THE OUTER BANKS OF THE FRASER RIVER DELTA;
ENGINEERING PROPERTIES AND STABILITY CONSIDERATIONS
by
STEVEN SCOTTON
B.A. Sc., University of British Columbia, 1971
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCES
in the
FACULTY- OF GRADUATE STUDIES .-
Dept. of Civil Engineering
We. accept this thesis as conforming to the required standard
THE UNIVERSITY OF BRITISH COLUMBIA
MAY, 1977
© Steven Scotton, 1978 In presenting this thesis in partial fulfilment of the requirements for
an advanced degree at the University of British Columbia, I agree that
the Library shall make it freely available for reference and study.
I further agree that permission for extensive copying of this thesis
for scholarly purposes may be granted by the Head of my Department or
by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Steven Scotton
Department of Civil Engineering
The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5
Date February 6th, 1978 ii
ABSTRACT
Roberts Bank and Sturgeon Bank are the leading edges
of the Fraser River Delta. In the past half century various
aspects of the delta, and the banks, have been studied by
geologists, geomorphologists and engineers. Published papers
and reports of these studies form the primary data base for this thesis. The geology and geomorphology reports comple• mented the engineering data.
Logs of 6 8 boreholes were found in the engineering reports made available for this thesis. These boreholes were located such as to give a reasonable coverage of both Roberts
Bank and Sturgeon Bank. The reported holes were sampled ext• ensively with Standard Penetration Test split spoon samplers and a few thin wall Shelby tube samples were taken. The engineering reports presented the results of numerous tests performed on the samples, including shear tests, triaxial tests and consolidation tests.
The upper 80 feet of sediments, which is the zone of concern for strength and stability analyses, are primarily granular in nature. These sediments exist at a medium to loose density with a relative density as low as 40 percent suggested for large areas of the banks. Some of the deeper sediments are moderately compressible in nature and are
presently normally consolidated.
The nature of the surficial sediments is such that,
in the existing seismic environment in which they are located,
there is the possiblity of earthquake induced liquefaction.
Methods of assessing the probability of liquefaction are discussed and the results of one such assessment are presented.
The subaqueous slopes of Roberts Bank and Sturgeon
Bank, which average 1.5 degrees but exceed 23 degrees in a few spots, are shown to be at least nominally stable with respect to mass wasting. There are some indications that these slopes could be subject to some erosional instability.
The physical environment of the banks (wind, wave, temperature) is not particularly harsh, and presents no problems to engineering development. Certain aspects of the ecology of the banks, however, are of sufficient importance to warrant consideration as part of the design process for any project on the banks. TABLE OF CONTENTS
Abstract Table of Contents List of Tables List of Figures Acknowledgements
INTRODUCTION
AREA OF STUDY
SLUMP STRUCTURE
ENGINEERING PARAMETERS
Subsurface Sediments.
Grain Size Distribution
Relative Density
Friction Angle
Consolidation Parameters
Atterburg Limits
Compression Index Estimates
SETTLEMENT CASE HISTORY
PROBABLE EARTHQUAKE ACCELERATIONS
LIQUEFACTION POTENTIAL OF THE BANKS
Liquefaction
Empirical Liquefaction Criteria
Analytical Liquefaction Potential
SUBAQUEOUS SLOPE STABILITY
Erosional Instability
Mass Wasting
Effect of Surface Waves
Effect of Earthquake Motions V
ADDITIONAL DESIGN CRITERIA 9 7
Wind 9 8
Wave 99
Ecology 101
CONCLUSIONS 102
APPENDIX 1
APPENDIX 2
APPENDIX 3 vi
LIST OF TABLES
TABLE Page
1. Test Results 29
2. Historical Earthquakes 50 3. Earthquake Probability Analysis 51 4. Earthquake Duration 62 5. Cumulative Winds - 1953 to 1971 98 VI1
LIST OF FIGURES
FIGURE Page
1. The Fraser Delta and the Strait of Georgia showing the location of Sturgeon Bank and Roberts Bank. 3 2. Photographs taken from a Pisces Submersible on March' 22 , 19 75. 5 3. Geologic Map of the Fraser River Delta .9 4. Interpreted Continuous Seismic Profile across the Slump Structures 11 5. Grain Size Distribution curves for the 3 surface samples taken on Sturgeon Bank 2 4 6. The Gibbs and Holtz and the Bazaraa curves of Relative Density vs. N - value 26
7. The de Mello relationship of jtfr vs. N - value 32 8. Possible relationship between the ratio of the Compression Index over the Void Ratio plus one (C /1+e), and the measured water contents - liquid limit and natural moisture content 41
9. Terminal of the Westshore Terminals Bulk Loading Facility showing the location of settlement Gauges 7 and 12 and the initial location of the coal stockpiles 44
10. Settlement of gauges 7 and 12 45
11. Extended settlement Record 48 12. Predicted maximum ground surface accelerations 52
13. Comparison of the Ohsaki and Kishida liquefaction criteria 56 14. Cumulative results of Standard Penetration Tests 59
15. Results of the Seed and Idriss Simplified Liquefaction analysis 64
16. Two Sections of the subaqueous slope plotted to natural scale 72 viii
17. Location of cross sections S and R 73
18. Freebody diagram of circular slip arc 77
19. Relationship between excess Pore Pressure and applied Shear Stress 83
20. Derivation of the failure criterion used to place the failure line on Fig. 19 84
21. Two possible relationships between the Pore Pressure Parameter and the Number of Cycles 86
22. Slope analysed by Sarma Program 88
2 3. Relationship between Critical Acceleration and Pore Pressure Parameter for surfaces 4 and 5 89
24. Long deep section analysed to approximate the possible origin of the slump structures 91
25. Tracing of Hypsographic Profiles H, I and J 94
26. Location of Hypsographic Profile lines H, I and J 95 ix
ACKNOWLEDGEMENTS /
The names of all the people who have given me assist• ance with this thesis would fill another volume. As I am limited in space I would like to hereby thank everybody who lent assistance and request that you not take offence if your name is not specifically mentioned.
In the Department of Civil Engineering I wish to thank Dr. W.D.L. Finn for his guidance during the research and his assistance during the writing of this thesis. Dr.
P.M. Byrne and Dr. R.G. Campanella are to be thanked for their encouragement and assistance. Thanks are also due to fellow grad student Neil Wedge for shared research and work.
