.11 142.5 0.84 1.2 1.56 1.71 1.91 1.02 142 0.77 1.09 1.41 1.55 1.74 0.82 140.3 0.62 0.88 1.13 1.24 1.39 0.79 139 0.6 0.84 1.08 1.18 1.32 Groundwater below ground surface River elevation c=0;φ =17 c=2.4;φ =17 c=4.8;φ=17 c=5.8;φ=17 c=7.2;φ=17 144.2 1.45 1.93 2.41 2.61 2.89 142.5 1.2 1.56 1.93 2.08 2.29 142 1.13 1.46 1.79 1.93 2.12 140.3 0.96 1.22 1.48 1.58 1.74 139 0.94 1.19 1.43 1.53 1.68 Effective parameters with groundwater below ground surface River elevation c'=0;φ' =17 c'=2.4;φ' =17 c'=4.8;φ'=17 c'=5.8;φ'=17 c'=7.2;φ'=17 144.2 1.34 1.84 2.32 2.52 2.8 142.5 1.11 1.47 1.83 1.98 2.19 142 1.04 1.34 1.69 1.83 2.02 140.3 0.88 1.13 1.39 1.49 1.64 139 0.86 1.1 1.34 1.44 1.59 Effective parameters with φ'= 31 River elevation c'=0; φ' =31 c'=2.4;φ'=31 c'=4.8;φ'=31 c'=5.8;φ'=31 c'=7.2;φ'=31 144.2 2.69 3.16 3.63 3.83 4.11 142.5 2.18 2.54 2.9 3.05 3.26 142 2.04 2.37 2.7 2.83 3.02 140.3 1.72 1.98 2.23 2.34 2.49 139 1.69 1.93 2.17 2.27 2.41
92 Even though the cohesion values presented above do not differ
significantly from values reported in the literature for cohesive materials on
riverbanks (Table 9), they are considered too high for the tested slope. In order
to determine the factors to which the slope was most sensitive, different strength
parameters were analyzed.
A consolidated undrained triaxial test with pore pressure measurements
completed for the lower soil layer yields an undrained friction angle φ=13o and an effective friction angle φ’=31o (Table 2). For the undrained analysis two different values of friction angle, 13o and 17o, were considered. The minimum value
considered in the study was φ=13o for it was the undrained friction angle measured in the test. For the maximum value, literature (Johnson, 1974;
Abramson et al., 1996) indicates that the undrained friction angle is about one
1 half of the effective friction angle (φ = φ ' ). In this case φ would be 15.5o, a 2
value of φ=17o was selected for the upper boundary to account for uncertainties
during testing.
In the case of the total cohesion, if the silty clay materials are considered
normally consolidated, the lowest cohesion value would be zero. Using this value
under undrained conditions (total stress approach) and a value of undrained
friction angle φ=17o, the model predicts a factor of safety less than 1.0 when the
surface water elevation drops below 142 m masl (Table 10; Figure 55). For river
elevation has been observed to rapidly drop below 142 m masl during the study
93
3.5
3.0
2.5 ty
fe 2.0 a of S or
t 1.5 c Fa
1.0
0.5 Below ground C = 0 kPa Below ground C = 2.4 kPa Below ground C = 4.8 kPa Below ground C = 5.8 kpa Below ground C = 7.2kPa At ground C = 0 kPa At ground C = 2.4 kPa At ground C = 4.8 kPa At ground C = 5.8 kPa At ground C = 7.2 kPa 0.0 138 139 140 141 142 143 144 145 River elevation (m masl)
Figure 55. Factor of safety vs. river elevation with groundwater below and at the surface (φ=17), undrained analysis.
94 period without triggering slope failure, a value of undrained cohesion of zero is not considered appropriate for this analysis. Results of triaxial testing and
consolidation tests (Table 2) indicate that the materials modeled are cohesive
and overconsolidated hence c > 0.
Increasing the cohesion to 2.4 kPa (50 psf) and leaving the friction angle
unchanged produces a factor of safety of 1.03 (Figure 55) under the worst case
scenario of rapid drawdown to a water surface elevation of 139 m masl (Figure
55). This safety factor indicates quasi-stable conditions. Increasing the
undrained cohesion successively to 4.8, 5.8 and 7.2 kPa (100, 120, 150 psf), and
keeping φ =17o, increases the factor of safety to 1.3, 1.4 and 1.5 respectively,
thus the slope is stable even under the worst-case drawdown conditions (Figure
55). Hydrostatic forces substantially contribute to the stability of the slope.
Decreasing the undrained friction angle to φ=13o, while retaining the same values for undrained cohesion (Table 10; Figure 56), causes a substantial reduction in the factor of safety. This indicates that failure should occur with c=
2.4 kPa and a surface water elevation of 141 m masl; however, the surface water elevation has been observed below 141 m masl and no complete failure has been detected in the monitored slope.
Comparison of different values of undrained cohesion in the circular analysis model with a predefined surface of failure passing through the pre- existing tension cracks and a fixed value of the undrained friction angle indicates a gradual decrease in the value of the factor of safety when the surface water level diminishes (Table 10). Hence cohesion and hydrostatic confining pressure
95
3.00 c=0 kPa;phi=17 c=2.4 kPa; phi= 17 c=4.8 kPa; phi=17 c=5.8 kPa: phi=17 c=7.2 kPa; phi=17 c=0 kPa; phi=13 2.50 c=2.4 kPa; phi=13 c=4.8 kPa; phi=13 c=5.8 kPa; phi=13 c=7.2 kPa; phi=13
2.00 y et saf
1.50 of r o t c a F
1.00
0.50
0.00 138 140 142 144
River elevation (m masl) Figure 56. Factor of safety vs. river elevation with groundwater at ground surface
96 are important parameters for the stability of clayey, low angle banks.
When the river stage decreases gradually, the bank material has time to
drain, keeping the groundwater table close to the river level (steady-state, Figure
52). Modeling these conditions with φ =17o and variation of the cohesion intercept of the soil from c= 0, 2.4, 4.8, 5.8 and 7.2 kPa (0, 50, 100, 120, 150 psf) yields an increase in the value of factor of safety of the slope (Table 10). The results of these trials (Figure 55) compared with the worst case rapid drawdown conditions indicate an increase of about 25% in the factor of safety in drained conditions for the lower water elevation (below 141 m masl). For surface water elevations above 141 m masl, the increase is less that 13%, sometimes with no difference at all (i.e., 144.2 m masl). Thus pore water pressure and the elevation of the groundwater surface are critical when the hydrostatic confining pressure is low (low surface water elevation).
The tension cracks present in the tested slope indicate incipient failure conditions but no complete failure has occurred. The calculated factors of safety are close to one, therefore, a factor of safety between 1.2-1.4 under rapid drawdown conditions is appropriate for the tested slope; factors of safety greater than 1.5, as discussed in previous chapters, indicate stable conditions in a slope.