Last but not least I wish to acknowledge the assistance of the secretaries, particularly Desi Cheung.
Dr. J.W. Murray of the Department of Geology provided valuable assistance during the research and critical review during the writing, for which I thank him.
The Vancouver Office of the Geological Survey of
Canada, and in particular Dr. J.L. Luternauer, have been of great assistance to me In this thesis - assisting with the field excursion to Sturgeon Bank, tolerating my presence around their offices, allowing me access to their great store of literature and data -thank you G.S.C. Others to whom I owe thanks are Cook, Pickering and
Doyle Ltd., Swan Wooster Engineering Co. Ltd., National
Harbours Board, Acres Consulting Services Ltd. and the firm
for which I am presently employed, R.M. Hardy and Associates
Ltd.
Finally I would like to thank my wife Marika for her patience, for supporting me and for her help with the hard• est part of the thesis, the typing.
Financial support for this thesis was kindly provided
by the National Research Council (Grant 67-1498) and Energy
Mines and Resources (Grant 65-1652) for which I am grateful. INTRODUCTION
Roberts Bank and Sturgeon Bank, comprising some 90 odd square miles of tidal flats, have in recent years taken on great importance as potential locations for large scale development, some of which has already taken place. The advantages of a location adjacent to deep sea shipping channels was recognized with the construction of the West
Shore Terminals Bulk Loading Facility, and future expansions to many times the size of the present installations have been proposed. Also proposed is an extension of the Vancouver
International Airport runway system out onto Sturgeon Bank.
This may represent only a small fraction of the interest in
Roberts Bank and Sturgeon Bank as potential sites for develop• ment. With the present and potential interest in the area, it appeared that a general investigation of the soils and engineering environment of Roberts Bank and Sturgeon Bank might be of value.
In this thesis an attempt has been made to compile all existing data available for Roberts Bank and Sturgeon Bank, especially subsurface data. This data was used to determine characteristic soil parameters for use in various types of stability analyses. The data gathered and most of the analyses performed conform to standard practice in the engineering community. Where possible and practical supple• mentary information, such as listings of computer programs used in analyses, have been included in the appendices. 2.
This thesis is concerned with general conditions at Roberts
Bank and Sturgeon Bank and the kinds of engineering problems that may be faced during further developments.
AREA OF STUDY Roberts Bank and Sturgeon Bank are located at approxi• mately 49° 00' to 49° 15' North Latitude and 123° 05' to 12 3° 15' West Longitude. This is the southwest corner of mainland British Columbia, Canada. These banks form the western (seaward) extremity of the delta of the Fraser River, and are the youngest part of the delta. Fig. 1 shows the location of Roberts Bank and Sturgeon Bank with respect to surrounding prominent features.
The Delta of the Fraser River, which has an area of about 130 square miles, extends from its apex at New
Westminster some 19 miles to the Strait of Georgia. The outer banks (Roberts Bank and Sturgeon Bank) which form the leading edge of the delta have a 23 mile perimeter with the
Strait of Georgia. Sturgeon Bank lies between the main channel of the Fraser River and the North Arm of the: Fraser
River. Roberts Bank extends south from the main channel to
Point Roberts and is bisected by Canoe Passage. Sturgeon
Bank and Roberts Bank will be collectively referred to as
"the banks." The top surfaces of the banks are tidal flats which are covered by water at high tide and exposed at low
tide. These flats slope very gently from the cultivated land
to the leading edge of the Delta, and are the sub aerial portion of the banks. From the leading edge, the delta dips beneath 3.
^ (Bowerf f
BurrardTV T—r-^r" \. < JEnlet- Point>~—— GreyV. VANCOUVER
T^FRASER jCr)) RIVER
Sturgeon //>ScL V^/
Bank V GULF •v- ISLANDS PointT_ \, \. Roberts
UNITED STATES j
%i ^Active sN OF AMERICA " -J r--Pass >
SCALE 1 inch = 8 miles
Sturgeon Bank and Roberts Bank,
Fig. 1 The Fraser Delta and the Strait of Georgia showing the location of Sturgeon Bank and Roberts Bank. 4. the surface of Georgia Strait in what Mathews and Shepard
(1962) have termed the fore-set beds. The banks have an average width of 4 miles from the edge of the cultivated land to the fore-slope of the delta. The subaqueous slopes average one and one-half degrees but exceed 23 degrees in a few spots, as plotted from Marine Charts, and contour maps in the "Outer Port Development" report (Swan Wooster, 1967).
The fore-set beds extend to a water depth of about 300 feet
(Luternauer and Murray, 1974).
The Strait of Georgia is a tidal body of water with constricted passages to the Pacific Ocean. It is protected
from most influences of the open ocean such as large ocean waves. The tidal effects, however, are significant and
intense tidal currents which sweep past the delta front are
generated in this semi-contained body of v/ater, responding
to the tidal changes of the open Pacific Ocean. A surface
expression of these currents is the manner in which the out—
flowing waters of the Fraser River are swept northward by
the flood tide. Evidence of the current action at depth is
shown in the underwater photos taken by the Pisces submer•
sible on March 22, 1975 (Luternauer, 1976) at 75 meters depth
and on the side-scan sonar recordings taken in July, 1976
(unpublished to date). Three of the photos, reproduced in
Fig. 2 through the courtesy of J.L. Luternauer, show sand
ripples consistent with sediment transport, which suggests
the existence of currents strong enough to transport the
sand. These are the only photos taken of the fore-slope,
and they were all taken in the same area, so they can not be 5.
Fig.2 Photographs taken from a Pisces Submersible on March 22, 1975. These photos were taken at 75 meters depth on the fore-slope of Roberts Bank opposite the super port and show evidence of erosion. Photos courtesy of Dr. J. L. Luternauer. 6.
used to determine trends in erosion or sediment transport.
Roberts Bank and Sturgeon Bank are not entirely comparable. The fore-slope of Sturgeon Bank, as expressed by subsurface depth contours, is remarkably smooth and regular, even in the vicinity of where the Middle Arm of the Fraser discharges during freshets. The fore-slope of Roberts Bank, although generally smooth, is crossed by a number of prominent gully features. One of the largest of these gullies, located approximately 2.3 miles south of the present location of the main channel, may represent a previous location of the main channel. The other irregularities are located such that they may be related to Canoe Passage, which is a distributary during freshets.