Comparison of drained and undrained approaches for slopes with groundwater level at the ground surface indicate that using effective strength parameters for steady-state conditions yields factors of safety about 7.5% lower than the ones obtained using an undrained approach (Figure 57). Therefore, the drained approach is more conservative.
97
3.5
3.0
2.5 y et 2.0 saf
of or 1.5 Fact
1.0
c=0; phi=17 c=2.4; phi=17 c=4.8; phi=17 c=5.8; phi= 17 0.5 c=7.2; phi=17 c'=0; phi'=17 c'=2.4; phi'=17 c'=4.8; phi'=17 c'=5.8; phi'=17 c'=7.2; phi'=17 0.0 138 139 140 141 142 143 144 145
River elevation (m masl)
Figure 57. Undrained vs. drained approach for stability analysis with groundwater below the ground surface (φ =17o)
98 Comparison of river elevation versus slope height was performed to
determine the critical pool elevation, defined as the ratio of water elevation (Hw) and slope height (H), (Hw/H), when the value of factor of safety equals unity
(Rinaldi & Casagli, 1999). From this analysis (Table 11, Figure 58) it is
concluded that, under rapid drawdown conditions, the critical pool ratio
Hw/H=0.38, equivalent to a river elevation close to 142 m masl for slopes with
zero cohesion. In the case of c=2.4 kPa, the critical pool elevation corresponds
to a river elevation of 139 m masl.
In both cases, steady-state and rapid drawdown with fixed failure surface,
values of factor of safety below 1.5 are reached by river elevations below 142 m
masl accompanied by cohesion values equal to or less than 5.8 kPa.
Table 11. Critical pool ratio with assumed base level 138.5 m masl, slope height 9.5 m for slope at Frederick’s Landing.
GROUNDWATER AT GROUND SURFACE River elevation Hw/H c=0;φ =17 c=2.4; ϕ=17 c=4.8; ϕ=17 c=5.8; ϕ=17 c=7.2; ϕ=17 144.2 0.600 1.45 1.93 2.41 2.61 2.89 142.5 0.421 1.16 1.47 1.83 1.98 2.19 142 0.368 1.01 1.34 1.66 1.80 1.99 140.3 0.189 0.82 1.08 1.33 1.44 1.59 139 0.053 0.79 1.03 1.27 1.37 1.52 GROUNDWATER BELOW GROUND SURFACE River elevation Hw/H c=0;φ =17 c=2.4; ϕ=17 c=4.8; ϕ=17 c=5.8; ϕ=17 c=7.2; ϕ=17 144.2 0.600 1.45 1.93 2.41 2.61 2.89 142.5 0.421 1.20 1.56 1.93 2.08 2.29 142 0.368 1.13 1.46 1.79 1.93 2.12 140.3 0.189 0.96 1.22 1.48 1.58 1.74 139 0.053 0.94 1.19 1.43 1.53 1.68
99
3.0
2.5
2.0
1.5 Factor of safety
1.0
At ground c = 0 kPa; phi = 17 At ground c= 2.4 kPa; phi = 17 0.5 At ground c= 4.8 kPa; phi = 17 At ground c= 5.8 kPa; phi = 17 At ground c= 7.2 kPa; phi= 17 Below ground c = 0 kPa; phi = 17 Below ground c = 2.4 kPa; phi = 17 Below ground c = 4.8 kPa; phi = 17 Below ground c = 5.8 kPa; phi = 17 Below ground c = 7.2 kPa; phi = 17 0.0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Hw/H
Figure 58. Critical pool ratio for slope at Frederick’s Landing.
100 XSTABL permits searching for the circular failure surface with the lowest fac tor of safety. Assuming the same strength conditions used in the previous
analyses of a fixed failure surface, a circular failure search was conducted. The
results for rapid drawdown conditions with cohesion of ze ro indicate failure of the slope for river elevations below 144.2 m masl and progressive increase in the stability with increased cohesion (Table 12, Figure 59). When the water table is low, instability only occurs at river elevations below 142 m masl assuming no cohesion. With cohesion greater than zero the slope is stable.
Table 12. Factor of safety calculations using Modified Bishop Method with free failure surface search
GROUNDWATER AT GROUND SURFACE River elevation c=0;φ =17 c=2.4;φ=17 c=4.8;φ=17 c=5.8;φ=17 c=7.2;φ=17 144.2 1.215 1.689 2.084 2.248 2.466 142.5 0.793 1.331 1.635 1.762 1.931 142 0.697 1.243 1.527 1.641 1.797 140.3 0.697 1.046 1.272 1.363 1.491 139 0.697 0.98 6 1.1 89 1 .274 1.392 GROUNDWATER AT G ROUND SU RFACE River elevation Top layer Middle layer Lower layer c=37;φ =0 c=25;φ=0 c=27;φ=13 FACTOR OF SAFETY FREE SEARCH 144.2 4.35 142.5 3.5 142 3.3 140.3 2.7 139 2.4 GROUNDWATER BELOW GROUND SURFACE River elevation c=0;φ =17 c=2.4;φ=17 c=4.8;φ=17 c=5.8;φ=17 c=7.2;φ=17 144.2 1.215 1.689 2.084 2.248 2.466 142.5 1.306 1.454 1.756 1.878 2.048 142 1.093 1.381 1.658 1.771 1.929 140.3 0.913 1.181 1.403 1.496 1.625 139 0.852 1.114 1.319 1.404 1.524
101 Water elevation: 139 m masl c = 4.8 kPa; Phi = 17 c = 4.8 kPa; Phi = 17 c = 4.8 kPa; Phi = 17
Assumed base level 138.5 m masl
Figure 59. Circular failure analysis with free surface search, undrained analysis.
102 6.2. WEDGE FAILURE ANALYSIS RESULTS The pos itions of ground water table and r iver stage are very important in
the analysis of wedge or planar failure. The tops of the banks at the edge of the
slope are particularly prone to failure (Figure 60). When groundwater is close to
the surface and the river stage is low, the soil wedge is more likely to fail. If the
river stage rises, the value of factor of safety increases.
The wedge failure model used, ARS, was developed by Simon et al.,
(2001). The model utilizes a predefined position of the wedge in the slope and a
specific inclination of the surface of failure for the wedge. After these inputs are
specified, the pro perties of the s lope ma terials are entered. The mode led slope
in this case was assumed to be homogeneous and that the positions of the
ground-water surface and river stage are static. The model accounts for matric
suction by incorporating it into the cohesion.
Using a value of c’ = 0 kPa, φ’ = 22o and φb = 15o, the calculations indicate that bank stability increases as the elevation of the groundwater table decreases.