The strike of the Sturgeon Bank fore-slope is pre• dominantly North-South. The strike of the Roberts Bank fore- slope varies from N.N.W. - S.S.E. in the North to W.N.W. - E.S.E. near Tsawwassen Ferry Terminal to N.W. - S.E. near Point Roberts. The depth contours on the Roberts Bank fore- slope are generally smooth curves, other than at the location of gullies, showing no abrupt changes in the general strike direction. The differences in strike direction between Roberts Bank and Sturgeon Bank should cause different responses to surface and internal waves and tidal currents.
The Fraser River has a drainage basin area of about 90,000 square miles and a discharge ranging from as low as 28,000 c.f.s. to as great as 350,000 c.f.s. (Hoos and Packman, 1974) . The drainage basin was completely covered by ice 7. during the last major glaciation, and the present delta began to form when the last major glaciation receded some 8,000 to 10,000 years ago. The products of glacial erosion have contributed, and continue to contribute to the large sediment load of the Fraser River. Mathews and Shepard (1962) showed that the delta is rapidly advancing (28 ft./yr. at 300 ft. depth) off the main channel of the river from the deposition g of 7 x 10 cubic feet of sediments per year.
Because of processes such as isostatic rebound and eustatic adjustment (Matthews, Fyles and Nasmith, 1970), it is not known whether the Delta grew regularly and smoothly to its present size, or if it had a complex pattern of growth
(Luternauer, 1974). There is some evidence to suggest that portions of Roberts Bank are much older than the rest of the banks (Dr. J.W. Murray, personal comment). The suggest• ion is that some of the southern Roberts Bank sediments are relic glacial or preglacial deposits. A detailed study of available borehole logs indicates that these possible differences in age and source of sediments do not appear to be reflected by corresponding changes in the engineering parameters.
Whether the delta developed regularly or irregularly, there is general agreement among most geologic investigators of the Fraser Delta that the surficial deposits of the banks are composed of recent sediments. Most of the sediments carried by the Fraser River are deposited off the mouth of
the South Arm (which is the main channel), but this deposi•
tion is not the only process effecting changes on the delta 8- front. The fore-set slopes are also subject to wave action and tidal currents. Fig. 3, which is reproduced from Figure
3.1 in "The Fraser River Estuary, Status of Environmental
Knowledge to 1974", shows a complex pattern of advancing, retreating and stable areas of the delta front. This figure also shows, very roughly, the area! distribution of the
surficial deposits. Members of the Geological Survey of
Canada, under the direction of John L. Luternauer, have made a number of expeditions onto the banks collecting
surface samples. An analysis of the results of this sampling
program has shown that there is a seasonal shift in the
gradation of the surficial deposits (Luternauer, 1976). In
general the surficial deposits vary from relatively clean
uniform sand near the leading edge of the banks to silty-
clayey-sandy deposits toward the dykes which mark the edge
of the cultivated land. There are significant areas of marsh
adjacent to the dykes along the eastern edge of much of the
banks. Mathews and Shepard (1962) presented the results of
a sampling program conducted on the subaqueous slopes of the
delta which showed that the sediments directly off the mouth
of the main channel are predominantly sand, and the sediments
become markedly finer as the water depth increases and as one
moves to the north.
SLUMP STRUCTURE
In 1962, Mathews and Shepard described the existence
of hummocky topography off the mouth of the main channel.
Since that time, these slump structures (as they came to be
known) have been the topic of one thesis (Mayers, 1968), G ene ralized GEOLOGIC MAP OF THE FRASER RIVER DELTA and adjacent areas
LEGEND RECENT
7 FRASER DELTA DEPOSITS
7a - twamp and bog deposits - peat or peat below veneer of till.
7b - tilt and clay deposit*, minor sand - tidal Hat, flood plain, upper fore slop*.
7c - sand deposits - mainly lidai flats.
7d - salt marsh.
6 CHANNEL AND FLOODPLAIN DEPOSITS OF LOWLAND STREAMS * silt, clay, sand and organic Stringers or pods.
5 BEACH DEPOSITS • sand and gravel.
PLEISTOCENE
4 EARLY POST-GLACIAL RAISED LITTORAL AND CHANNEL DEPOSITS - sand, gravel and a few shell beds.
3 GL AC IO - MARINE DEPOSITS - silts and clays deposited in offshore environment.
2 GLACIAL DEPOSITS - sandy to silry till deposited as ground moraine or subsequent till -like deposits derived from floating glacier ice .
1 IN TE RG LACI AL AND OLDER DEPOSITS - sand and lesser amounts of silt, clay and peat in sea cliffs .
dyked land.
ytffijgt^ dredge spoil dumping area.
-•— d —principal dredging areas.
areas of crescent shaped swales possibly //// caused by former - land-slide movements.{?)
areas of incipient slumping.
general areas of delta - front advance or retreat .
— I nter national Boundary.
Geologic boundary (shore -high tide line may also be a geologic boundary)
cable area
Fig. 3 Geologic Map of the Fraser River Delta. Reproduced from "The Fraser River Estuary, Status of Environmental Knowledge to 1974" by permission of Environment Canada and J.L. Luternauer. mentioned in another (Tiffin, 1969) and discussed in numerous papers. In January 1966 a number of continuous seismic pro• filing sections were taken across the slump structures, and the authors of the theses and papers which postdate the continuous seismic profiles have based their interpretations of the structures on these records. Dr. J.W. Murray of the
Department of Geology and the Institute of Oceanography at the University of British Columbia has made the interpreted results of the continuous seismic profiles available for presentation in this thesis. Fig. 4 shows the profile running approximately East-West through the center of the slump structures, and a location plan and three additional profiles have been included in Appendix I.
Five distinct reflecting horizons have been shown on the profiles and are identified by the block letters A through
E. Horizon A is a bedrock reflector, horizons B and C are relatively flat-lying sediment reflectors, horizon D is the sediment-water interface and horizon E represents the top of the deformed slump structures where buried by more recent
sediments. M. denotes a multiple reflection of the sediment- water interface and as such is not a reflecting horizon.