Failure is thus most likely to occur with rapid drawdown conditions that leave the groundwater table at a higher elevation (Figure 60).
When the surface water level rises, the increase in hydrostatic confining
pressure increases the factor of safety of the slope. In the modeled slope (Figure
51), assuming a surface water elevation at the top of the slope (142 m masl) and
full saturation of the soil, the calculations of stability indicate stable conditions
with a factor of safety of 2.16 (Tab le 13).
103 144.00 bank profile 142.00 base of layer 1
) 140.00
M base of layer 2 ( N O I base of layer 3 138.00 AT
EV base of layer 4
EL 136.00 failure plane
134.00 water surface
132.00 water table 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 STATION (M)
Water table depth (m) below bank top
0
Pore Pressure From Water Table (kPa)
Layer 1: 10.791 Layer 2: 28.9395 Layer 3: 39.7305 Layer 4: 48.069 Layer 5: 54.936
Factor of Safety: 2.157516 Stable
Figure 60. Wedge failure modeling with rapid drawdown conditions.
104 Table 13. Values of factors of safety for wedge failure analysis
LIMIT EQUILIBRIUM FOR WEDGE FAILURE (ARS model) TRIAL FAILURE ANGLE ELEV EMERGING FAILURE PL RIVER ELEVATION (m masl) GW F R OM S R F (m) F S C' ϕ' 5 12 142 0 2.1 6 0 22 6 AND 7 12 140 140 0 0.82 0 22 12 140 0.2 1.1 1 0 22 12 140 0.4 1.3 9 0 22 12 140 0.5 1.5 4 0 22 8 12 139 139 0 0.48 0 22 12 0.2 0.7 1 0 22 12 0.3 0.8 2 0 22 12 0.5 1.0 4 0 22 12 0.6 1.1 6 0 22 12 0.8 1.3 8 0 22 12 1 1.6 0 22 12 2 2.4 8 0 22 9 15 139 139 0.3 0.41 0 22 15 0.5 0.6 3 0 22 15 0.8 0.9 6 0 22 15 1 1.1 9 0 22 15 2 2.0 6 0 22 10 15 139 139 0.3 0.47 0 31 15 0.5 0.8 0 31 15 0.7 1.1 3 0 31 15 1 1.6 2 0 31 15 2 2.6 6 0 31 11 12 140 142 0 5.84 5.8 22 12 0.3 6.6 5.8 22 12 AND 13 12 140 140 0 2.91 5.8 22 12 0.2 3.1 9 5.8 22 12 0.5 3.6 2 5.8 22 12 0.8 4.0 5 5.8 22 12 1 4.3 3 5.8 22 12 2 5.4 3 5.8 22 12 3 4.55 5.8 22
105 Table13. Values of factors of safety for wedge failure analysis (continuation)
LIMIT EQUILIBRIUM FOR WEDGE FAILURE (ARS model) TRIAL FAILURE ANGLE ELEV EMERGING FAILURE PL RIVER ELEVATION (m masl) GW FROM SRF (m) FS C' ϕ' 14 12 139 139 0 2.12 5.8 22 12 0.2 2.35 5.8 22 12 0.5 2.68 5.8 22 12 1 3.24 5.8 22 12 2 4.17 5.8 22 15 15 139 139 0 1.7 5.8 22 15 0.3 2.03 5.8 22 15 0.5 2.26 5.8 22 15 0.8 2.59 5.8 22 15 1 2.81 5.8 22 16 15 139 139 0 1.6 5.8 31 15 0.3 2.09 5.8 31 15 0.5 2.42 5.8 31 15 0.8 2.92 5.8 31 15 1 3.25 5.8 31 15 2 4.34 5.8 31 17 20 139 139 0 0.8 5.8 31 20 0.3 1.42 5.8 31 20 0.5 1.83 5.8 31 20 0.7 2.24 5.8 31 20 1 2.86 5.8 31 20 2 4.23 5.8 31 18 20 140 140 0 0.14 0 22 20 0.3 0.53 0 22 20 0.5 0.78 0 22 20 0.6 0.91 0 22 20 0.8 1.17 0 22 20 1 1.42 0 22 20 2 2.35 0 22 19 20 140 140 0 0.14 0 22 0.5 0.78 0 22 0.8 1.17 0 22 1 1.42 0 22 2 2.35 0 22
106 Table 13. Values of factors of safety for wedge failure analysis (continuation)
LIMIT EQUILIBRIUM FOR WEDGE FAILURE (ARS model) TRIAL FAILURE ANGLE ELEV EMERGING FAILURE PL RIVER ELEVATION (m masl) GW FROM SRF (m) FS C' ϕ' 20 20 139 139 0 0 0 22 0.2 0 0 22 0.8 0.4 0 22 1 0.67 0 22 1.5 1.23 0 22 2 1.77 0 22 21 20 139 139 0.5 0 0 31 0.8 0.42 0 31 1 0.83 0 31 1.5 1.52 0 31 2 2.14 0 31 22 20 140 142 0 5.14 5.8 22 0.5 6.36 5. 8 22 23 20 139 139 0.2 1.6 5.8 22 0.5 2.01 5.8 1 2.71 5.8 2 3.86 5.8 24 20 140 140 0 2.01 5.8 22 0.1 2.14 5.8 0.3 2.4 5.8 0.5 2.65 5.8 1 3.29 5.8 25 20 140 140 0.3 2.4 5.8 22 0.5 2.65 5.8 0.8 3.04 5.8 1 3.29 5.8 2 4.28 5.8 26 20 139 139 0 1.32 5.8 22 0.1 1.46 5.8 0.3 1.73 5.8 0.5 2.01 5.8 1 2.71 5.8 27 20 139 139 0 0.8 5.8 31 0.3 1.42 5.8 0.5 1.83 5.8 0.7 2.24 5.8 1 2.86 5.8 2 4.23 5.8
107 Modifying the surface water elevation from 139 to 140 m masl and also
lowering the position of the water table decreases the factor of safety of the slope
(Table 13). As illustrated by Figure 60, the presence of wedge failures along the
banks of the Licking River indicates that these hydrologic conditions (i.e., high
GWT and low river elevation) occur frequently. Varying the strength parameters
of the soil to c’= 5.8 kPa (120 psf) and φ’ = 31o (Table 13) indicates that wedge failure will not occur even under the worst-case conditions of rapid drawdown.
In summary, a value of effective cohesion of 5.8 kPa (120 psf) is considered to be the upper boundary for this strength parameter in the stability analysis of riverbanks in the case when more site-specific soil strength information is not available. Therefore, values of undrained cohesion in the range of 2.4-5.8 kPa (50-120 psf) are considered more appropriate for stability analysis studies in riverbanks under fluctuating river stages.
In addition, fluctuations in surface water elevations and water table within the slope critically affect the stability of the riverbanks. Lowering the surface water elevation under rapid drawdown conditions with a fully saturated slope decreases the slope’s stability. Under drained conditions stability improves. The stability analysis also indicates particular sensitivity to changes in the cohesion value and demonstrates the great influence that pore water pressure and hydrostatic confining pressure exert on the stability of the river banks. River elevations below 140 m masl are considered critical for failures to occur under rapid drawdown conditions when slopes have been under water for several days.
108 Small wedge failures occur when water elevation drops after high stage or
intermediate stage is maintained in the river. Deep-seated slides compromising
a considerable part of the slope develop slowly, with initial appearance of tension
cracks that gradually widen and deepen into the slope. Therefore, the stability of the slope decreases by the percolation of water within the tension cracks, and by changes in water elevation of the river and the development of positive pore water pressure.
109 CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS The lower Licking River valley is located in the northern Kentucky area in the
vicinity of Cincinnati. The riverbanks exhibit instability features related chiefly to
high water stage and locally to erosion. Geotechnical exploration of a site at the
City of Wilder, indicated that the materials underlying the riverbanks comprise, in
the upper 4 meters (~12 feet), yellowish brown and greenish gray silty clays;
values of total cohesion and friction angle measured by a consolidated undrained
triaxial test with pore pressure measurements in the yellowish brown silty clay
yielded values of c=27 kPa (560 psf) and φ=13o. Monitoring of river stage during a one-year period indicates fluctuations in water elevation for 142-144 m masl during winter and spring and 139-140 m masl during summer; one winter flood event reached 146 m masl.
• Four types of failures were observed in the banks of the Licking River:
circular, wedge, slumps and piping. Circular failures are most commonly
present in lower banks, whereas wedge failures occur in higher cut banks.
Slumps occur in lower banks that are submerged over long periods of
time. Piping occurs in mid-slope and causes removal of soil particles that
subsequently leads to collapse of the bank.
• The riverbank studied was fully saturated immediately following two
closely-spaced floods. Such saturation has a strong effect on the
mechanical properties of soils. Therefore antecedent events are important
to consider in the stability of slopes.
110 • A reduction of matric suction in a soil is produced by infiltration during and
after a rainfall, by percolation during floods.
• Matric suction changes at a rapid rate during rainfall and floods. Thus it is
an inappropriate parameter to use in the calculation of stability of slopes
that are frequently flooded. The influence of suction in the strength of the
materials can be considered of importance in the long-term stability
conditions where pore pressure has dissipated (drained conditions).
• In the analysis of stability of natural slopes, even though matric suction
increases the strength of the materials, the results of this study show that
slope stability studies using the assumption of saturation give more
realistic and conservative results.
• Modeling of bank failures demonstrates that cohesion of the material is a
critical parameter in the stability of riverbanks. High values of cohesion
result in stable slopes even under worst-case rapid drawdown conditions.
Lower values result in failure. Values of cohesion of 5.8 kPa (120 psf) are
considered a good approximation in case of lack of laboratory data for
these riverbank materials.
• Riverbanks are more susceptible to failure when under rapid drawdown
conditions after being under water for a prolonged period of time. For the
lower Licking River, banks are more likely to fail when river elevations are
lower than 140 m masl.
• The results of this research confirm the results obtained in previous
investigations in Italy and Missouri regarding the behavior of matric
111 suction in the riverbanks and the decrease in factor of safety of slopes
during rapid drawdown conditions.
The results presented in this research are a first step towards the understanding of failures of the local cohesive clayey riverbanks. The analysis of seepage forces developed during flood recession is of paramount importance in accessing the stability of these riverbanks.
112 REFERENCES ABRAMSON, L., LEE, T., SHARMA, S. & BOYCE, G., 1996. Slope stability and
stabilization methods. John Wiley and Sons. 629p
AMERICAN SOCIETY FOR AND TESTING MATERIALS (2002). Annual book of
ASTM standards, sec 4, vol 04.08, West Conshohocken, PA.
AUSILIO, E. & CONTE, E., 1999. Settlement rate of foundations on unsaturated
soils. Canadian Geotechnical Journal 36: 940-946.
ASHFORD, S., ROTH, L., MADSON, S. & ANDERSON, D., 1992. Embankment
design. Proceedings of the Stability and performance of slopes and
embankments – II conference. Geotechnical special publication No 31,
volume II: 1112-1125. American Society of Civil Engineering.
BAIR, F., 1992 (Editor). The weather almanac. Sixth edition, Gale Research Inc.
BOWLES, J. E., 1992. Engineering properties of soils and their measurement.
McGraw-Hill, fourth edition. 241p
BRETT, C. & ALGEO, T., 2001. Stratigraphy of the Upper Ordovician Kope
Formation in its type area (northern Kentucky), including a revised
nomenclature. In: Algeo, T.J. and C.E. Brett, Eds. Sequence, Cycle, and
Event Stratigraphy of Upper Ordovician and Silurian Strata of the
Cincinnati Arch Region. Field Trip Guidebook 1, Series XII, Society for
Sedimentary Geology, p. 47-64.
BREUER, J., 1965. Mineralogy and distribution of clay sediments in the Great
Miami River Basin. Unpublished MS thesis, Department of Geology,
University of Cincinnati.
113 CASAGLI, N., RINALDI, M., GARGINI, A. & CURINI, A., 1999. Pore water
pressure and streambank stability: results from a monitoring site on the
Sieve River, Italy. Earth Surface Processes and Landforms 24: 1095-
1114.
CHOWDHURY, R. & FLENTJE, P., 2002. Uncertainties in rainfall-induced
landslide hazard. Quarterly Journal of Engineering Geology and
Hydrogeology 35: 61-70.
CINCINNATI METROPILITAN SEWER DISTRICT. 2003. Precipitation data at
Cincinnati 1996-1997.
DAPPORTO, S., RINALDI, M. & CASAGLI, N., 2001. Failure mechanisms and
pore water pressure conditions: analysis of a riverbank along the Arno
River (Central Italy). Engineering Geology 61: 221-242.
DARBY, S., GESSLER, D. & THORNE, C., 2000. Computer program for stability
analysis of steep cohesive riverbanks. Earth Surface Processes and
Landforms, technical communication 25, 175-190.
DAS, B., 1997. Advanced soil mechanics. Taylor and Francis, second edition.
457p.
DURRELL, R., 1995. A recycled landscape: Cincinnati Museum of Natural
History Quarterly, v 14, p 8-15.
FREDLUND, D. & RAHARDJO, H. 1993. Soil mechanics for unsaturated soils.
John Wiley and Sons. 517p.
FREEZE, R. & CHERRY, J., 1979. Groundwater. Prentice Hall, Inc. 604pp.