There is basic agreement as to the physical character•
istics of the slump structures amongst investigators who made use of the continuous seismic profiles. To paraphrase
Tiffin (1969), the slump structures appear to be part of a
single massive slide layer moving over a deep glide plane at
least 250 to 300 feet deep in places. When the slide mass
came to rest, the soils buckled to form wavelike undulations SEC. INTERPRETED CONTINUOUS SEISMIC PROFILE
THROUGH THE SLUMP STRUCTURES somewhat resembling a waffle in that the undulations form a wave pattern both in the down-slope direction and in the cross slope direction. The undulations, viewed from either direction, have a relief of 50 to 100 feet and a wavelength of about 2,000 to 2,500 feet. Discontinuities of reflectors within the slide mass have been concluded to be consistent with rupture phenomena associated with one single mass move• ment. Later sedimentation has been filling in the troughs and encroaching on the slide material from the top down as
evidenced by horizon E.
Tiffin (1969) made some estimates of the age of forma•
tion of the slump structures using the sedimentation rates worked out by Mathews and Shepard (1962). He calculates a minimum age of 6 0 years and a probable age of about 160 years.
He revises this estimate to 200 years in a 1971 paper co-
authored with Murray, Mayers and Garrison. However, unless
the age can be related to a specific event such as an earth•
quake, then the age is of academic interest only. There is
no known event which might have triggered a slide which
coincides with the estimated age of this slide.
No other features similar to the above described
slump structures have been reported off the Fraser Delta.
This does not rule out the existence of others, since the
subaqueous investigations carried out to date have not been
detailed enough to give total knowledge of the subaqueous
landforms. This is the only known large scale slide on the
subaqueous part of the Fraser Delta and it is located off
the mouth of the main channel; therefore there is some indication that the rapid deposition which occurs off the mouth of the main channel created a deposit of sediments which had more potential for sliding than adjacent delta deposits. The conclusion of the geologists and gecphysicists that the slump structures represent, one specific event rather than a series of events is evidence that something unusual triggered the slide. The estimated age (160 to 200 years) of the slide and the lack of evidence of subsequent slides
suggest that the event which triggered the slide is reasonably rare.
Mayers (1968) cited six possible triggering agents which could have started the slide
Among these, earthquakes, faulting, internal waves, surface waves, river floods and the introduction pf peptizing agents to the flocculated sediments, are possibilities.
Of these possibilities, it is unlikely that internal or i •
surface waves could be the necessary rare event. The Strait
of Georgia is a semi-confined body of water of finite size
and it is almost certain that the maximum possible waves are
generated a number of times per century and probably more
often than that. One possible exception would be a freak
earthquake generated wave. Mayers himself rules out faulting
as a trigger mechanism, The introduction of peptizing agents,
which Mayers relates to river floods, does not appear to.be
a rare event. A river flood or an earthquake definitely
fulfills the criterion of a rare event, the bigger the flood
or earthquake the rarer the event,.
The Fraser River has had unusually large floods twice during recorded history (1894 and 1903), but there were no
reported slides associated with either event. This is not
surprising since at that time there would be no way of know•
ing if a subaqueous slide had occurred or not, however, the continuous seismic profiles do not indicate any slide deposits consistent with these dates (unless the minimum age of 60 years estimated for the slump structures can be shown to be more reasonable than the 200 year estimate). Both floods
referred to overflowed the customary channels of the Fraser
River. It would seem logical that once a river has over•
flowed its channels and flooded the lowlands it would take a very large increase in flow to produce a small increase in
sedimentation at the mouth of a channel.
Of the six possible triggers originally mentioned,
only earthquake and river flood are probable. The seismic
activity of the area surrounding the Fraser Delta is well
known and documented (Milne, 1963). There are many earth•
quakes in the area every year which, although below the
level of human detection, have a measurable energy at the
banks. Every few years there is an earthquake which is
noticeable to the people of the lower mainland. As if to
exemplify this point there have been two this year (1976)
which were within the range of human detection. The
potential certainly exists for an earthquake, with sufficient
energy release to trigger a slide, to have occurred in the
past and to occur in the future.
Earthquake would appear to be the most probable trigger
mechanism for the slide, but river flood can not be ruled out. The combination of earthquake during severe flooding is also a possibility. If intense seismic studies were carried out on the delta with equipment which could produce good resolu• tion through some 1,200 feet of sediments it is quite possible that more relic slump structures would be found buried in the delta. If such structures were found and reasonable estimates of their age were made then it might be possible to gain some appreciation for the frequency of the triggering events.
Subaqueous slides are of concern to the engineer primarily if they will affect a project or installation. For the Fraser Delta, if the suppositions that the slides are rare events and are only probable at the mouths of major channels are valid, then they are only of minimal concern to the engineer. The major channels of the Fraser are maintained as navigable channels, therefore, the only structures likely to be directly affected by a slide would be jetties and navigation aids (such as lights). The only other major category of engineering installations which could be directly affected is subaqueous services such as pipelines (gas, oil) and cables (telephone, electric). The occurrence of a massive subaqueous slide could trigger a destructive water wave, such as happened at Kitimat, B.C. early in 1976, which could affect engineering structures not only on the banks but elsewhere along the shore in the vicinity. It is not possible to predict, or design for, the effects of such waves, however they have been mentioned as a possible in• direct effect of a subaqueous slide. ENGINEERING PARAMETERS
The sources for all the borehole data and most of the
laboratory test data for the banks, which form the basis of
all the following observations and conclusions, are: Cook,
1967, 1968; Cook, Pickering and Doyle Ltd., 1974; Swan
Wooster Engineering Co. Ltd., 1967. These reports will be
referred to collectively as "the engineering reports." A
search of this information has yielded the borehole logs and
locations of 68 boreholes drilled on the banks and the
results of various tests performed on samples recovered,
from these boreholes. The boreholes have a spacing which is
generally in excess of 1.5 miles, with a closer spacing off
Sea Island in the vicinity of the proposed airport runway
extension; in the vicinity of the Westshore Terminals bulk
loading facility; and along the Tsawwassen Ferry Terminal
causeway. The majority of the boreholes were drilled to
less than 80 feet below the sediment surface, but six of the
holes were drilled between 260 and 460 feet below the
surface.
Subsurface Sediments
The borehole log attempts to depict graphically the
soil column penetrated by the borehole, using common symbols
for sand, silt, clay and organic soil. This graphical
representation allows one to form a visual impression of the
subsurface soils. This form of presentation requires the
draftsperson to divide the soil profile into distinct layers.