114 GIBBONS, A., 1973. Geologic map of parts of Newport and Withamsville
quadrangle, Campbell and Kenton counties, Kentucky. US Geological
Survey, 7.5 minute quadrangles, scale 1:24000.
HAGERTY, D., SPOOR, M. & ULLRICH, C., 1981. Bank failure and erosion of
the Ohio River. Engineering Geology 17: 141-158
HAGERTY, D., SHARIFOUNNASAB, M & SPOOR, m., 1983. River bank
erosion – A case study. Bulletin of the Association of Engineering
Geologists, vol. XX, No 4: 411-437.
HOSTERMAN, J. & WHITLOW, S., 1981. Clay mineralogy of Devonian shales in
the Appalachian basin. U.S. Geological Survey, open-file report 81-585.
170p
JOHNSON, S., 1974. Analysis and design relating to embankments.
Proceedings on the Conference on Analysis and Design in Geotechnical
Engineering, ASCE, vol II.
KARUBE, D. & KAWAI, K., 2001. The role of pore water in the mechanical
behavior of unsaturated soils. Geotechnical and Geological Engineering
Journal 19 (3-4): 209 – 239.
KENTUCKY GEOLOGICAL SURVEY, 2004. Geologic map of Kentucky.
http://www.uky.edu/KGS/gis/geology.html.
KENTUCKY OFFICE OF GEOGRAPHIC INFORMATION, 2004. Digital
elevation model of the Newport and Covington quadrangles, 30 m
resolution. http://ogi.ky.gov/data/elevation.htm
115 KOHRS, R., 2003. Centimeter-scale characterization, correlation, and
microfabric analysis of event beds within the Alexandria submember of the
Kope Formation (Upper Ordovician, Edenian) in Cincinnati, OH and
Northern Kentucky. Unpublished MS Thesis, Department of Geology,
University of Cincinnati. 129p
LONDONO, A., 1995. Variacion del regimen de infiltracion en un suelo en
funcion de la intensidad de lluvia y pendiente del terreno. Tesis de grado,
Facultad de Minas, Universidad Nacional de Colombia. 138p. Medellin.
LOWE, J. 1966. Stability analysis of embankments. Proceedings of the Stability
and Performance of Slopes and Embankments Conference, Soil
Mechanics and Foundation Division, ASCE, 1-33.
LUFT, S., 1971. Geology of part of the Covington quadrangle, northern
Kentucky. US Geological Survey 7.5 minute quadrangles, scale 1:24000.
MARTIN, R., 1978. Structures and clayey sediments from a pre-Illinoian glacial
lake, Claryville area, Campbell County, Kentucky. Unpublished MS
Thesis, Department of Geology, University of Cincinnati. 120p.
NEWELL, 1986. Physiography. In: McDOWELL, R., (Ed). The geology of
Kentucky, a text to accompany the geologic map of Kentucky. U.S
Geological Survey, professional paper 1151-H. 73p.
NG, C. & SHI, Q., 1998. Influence of rainfall intensity and duration on slope
stability in unsaturated soils. Quarterly Journal of Engineering Geology
31: 105-113.
116 NORTHERN KENTUCKY PLANNING COMMISSION. 2002. GIS topographic
data and soil survey, contour lines every 2 feet.
POTTER, P., 1996. Exploring the geology of the Cincinnati/Northern Kentucky
region. Kentucky Geological Survey, Special Publication 22, Series XI.
115p.
RAHARDJO, H., LI, X., TOLL, D & LEONG, E., 2001. The effect of antecedent
rainfall on slope stability. Journal of Geotechnical and Geological
Engineering, 19: 371-399.
REID, M., NIELSEN, H. & DREISS, S., 1988. Hydrology factors triggering a
shallow hillslope failure. Bulletin of the Association of Engineering
Geologists, vol. XXV, No 3: 349-361.
RINALDI, M. & CASAGLI, N., 1999. Stability of streambanks formed in partially
saturated soils and effects of negative pore water pressures: the Sieve
River (Italy). Geomorphology 26: 253-277.
SATIJA, B., 1978. Shear behavior of partly saturated soils. Unpublished PhD
dissertation. Indian Institute of Technology, Delhi. 327p.
SHERARD, J., WOODWARD, R., GIZISCHI, S. & CLAVENGUER, W., 1963.
Earth and earth-rock dams. John Wiley & Sons, Inc.
SIMON, A., CURINI, A., DARBY, S. & LANDGENDOEN, E., 2000. Bank and
near-bank processes in an incised channel. Geomorphology 35: 193-217.
SIMON, A., CURINI, A., THOMAS, R., LANGENDOEN, E. & LAYZELL, A., 2001.
Bank stability and toe erosion model. USDA-ARS-NSL Channel and
Watershed Processes Research Unit.
117 SPRINGER, F. Jr. 1981. Influence of rapid drawdown events on river bank
stability. Unpublished Master’s of Engineering thesis, Department of Civil
Engineering, University of Louisville. 108p
SIMON, A., THOMAS, R., CURINI, A. & SHIELDS, D., 2002. Case study:
channel stability of the Missouri River, Eastern Montana. Journal of
Hydraulic Engineering 128 (10): 880 – 890.
SOIL CONSERVATION SERVICE, 1973. Soil survey of Boone, Campbell and
Kenton counties, Kentucky.
TERZAGHI, K. & PECK, R., 1948. Soil mechanics in engineering practice, John
Wiley & Sons, New York, N.Y.
TOBIN, R., 1982. A model for cyclic deposition in the Cincinnatian Series of
Southwestern Ohio, Northern Kentucky and Southeastern Indiana.
Unpublished PhD Dissertation, Department of Geology, University of
Cincinnati. 483p.
TONNING, B., 1998. The Licking River region in Kentucky: status and trends.
18p.
U.S. ARMY CORPS OF ENGINEERS, 1979. Reconnaissance report,
streambank erosion / stability problem Licking River, Covington, Kentucky.
Section 14, 1946 Flood Control Act.
U.S. ARMY CORPS OF ENGINEERS (USACE), 2002a. Great Lakes and Ohio
River navigation systems commerce report, 2002. U.S. Army Corps of
Engineers, Great Lakes and Ohio River Division, Huntington District. 93p.
118 U.S. ARMY CORPS OF ENGINEERS (USACE), 2002b. Kentucky River, lock
and dam No. 10-Upper Pool, Madison and Clark Counties, Kentucky.
Project No. 22181A. 36p.
U.S. ARMY CORPS OF ENGINEERS (USACE)., 2003. Ohio River stage at mile
470. 1990-2003.
U.S. GEOLOGICAL SURVEY, 2004. Peak Streamflow for the Nation. USGS
03255000 Ohio River at Cincinnati, OH.
http://nwis.waterdata.usgs.gov/nwis/peak?site_no=03255000&agency_cd
=USGS&format=html.
U.S. GEOLOGICAL SURVEY, 2004. Real-time streamflow. USGS 03255000
Ohio River at Cincinnati, OH.
http://nwis.waterdata.usgs.gov/nwis/uv?format=html&period=7&site_no=0
3255000.
U.S. GEOLOGICAL SURVEY, 2004. Real-time streamflow. USGS 03253500
Licking River at Catawba, Ky.
http://nwis.waterdata.usgs.gov/nwis/uv?dd_cd=02&format=gif&period=7&s
ite_no=03253500.
U.S. GEOLOGICAL SURVEY, 2004. National elevation database. 30m DEM.
http://ned.usgs.gov/.
VASSALLO, R. & MANCUSO, C., 2000. Soil behavior in the small and large
strain range under controlled suction conditions. In: Experimental
119 evidence and theoretical approaches in unsaturated soils. Tarantino &
Mancuso (eds), pp 75- 89. Rotterdam.
WOOD, A., SIMON, A., DOWNS, P. & THORNE, C., 2001. Bank-toe processes
in incised channels: the role of apparent cohesion in the entrainment of
failed bank materials. Hydrological Processes 15: 39-61.
120 APPENDIX Output files for fixed failure surface and free failure surface search trials XSTABL File: TRIAL32 fixed failure surface7-15-04 10:03
*************************************** X S T A B L Slope Stability Analysis using the Method of Slices Copyright (C) 1992 - 2002 Interactive Software Designs, Inc Moscow, ID 83843, U.S.A All Rights Reserved Ver. 5.206 96 - 1907 **************************************** Problem Description : trial32 ------SEGMENT BOUNDARY COORDINATES ------19 SURFACE boundary segments Segment x-left y-left x-right y-right Soil Unit No. (m) (m) (m) (m) Below Segment
1 0 138.5 20 138.7 3 2 20 138.7 30 138.9 3 3 30 138.9 31 139 3 4 31 139 32 139.8 2 5 32 139.8 32.8 140.3 2 6 32.8 140.3 35 141.5 1 7 35 141.5 39 142 1 8 39 142 42 142.5 1 9 42 142.5 43.4 143 1 10 43.4 143 44 143.3 1 11 44 143.3 45 143.5 1 12 45 143.5 47 143.8 1 13 47 143.8 48 144.2 1 14 48 144.2 49 144.4 1 15 49 144.4 50 144.7 1 16 50 144.7 52 145 1 17 52 145 65 147 1 18 65 147 70 148 1 19 70 148 75 148.2 1
121 8 SUBSURFACE boundary segments Segment x-left y-left x-right y-right Soil Unit No. (m) (m) (m) (m) Below Segment 1 32.8 140.3 39 141 2 2 39 141 49 142.6 2 3 49 142.6 63 143 2 4 63 143 75 143 2 5 31 139 39 139.7 3 6 39 139.7 49 141 3 7 49 141 63 141.2 3 8 63 141.2 75 141.3 3 ISOTROPIC Soil Parameters 3 Soil unit(s) specified Soil Unit Weight Cohesion Friction Pore Pressure Water Unit Moist Sat. Intercept Angle Parameter Constant Surface No. (kN/m3) (kN/m3) (kPa) (deg) Ru (kPa) No. 1 18.5 19.3 37 0 .000 .0 1 2 18.7 19.5 25 0 .000 .0 1 3 18.7 19.6 27 13 .000 .0 1 UNDRAINED STRENGTHS as a function of effective vertical stress have been specified for 3 Soil Unit(s) Soil Unit # Parameter a Parameter Psi 1. 37.0 00 2. 25.0 00 3. 27.0 13.00 1 Water surface(s) have been specified Unit weight of water = 9.81 (kN/m3) Water Surface No. 1 specified by 18 coordinate points PHREATIC SURFACE Point No. x-water(m) y-water(m) 1 0 139 2 31 139 3 32 139.8 4 32.8 140.3 5 35 141.5 6 39 142 7 42 142.5 8 43.4 143 9 44 143.3 10 45 143.4 11 47 143.8 12 48 144.2 13 49 144.4 14 50 144.7 15 52 144.9 16 64 145.3 17 70 146 18 75 146.3
122 A SINGLE FAILURE SURFACE HAS BEEN SPECIFIED FOR NALYSIS Trial failure surface is CIRCULAR, with a radius of 18.39 meters Center at x = 36.00 ; y = 156.70 ; Segment. Length = .50 meters The CIRCULAR failure surface was estimated by the following 43 coordinate points Point No x-surf(m) y-surf(m) 1 31 139 2 31.48 138.87 3 31.97 138.75 4 32.46 138.65 5 32.95 138.56 6 33.44 138.49 7 33.94 138.42 8 34.44 138.37 9 34.94 138.34 10 35.44 138.32 11 35.94 138.31 12 36.44 138.31 13 36.94 138.33 14 37.43 138.36 15 37.93 138.41 16 38.43 138.47 17 38.92 138.54 18 39.42 138.63 19 39.91 138.73 20 40.39 138.84 21 40.88 138.97 22 41.36 139.1 23 41.83 139.26 24 42.31 139.42 25 42.77 139.6 26 43.24 139.79 27 43.69 139.99 28 44.14 140.21 29 44.59 140.44 30 45.03 140.68 31 45.46 140.93 32 45.89 141.19 33 46.3 141.46 34 46.71 141.75 35 47.12 142.05 36 47.51 142.35 37 47.9 142.67 38 48.27 143 39 48.64 143.34 40 49 143.69 41 49.35 144.05 42 49.69 144.41 43 49.91 144.67