This is a straightforward procedure where distinct layers of 17. soil exist and the driller has made a reasonably conscientious log of the hole to complement the samples. In areas such as the banks where the layers do. not appear to be distinct, but grade one into the other, the procedure of graphical presenta- tion becomes somewhat arbitrary. The draftsperson must divide the soil into layers based on the visual classification of the samples, grain size determinations performed on samples and the driller's log. In turn, in this type of soil, the drillers log is also subjective; based on the cuttings in the return wash water, the rate of advance and "feel" of the drill and influenced by the recovered samples.
The boreholes were sampled extensively with a 2-inch
Standard Penetration Test sampler, and a few 3-inch Fixed
Piston Shelby Tube samples were taken in select boreholes.
The borehole logs presented N-values (number of blows of a
140 lb. hammer dropped 30 inches to produce 12 inches of penetration) for the 2-inch Standard Penetration Test samples, moisture contents where appropriate, and/or relative quantities of sand and silt (represented in bar graph form) for most of the samples. A number of the 3-inch Shelby Tube samples were tested in shear tests, triaxial tests and consolidation tests. The results of these tests were also presented in the engineering reports.
A reasonable estimate of the lateral continuity of the banks sediments would be of value in helping determine optimum borehole spacing for proposed projects on the banks.
The somewhat arbitrary nature of the borehole log presenta• tion makes it difficult to form an impression of continuity based on visual inspection. When the location of the Westshore
Terminals bulk loading facility was finalized, nine boreholes
were drilled with a much closer spacing than was used during
the preliminary study. Although the Test Hole Location Plan
is presented without a scale, the hole spacing appears to
range from 700 feet to 1,500 feet. An inspection of the
borehole logs does not reveal any distinctly identifiable
layer of sediments which could be used to trace continuity.
There is a layer of sediments with more than 40 percent silt
and moisture contents of about 33 percent which starts at -^57
feet in borehole 1. Borehole 1 bottomed at -80 feet, still
in the layer of soil just described. Surrounding borehole 1
are boreholes 3, 8, 7 and 2 from nearest to farthest. Bore•
hole 3 has similar soil from -68 feet to beyond -80. feet;
boreholes 8 and 7 have no similar identifiable layer and
borehole 2 has a similar layer from -61 feet to more than
-82 feet. Borehole 8 is approximately between boreholes 1
and 2, therefore there does not appear to be reasonable
continuity even at 700 foot spacing.
The lack of lateral continuity of the. banks' sedi• ments, even at 700 feet spacing, is not unreasonable in
light of the depositional environment. The small distributary
channels which are active primarily during periods of high
runoff (which corresponds to maximum sediment transport)
frequently alter their routes across the banks. The bed
load of these channels can be expected to be significantly
coarser than the suspended sediments. Some of the suspended
sediments will drop out of suspension on the banks adjacent to the channel if the flow spreads out over the banks and slows to less than the critical velocity necessary to maintain suspension. When the channel shifts position some of the sediments previously deposited are eroded, and some replacement by sediments with a different grain size distribu• tion takes place. Previous to the stabilization of the main channels by the construction of jetties the main channels also changed positions with time.
Of less importance to the question of lateral contin• uity, but worthy of mention, is the transport of deposited sediments by wave action and current action. Under normal circumstances neither of these processes would be expected to produce discontinuities in the sediments but rather gradual gradational changes. Discontinuities could conceiv• ably be produced if these processes were somehow focused on a specific section of the delta front, but there is no evidence to suggest that this has occurred.
A few of the borehole logs mention thin clay and clayey silt layers and a very few of the borehole logs describe a major "layer" of soil as being clayey silt.
These descriptions are based on visual classifications and grain size analyses of recovered samples. The results of the shear tests and triaxial tests which have been reported in the engineering reports indicate classical cohensionless behaviour for all samples tested. The log of one of the six deep boreholes makes no mention of the presence of clay in the entire 410 feet of hole. The remaining five boreholes all describe layers of clayey silt, or silt with some clay 20. at various depths; but nowhere does one get the impression that the clay forms a dominant fraction of the sediments. The only tests which have been performed on samples from below -80 feet are a few moisture contents, Atterburg Limits, torvane and/or penetrometer tests, and #200 sieve screening to deter• mine approximate sand-silt quantities. Prom these tests it is not possible to determine whether there is sufficient clay content in the deep sediments to give these sediments any cohesive soil characteristics.. The boreholes have shown that the surface 80 feet of sediments, and probably much deeper, are primarily granular soils and no cohesion should be assumed or used when performing strength or stability analyses of the banks' sediments.
The total depth of recent sediments on the banks is not known at most locations. One borehole, located approximately 0.35 miles N.W. of the Westshore terminals causeway, penetrated into glacial till at -245 feet. There are also a few boreholes on the shore end of the Tsawwassen Ferry Terminal causeway which penetrated through the recent sediments. The deepest contact with soils which did not appear to be recent sediments, for the causeway holes, is reported as -51 feet for a hole approxi• mately 0.6 miles from the shore. This borehole was the most seaward of the causeway holes in which it was reported the
bottom of recent sediments was encountered. The total depth of sediments, although of great academic Interest to many people, is of only moderate interest to the soils engineer. If the sediments are shallow enough
(less than 60-80 feet), then the option of founding the 21. project on end bearing piles or caissons exists. The bore• hole logs indicate that this condition is met only in the southwest corner of Roberts Bank near Point Roberts. The strength of the soil, because the soil is cohesionless, is directly proportional to the effective stress acting on the point in question. Under normal conditions (hydrostatic pore pressure) the effective stress is proportional to the depth and deep seated failure is generally ruled out. An increase in the effective stress will cause consolidation of susceptible soils at any depth; however, for any particular loading and soil conditions there is some depth at which the consolidation due to the loading becomes negligible and knowledge of the complete sediment profile becomes unnecessary.
Soil is unlike any other engineering material, and a large number of parameters are necessary to define the various aspects of soil behaviour. The parameters are measures of specific properties of the soil such as physical properties and stress-strain characteristics. There are also numerous indices, such as the Atterburg Limits for soils with some plasticity, which measure some property of the soil related to some defined aspect of the soils' behaviour. The indices give an Indication of the probable behaviour trends of the soil. This thesis is dealing with an extensive area from which relatively few samples of the soil have been tested, and in cases such as this the indices are used to obtain estimates of the parameters or to predict probable engineering performance using correlations between indices and past field behaviour.