123 SELECTED METHOD OF ANALYSIS: Simplified Bishop SUMMARY OF INDIVIDUAL SLICE INFORMATION Slice x-base(m) y-base(m) height(m) width(m) alpha beta weight(kN) 1 31.24 138.94 0.26 0.48 -15 38.66 2.4 2 31.73 138.81 0.77 0.49 -13.44 38.66 7.3 3 31.98 138.75 1.04 0.03 -11.88 38.66 0.6 4 32.23 138.7 1.24 0.46 -11.88 32.01 11.1 5 32.63 138.62 1.57 0.34 -10.32 32.01 10.5 6 32.88 138.58 1.77 0.15 -10.32 28.61 5.2 7 33.2 138.52 1.99 0.49 -8.77 28.61 19.2 8 33.69 138.45 2.33 0.5 -7.21 28.61 22.6 9 34.19 138.4 2.66 0.5 -5.65 28.61 25.8 10 34.69 138.36 2.97 0.5 -4.09 28.61 28.9 11 34.97 138.34 3.15 0.06 -2.53 28.61 3.9 12 35.22 138.33 3.2 0.44 -2.53 7.13 27.2 13 35.69 138.31 3.27 0.5 -0.98 7.13 31.9 14 36.19 138.31 3.34 0.5 0.58 7.13 32.5 15 36.69 138.32 3.39 0.5 2.14 7.13 33 16 37.19 138.35 3.43 0.5 3.7 7.13 33.3 17 37.68 138.39 3.45 0.5 5.25 7.13 33.4 18 38.18 138.44 3.46 0.5 6.81 7.13 33.4 19 38.68 138.5 3.45 0.49 8.37 7.13 33.3 20 38.96 138.55 3.45 0.08 9.93 7.13 5.1 21 39.21 138.59 3.44 0.42 9.93 9.46 27.9 22 39.66 138.68 3.43 0.49 11.48 9.46 32.8 23 40.15 138.78 3.41 0.49 13.04 9.46 32.3 24 40.64 138.9 3.37 0.48 14.6 9.46 31.7 25 41.12 139.04 3.32 0.48 16.16 9.46 31 26 41.6 139.18 3.25 0.48 17.71 9.46 30.1 27 41.92 139.29 3.2 0.17 19.27 9.46 10.3 28 42.15 139.37 3.19 0.31 19.27 19.65 19 29 42.54 139.51 3.18 0.47 20.83 19.65 28.9 30 43 139.7 3.16 0.46 22.39 19.65 28.4 31 43.32 139.83 3.14 0.16 23.94 19.65 10 32 43.55 139.93 3.14 0.29 23.94 26.57 17.9 33 43.85 140.07 3.16 0.31 25.5 26.57 18.8 34 44.07 140.17 3.14 0.14 25.5 11.31 8.8 35 44.35 140.32 3.05 0.42 27.06 11.31 24.9 36 44.58 140.43 2.99 0.02 27.06 11.31 1.4 37 44.79 140.55 2.91 0.41 28.62 11.31 23.2 38 45.01 140.67 2.83 0.03 28.62 8.53 1.5 39 45.24 140.8 2.74 0.43 30.17 8.53 22.9 40 45.67 141.06 2.54 0.43 31.73 8.53 20.9 41 46.09 141.33 2.34 0.42 33.29 8.53 18.9 42 46.51 141.61 2.12 0.41 34.85 8.53 16.8 43 46.86 141.86 1.92 0.29 36.41 8.53 10.6 44 47.06 142 1.82 0.12 36.41 21.8 4.1 45 47.31 142.2 1.72 0.39 37.96 21.8 13.1 46 47.52 142.36 1.65 0.01 39.52 21.8 0.4 47 47.71 142.52 1.57 0.37 39.52 21.8 11.3 48 47.95 142.72 1.46 0.1 41.08 21.8 2.9 49 48.14 142.88 1.35 0.27 41.08 11.31 7.1 50 48.46 143.17 1.12 0.37 42.64 11.31 8 51 48.82 143.51 0.85 0.36 44.19 11.31 5.9 52 49.17 143.87 0.58 0.35 45.75 16.7 3.9 53 49.52 144.23 0.33 0.34 47.31 16.7 2.1 54 49.8 144.54 0.1 0.23 48.87 16.7 0.4
124 SLICE INFORMATION ... continued : Slice Sigma(kPa) c-value(kPa) phi U-base(kN) U-top(kN) Q-top(kN) Delta 1 5.7 27.8 0 0.8 0 0 0 2 12.5 29.4 0 2.3 0 0 0 3 16 30.2 0 0.2 0 0 0 4 17.5 30.6 0 4.1 0 0 0 5 21.4 31.5 0 3.9 0 0 0 6 22.9 31.9 0 2 0 0 0 7 25.3 32.5 0 7.5 0 0 0 8 29.1 33.4 0 8.8 0 0 0 9 32.7 34.3 0 10.1 0 0 0 10 36.2 35.2 0 11.2 0 0 0 11 38 35.7 0 1.5 0 0 0 12 31.9 34.3 0 13.5 0 0 0 13 32.3 34.4 0 15.8 0 0 0 14 32.7 34.6 0 16.1 0 0 0 15 32.9 34.7 0 16.4 0 0 0 16 33 34.8 0 16.5 0 0 0 17 32.9 34.8 0 16.7 0 0 0 18 32.7 34.8 0 16.7 0 0 0 19 32.4 34.8 0 16.7 0 0 0 20 32 34.8 0 2.6 0 0 0 21 32.4 34.9 0 13.9 0 0 0 22 32 34.9 0 16.4 0 0 0 23 31.4 34.8 0 16.3 0 0 0 24 30.7 34.7 0 16.1 0 0 0 25 29.9 34.6 0 15.8 0 0 0 26 28.9 34.4 0 15.5 0 0 0 27 28.1 34.3 0 5.4 0 0 0 28 30.6 34.9 0 9 0 0 0 29 30.2 34.9 0 13.8 0 0 0 30 29.7 34.8 0 13.8 0 0 0 31 29.1 34.8 0 4.9 0 0 0 32 31.7 35.4 0 7.9 0 0 0 33 31.4 35.4 0 8.4 0 0 0 34 25.6 34 0 4.8 0 0 0 35 24.7 33.9 0 13.8 0 0 0 36 25.6 25 0 0.8 0 0 0 37 24.8 25 0 12.9 0 0 0 38 25 25 0 0.8 0 0 0 39 23.6 25 0 12.5 0 0 0 40 21.2 25 0 11.7 0 0 0 41 18.7 25 0 10.8 0 0 0 42 16 25 0 9.9 0 0 0 43 13.6 25 0 6.4 0 0 0 44 14.2 25 0 2.2 0 0 0 45 12.9 25 0 7.3 0 0 0 46 11.7 25 0 0.2 0 0 0 47 7.8 37 0 6.4 0 0 0 48 6.1 37 0 1.7 0 0 0 49 3.6 37 0 4.6 0 0 0 50 0.8 37 0 5.3 0 0 0 51 -2.4 37 0 4 0 0 0 52 -5.4 37 0 2.6 0 0 0 53 -8.7 37 0 1.5 0 0 0 54 -11.8 37 0 0.3 0 0 0 For the single specified surface: Simplified BISHOP factor of safety = 3.320 Resisting Moment = 126.06E+02 kN-m WARNING - This method is valid only if the failure surface approximates a circle
125 XSTABL File: TRIAL212 7-14-04 1:48 * X S T A B L * * Slope Stability Analysis * * using the * * Method of Slices * * Copyright (C) 1992 - 2002 * * interactive Software Designs, Inc. * * Moscow, ID 83843, U.S.A. * * All Rights Reserved * * Ver. 5.206 96 - 1907 * Problem Description : trial212, free surface search
SEGMENT BOUNDARY COORDINATES 19 SURFACE boundary segments
Segment x-left y-left x-right y-right Soil Unit No. (m) (m) (m) (m) Below Segment
1 0 138.5 20 138.7 3 2 20 138.7 30 138.9 3 3 30 138.9 31 139 3 4 31 139 32 139.8 2 5 32 139.8 32.8 140.3 2 6 32.8 140.3 35 141.5 1 7 35 141.5 39 142 1 8 39 142 42 142.5 1 9 42 142.5 43.4 143 1 10 43.4 143 44 143.3 1 11 44 143.3 45 143.5 1 12 45 143.5 47 143.8 1 13 47 143.8 48 144.2 1 14 48 144.2 49 144.4 1 15 49 144.4 50 144.7 1 16 50 144.7 52 145 1 17 52 145 65 147 1 18 65 147 70 148 1 19 70 148 75 148.2 1
8 SUBSURFACE boundary segments
Segment x-left y-left x-right y-right Soil Unit No. (m) (m) (m) (m) Below Segment
1 32.8 140.3 39 141 2 2 39 141 49 142.6 2 3 49 142.6 63 143 2 4 63 143 75 143 2 5 31 139 39 139.7 3 6 39 139.7 49 141 3 7 49 141 63 141.2 3 8 63 141.2 75 141.3 3
126 ISOTROPIC Soil Parameters 3 Soil unit(s) specified Soil Unit Weight Cohesion Friction Pore Pressure Water Unit Moist Sat. Intercept Angle Parameter Constant Surface No. (kN/m3) (kPa) (deg) Ru (kPa) No. 1 18.5 19.3 4.8 17 0 0 1 2 18.7 19.5 4.8 17 0 0 1 3 18.7 19.6 4.8 17 0 0 1
UNDRAINED STRENGTHS as a function of effective vertical stress have been specified for 3 Soil Unit(s) Soil Unit Parameter Parameter # a Psi
1 4.8 17 2 4.8 17 3 4.8 17 1 Water surface(s) have been specified Unit weight of water = 9.81 (kN/m3) Water Surface No. 1 specified by 17 coordinate points
PHREATIC SURFACE Point x-water y-water No. (m) (m) 1 0 139 2 31 139 3 32.8 140.3 4 35 141.5 5 39 142 6 42 142.5 7 43.4 143 8 44 143.3 9 45 143.4 10 47 143.8 11 48 144.2 12 49 144.4 13 50 144.7 14 52 144.9 15 64 145.3 16 70 146 17 75 146.3
A critical failure surface searching method, using a random technique for generating CIRCULAR surfaces has been specified. 25 trial surfaces will be generated and analyzed. 5 Surfaces initiate from each of 5 points equally spaced along the ground surface between x = 20.0 m and x = 45.0 m Each surface terminates between x = 45.0 m and x = 55.0 m Unless further limitations were imposed, the minimum elevation at which a surface extends is y = 132.0 m 1.0 m line segments define each trial failure surface.
127 ------ANGULAR RESTRICTIONS ------
The first segment of each failure surface will be inclined within the angular range defined by : Lower angular limit := -45.0 degrees Upper angular limit := (slope angle - 5.0) degrees
************************************************************************ -- WARNING -- WARNING -- WARNING -- WARNING -- (# 48) ************************************************************************ Negative effective stresses were calculated at the base of a slice. This warning is usually reported for cases where slices have low self weight and a relatively high "c" shear strength parameter. In such cases, this effect can only be eliminated by reducing the "c" value. ************************************************************************ ------USER SELECTED option to discard surfaces with effective normal stresses less than zero ------
ERROR #48: NEGATIVE effective stress calculated for at least 1 slice(s) out of 35 slices for surface # 13
Circular surface (FOS= 2.5819) is defined by: xcenter = 18.18 ycenter = 238.54 Init. Pt. = 32.50 Seg. Length = 1.00 ------ERROR #48: NEGATIVE effective stress calculated for at least 1 slice(s) out of 38 slices for surface # 15
Circular surface (FOS= 2.8668) is defined by: xcenter = -11.12 ycenter = 373.57 Init. Pt. = 32.50 Seg. Length = 1.00 ------ERROR #48: NEGATIVE effective stress calculated for at least 1 slice(s) out of 17 slices for surface # 19
Circular surface (FOS= 2.4370) is defined by: x center = 41.66 y center = 144.22 Init. Pt. = 38.75 Seg. Length = 1.00
128 Factors of safety have been calculated by the:
* * * * * SIMPLIFIED BISHOP METHOD * * * * *
The most critical circular failure surface is specified by 31 coordinate points
Point x-surf y-surf No. (m) (m)
1 26.25 138.82 2 27.2 138.5 3 28.15 138.21 4 29.12 137.96 5 30.1 137.75 6 31.08 137.58 7 32.07 137.44 8 33.07 137.35 9 34.07 137.29 10 35.07 137.27 11 36.07 137.29 12 37.07 137.36 13 38.06 137.46 14 39.05 137.6 15 40.04 137.77 16 41.01 137.99 17 41.98 138.25 18 42.93 138.54 19 43.88 138.87 20 44.81 139.24 21 45.72 139.64 22 46.62 140.08 23 47.5 140.55 24 48.36 141.06 25 49.21 141.6 26 50.02 142.18 27 50.82 142.78 28 51.59 143.42 29 52.34 144.08 30 53.06 144.78 31 53.49 145.23
**** Simplified BISHOP FOS = 1.189 ****
******************************************************************** ** Out of the 25 surfaces generated and analyzed by XSTABL, ** ** 3 surfaces were found to have MISLEADING FOS values. **
********************************************************************
129 The following is a summary of the TEN most critical surfaces Problem Description : trial212
FOS Circle center Initial terminal Resisting Radius Slice (BISHOP) Moment x-coord y-coord (m) x-coord x-coord (m) (m) (m) (m) (kN-m) 1 1.189 35 162.73 25.46 26.25 53.49 1.06E+04 2 1.204 34.43 167.71 30.02 26.25 54.49 1.20E+04 3 1.221 33.78 162.24 24.59 26.25 51.2 8.33E+03 4 1.29 32.52 158.97 21.1 26.25 47.31 5.37E+03 5 1.322 31.95 160.79 22.7 26.25 46.99 5.31E+03 6 1.385 30.33 161.82 25.32 20 48.63 1.01E+04 7 1.395 33.62 153.14 19.85 20 51.7 1.57E+04 8 1.406 35.19 153.32 21.08 20 54.73 2.12E+04 9 1.497 27.83 186.89 48.83 20 53.21 1.64E+04 10 1.547 41.76 150.27 13.74 32.5 54.6 6.83E+03
* * * END OF FILE * * *
130