The samples recovered from, and the 'N-values recorded for the standard penetration tests taken at five feet intervals in virtually every borehole, from the surface to 80 feet depth, represent the largest possible source of information about the sediments. The samples, although disturbed, were used for moisture content determinations, grain size analysis, and Atterburg limit determinations where appropriate. The engineering community recognizes the crudeness and variability of the standard penetration test, however with the N-values representing such a large pro• portion of the available information every effort was made to utilize the N-values. The two main parameters for a cohesionless soil which can be estimated from the N-values are the Relative Density, D^, and the effective angle of internal friction 0 .
Grain Size Distribution
The samples recovered from the standard penetration test are of very little use for most test purposes due to the very disturbed nature of the samples, however one exception to this is the grain size analysis test. If the assumption that the sample recovered is representative of the soil sampled is valid, then the amount of disturbance does not influence the test results. The majority of the samples recovered from the standard penetration tests were given a "one sieve analysis" to determine the percentage of soil passing the #200 sieve, which has been set as the arbitrary division between sand and silt. A number of the standard penetration test samples and many of the fixed piston shelby tube samples were given complete mechanical grain size analyses. For many of these samples the soil passing the #200 sieve was used to perform hydrometer tests, which allowed complete grain size distribution curves to be plotted. Three surface samples were taken on Sturgeon Bank in July, 1975, and mechanical grain size analysis tests were performed on the three samples. Hydrometer tests were not performed on the samples as no sample had more than 5% passing the #200 sieve. The grain size distribution curves of the three surface samples are presented in Fig. 5. These curves are very typical of the curves presented in the engin• eering reports for samples with low silt contents. The three samples have uniformity coefficients of 1.7, 2.1 and 1.2 which classifies these samples as uniform. From the grain.size distribution curves presented in the engineering reports, it appears that the uniformity coefficient of the banks' sediments increases as the silt content increases, until the silt content dominates. For example, a sample with 14 percent passing #200 has a uniformity coefficient of 4.9; a sample with 28 percent passing #200 has a un• iformity coefficient of 23.7; and a sample with 70 percent passing #200 has a uniformity coefficient of 10.0. These are specific values from specific samples which appear to represent the general trend and these values are not meant to be used as a definite relationship.
The uniformity of the banks' sediments is a function of the depositional environment. For any given velocity of moving water there is a finite range of particle sizes 24.
GRAIN SIZE DISTRIBUTION
FRASER DELTA STUDY Project Job. No. Sturgeon Bank Location of Project _ Boring No. Sample No. 1-Q> 2-A, 3- Q
Description of Soil Fine-Med. Sand /NOPT H NF SAMP!E —SurfflCP
s Tested By. ~ - Scotton Dafe of Testing August 8, 1975
Gravel Sand Fines
Coarse to Fine Silt Clay medium U.S. standar d siei/ e sizes • In . j do
c c o© o Q.
Grain diameter, mm
Visual soil description Grey Fine-Med. Sand, some silt
Soil classification: SP System Unified Soil Classification
Fig. 5 Grain Size Distribution curves for the 3 surface samples taken on Sturgeon Bank. 25.
which can be transported in suspension and bed load. As the
sediment laden river water reaches the edge of the delta
it spreads out and slows down. As the velocity decreases,
the size of particle which can be kept in motion also decreases,
and there is a gradational. deposition of the sediments.
Further reworking of the sediments by waves and currents
tends to increase the uniformity of the sediments.
A compilation of the results of all the one sieve
analyses indicates that the surface 80 feet of sediments in
the areas adjacent to the main channel of the Fraser- (north
and south side) and south and central Sturgeon Bank have a
higher silt content than the overall average. There is no
recognizable trend, however, for the grain size distribution
with respect to depth for the surface 80 feet of sediments.
The six deep boreholes indicate that there is a general trend
to finer grain sizes over great depths.
Relative Density
Bazaraa (1967) and Gibbs and Holtz (1969) have sug•
gested methods for estimating the Relative Density, D^, from
standard penetration test blow counts (N-values). Both methods involve the interpolation of the relative density
from a family of curves of relative density plotted on a .
graph with vertical effective stress as the ordinate and
N-Blows per foot as the abscissa. The two families of
curves are shown in Fig. 6, with the Gibbs & Holtz curves 26.
i ,—i 1—, 1 1 1 10 O I 2 3 4 5 6
VERTICAL PRESSURE - Kips/sq.ft.
Fig. 6 The Gibbs and Holtz (___) and the Bazaraa ( ) Relative Density vs. N-value relationships. shown as solid lines and the Bazaraa curves shown as dashed lines.
In his excellent State-of-the Art paper on the
Standard Penetration Test, de Mello (1971) compared data from many sources with the Gibbs and Holtz vs N-value in• terpretation of the U.S.B.R. tests. He found cases with reasonable agreement, cases where the estimated values were too high and cases where the estimated values were too low.
Although the estimated values based on the N-values may not be the absolutely correct values, the standard penetration test can indicate variational trends within a given deposit.
When the deposit being tested is composed of sediments with reasonably similar mineralogy, grain size distribution, and degree of angularity throughout, the estimated, or apparent,
values will most probably not be the correct actual values, but they will bear the correct relationship to each other. In other words, if test A has an apparent relative density less than the apparent relative density of test B then the actual relative density at A is less than at
B.
The relative density of the banks sediments was estimated for every recorded standard penetration test using both relationships shown in Fig. 6. The Bazaraa method for estimating the relative density gave values which were generally 15 to 20 percentage points lower than the values indicated by the Gibbs and Holtz method. The Bazaraa method indicated an apparent D of less than 40 percent (D = 40 28 . percent is the lower bound for both methods, so values below 40 percent can not be established) for the mean conditions encount• ered, while the Gibbs and Holtz method indicated a mean value of
50 percent to 55 percent for Dr. The mean values are tempered to some extent by value judgements made during analysis. The value judgements involved the casting out of results which appeared to have been influenced by a "high" silt content. The rationale for this was that during the analysis of the borehole logs it became apparent that there was a consistent and signi• ficant decrease in the blow counts with an increase in silt content. In many cases these silty layers were bracketed by sands with similar apparent relative densities and it seemed unreasonable for the intervening silty layer to have such a reduced apparent relative density as indicated by the reduced blow counts. It is obvious that when the condition of similar grain size distributions is violated the apparent relative densities are no longer comparable.
Nowhere in the engineering reports could an evaluation cf the relative density of the banks' sediments be found with which to compare the values derived from the N-values. In ordei"
to determine which method of estimating Dr gave the most reason• able results for the banks' sediments, three surface samples were taken on Sturgeon Bank near the location of three of the boreholes for which relative density was estimated. These are the same three samples which were mentioned in the previous section on grain size distribution. Nominal 3.4 inch I.D. Shelby tubes, 2 9 inches long, were carefully pushed into the un• disturbed sediments. The depth of penetration was marked on the outside of the tube and then the tube was dug out with a shovel (as opposed to being pulled out) and the bottom covered before lifting the tube from the soil to prevent the loss of any soil. The soil in the tube, which densified during sampling and handling, was assumed to have occupied the in situ volume represented by the mark on the outside of the tube. In the lab, the samples were each tested for maximum and minimum density (non-standard tests), specific gravity and grain size distribution (standard procedures), and the results of these tests are shown in Table 1.
Table 1 TEST RESULTS
Relative Void Specific Sample Density Ratio Gravity
1 43.7% .93 2.70 . 15 mm .088 mm 2 33.0% .84 2.70 . 2 7 mm . 13 mm 3 37.0% .80 2.71 . 27 mm .23 mm
These relative densities compare quite well with the relative densities indicated for this area by the Bazaraa method which indicates that the Bazaraa apparent relative densities may be more reasonable for these deposits than the Gibbs and
Holtz apparent relative densities. Either relationship would serve to indicate the variational trends, but the
Bazaraa apparent relative densities would appear to be more appropriate for use in making rough approximations of the soil characteristics.
A study of the borehole logs leads to a few general observations about the apparent relative density. There were enough boreholes where the apparent relative density remained reasonably constant with depth (for the surface 80 feet) to suggest that this is the norm rather than the exception for the banks sediments. A constant relative density with depth for granular soils is to be expected if the depositional environment has remained basically the same throughout the deposition of the sediment column. Granular soils undergo very little densification due to the addition of load. Vibration is necessary to induce intergranular movement, allowing the formation of denser packing arrangements. Under normal conditions there is not sufficient vibration to allow the intergranular movements. The north edge of Roberts Bank adjacent to the main channel and the leading (western) edge of Sturgeon Bank have apparent relative densities lower than the mean; while central Sturgeon Bank west of Sea Island has apparent relative densities higher than the mean.
Friction Angle
In the previously mentioned State-of-the Art paper on the Standard Penetration Test, de Mello (1971)proposed a relationship between the overburden stresso", the N-value and the angle of internal friction, 0. He also presented the results of his relationship in graphical form, and in 1975
Schmertmann presented an adaptation of the de Mello graphical presentation. The form of the Schmertmann presentation is a family of curves of 0' (effective angle of internal friction) plotted on a graph with N-value as the ordinate and over• burden stress as the abscissa. A version of the Schmertmann adaptation of the de Mellow relationship is shown in Fig. 7.
Using this figure., the effective angle of internal friction was estimated for every recorded standard penetration test.
The same comments which were made about the apparent relative densities also apply to the interpreted apparent, friction angles. The apparent friction angles may.not.be. the absolutely correct friction angles but the comparative relationship between different tests is established. The results of tests on soils with "high" silt contents were ignored because they did not conform to the condition of similar grain size distributions for comparison of results.
The apparent effective friction angles determined from the N-values ranged from 22 degrees to 48 degrees, with an apparent effective friction angle of approximately 35 degrees being associated with the mean conditions encountered by the boreholes. One shear test is reported in the engineer• ing reports (Cook, 1967) for which the effective friction angle was 1.8.5 degrees at 10 percent strain for a sample with 88 percent passing the #200 sieve. Such a material would not generally be encountered in the surface 80 feet, although this sample came from -50 feet. For the other shear and triaxial tests reported in the engineering reports the range in silt content was from 2 percent to 44 percent passing the #200 sieve and the range in effective friction angle was from 34.5 degrees to 40 degrees. The mean of these latter tests gives an effective friction angle of 37 degrees as an "average" effective angle of internal friction.
The trend of the indicated effective friction angles 32.
Fig. 7 The de Mello Effective Angle of Internal Friction i (0 ) vs. N-Value relationship, as reported by Schmertman (1975). is very similar to the trend of the apparent relative densities. Lower than average values are indicated for the north edge of Roberts Bank and the west edge of Sturgeon
Bank and above average values are indicated for central
Sturgeon Bank west of Sea Island. In the cases where the apparent relative density remains reasonably constant with depth, the indicated effective friction angle also remains reasonably constant with depth.
The agreement of the effective friction angle trends with the relative density trends is totally reasonable, including the trend of constant friction angle with depth.
The "critical void ratio" concept (Taylor, 1949) explains this aspect of the soil behaviour. For a specific cohesion- less soil at a constant void radio (constant relative density) there is a "critical effective stress" in excess of which the shear strength of the soil will be directly proportional to the effective stress. The constant of proportionality is the tangent of the effective friction angle. For a loose soil such as the banks' sediments, the "critical effective stress" is very low. This "critical effective stress" is exceeded in the surface few feet of sediments, therefore the effective friction angle should be constant with depth after the initial few feet, where the soil and relative density are similar with depth.
Consolidation Parameters
The few fixed piston Shelby Tube samples taken of the banks' sediments were assumed to be reasonably undisturbed, 34. and these samples were used to perform tests whose results are sensitive to sample disturbance. One of these tests with great importance is the consolidation test, as settlement will be one of the governing factors for any project on the banks.
The results of six consolidation tests'were found in the engineering reports, and the samples tested were from depths ranging from -50 feet to -300 feet.
The engineering reports present the results of the consolidation tests in the form of plots of void ratio vs log effective stress. The compression index is the change in void ratio for a change of effective stress of one order of magnitude,
There is no unique compression index for most soils (except, possibly, some remoulded soils) because the shape of the void ratio vs log effective stress curve is not usually a straight line. There are, however, usually two distinct parts of the curve which can be approximated by straight lines — the rebound, curve and the virgin curve. The rebound curve represents the soil response to effective stresses which are less than the maximum effective stresses to which the soil has previously been subjected. The virgin curve represents the soil response to effective stresses which are greater than previous stress levels. Since the shape of the void ratio vs log effective stress curves do not indicate any preconsolidation (consolida• tion under stresses in excess of existing In situ stresses), and there is no geologic evidence to suggest any preconsoli• dation, the compression index of the virgin curve is of the most value to the soils engineer. The compression indices of the samples tested ranged from 0.22 to 0.36 and there was no apparent trend with respect to depth. The compression index can be used to estimate settlements due to different load conditions.
The accepted method of estimating settlements is by the formula ' C_ • p p S = H log10 o •+
1 + e 0 Po (Terzaghi and Peck, 1948) where S = settlement in feet,
H = thickness of the layer in feet, Cc = compression index,
eQ = initial in situ void ratio, Po = existing in situ effective vertical stress in p.s.f., and P = change in vertical stress in p.s.f. Any other set of compatible units can be used with this formula. The consolidation tests
provide values for Cc and the relationship Gw = Se ... (4-2) where G = specific gravity of solids, w = natural moisture content, S = degree of saturation, and e = void ratio of the sample (Lambe and Whitman, 1969), provides a value for the void ratio if the specific gravity of the solids is known, the moisture content has been determined and 100 percent
saturation can be assumed.
Consolidation is a time dependant process; therefore, along with an estimate of the total settlement expected, the engineer must also know the nature of the settlement with
respect to time. The coefficient of consolidation, Cv, must be determined to allow estimates of the settlement with
respect to time to be made. Cv is not a constant for a given soil, but is a function of the effective stress and the stress history of the soil. From one dimensional consolidation theory (Terzaghi and Peck, 1948) comes the equation 36.
2 t = Ty H ... (4-3)
where t = time to n percent consolidation, Tv = time factor for n percent consolidation, H = length of drainage path, and
C = coefficient of consolidation. Graphs or tables of values for T for a range of degrees of consolidation for various boundary conditions can be found in most basic soil
mechanics text books. Although values of Cv can be derived
from the standard consolidation test, no values of Cv for the banks' sediments have been reported in the engineering reports.
One dimensional consolidation theory assumes no lateral
drainage of porewater during the consolidation process.
Standard practice for estimating settlement times is to set
H equal to one-half the total thickness of the layer in
question for a double drainage situation. This practice
assumes no intermediate drainage layers. Both assumptions
just mentioned lead to conservative estimates of consolidation
times. For any project of finite size there will be some
degree of lateral drainage which will speed up the consolida•
tion process. The nature of the banks' sediments make it
very probably that there are numerous thin layers of more
permeable sediments distributed through the consolidating
layer which shorten the drainage path H.
Experience has shown that due to these departures from
one dimensional consolidation theory, even when Cv values are
measured from consolidation tests the settlement time
calculations only provide an upper bound. The general
practice is to install settlement gauges when loading is begun and monitor them, plotting the settlements as the readings are taken. This is best illustrated by example and a case history from, the Westshore Terminals bulk loading facility will he discussed later. The settlement times shown in the case history are representative of settlement times for other projects at various locations on the delta (personal knowledge) and it is reasonable to assume similar behaviour at other locations on the banks.
Atterburg Limits
The Atterburg Limits are determined by procedures which completely remould the soil and hence the disturbed nature of the samples recovered from the Standard Penetration
Test has no effect upon the results of the Atterburg Limit determinations. Most of the samples recovered from the banks were too coarse for Atterburg limit, determinations, but the limits were determined for many of the silt and clayey silt samples. The Plastic Limit ranged from 18 percent to 30 percent; the Liquid Limit ranged from 32 percent to 50 percent; the in situ Moisture Content ranged from 23 percent to 42 percent; the Plasticity Index ranged from 4 percent to 26 percent and the Liquidity Index ranged from -0.3 to 1.8 for the samples tested. The sample with the Liquidity Index of
-0.3 is a single unusual sample and the next lowest value is 0.3.
Samples tested from the top 80 feet of sediments gave widely divergent results and no general trends of the indices are apparent. Samples tested from below -90 feet have a range of Liquidity Index from 1.0 to 0.4 and there 38. appears to be a general trend of decreasing Liquidity Index with increasing depth. As there are results from only seven samples from -90 feet, and one of these does not fit the stated pattern, this indicated trend should not be relied upon without additional supporting data.
A Liquidity Index of 1.0 indicates a natural moisture content equal to the Liquid Limit. If the natural moisture content is greater than the Liquid Limit then the Liquidity
Index is greater than 1.0 and vice versa. A soil with a natural moisture content equal to or greater than the Liquid
Limit is generally considered to be normally consolidated.
A soil at depth with a natural moisture content less than the
Liquid Limit does not necessarily indicate overconsolidation, since the sediments will undergo some consolidation due to the stress of the soils deposited above them. This con• solidation will reduce the natural moisture content but the sample may still be normally consolidated for the in situ stress conditions. It is the opinion of this writer that the trend to decreasing Liquidity Index with depth below -90 feet reflects this consolidation to the in situ stress conditions, and does not represent any overconsolidation.
The Atterburg Limit results were included for the sake of complete reporting of available information. The soils being tested are predominantly silt with little clay content, and the results would probably have very poor reproducibility. The Atterburg Limits were proposed for clay soils, which experience has shown give reasonably reproducible results. It is the reproducability of the results which gave 39. the Atterburg Limits some credibility as a guide to properties of the soil. Soils which are predominantly silt do not have this reproducability emd the Atterburg Limits determined for these soils should be used only to indicate trends with respect to area or depth.
Compression Index Estiraa.tes
Despite the caution about the use of Atterburg Limits determined for predominantly silty soils, an effort was made to evaluate the usefulness of the Limits for estimating other soils parameters. Terzaghi (1948) presented a relationship
for estimating the compression index, Cc» from the liquid limit, L , for clays of medium to low sensitivity. The proposed w relationship1 is C c =0.009 (Lw -10%). ...(4-4) Atterburg Limits were determined, and presented in the engineering reports, for the six samples upon which the previously discussed consolidation tests were performed.
Relationship (4-4) was applied to the reported liquid limits for purposes of comparing the calculated compression indices to the measured compression indices. The measured compress• ion indices ranged from 0.22 to 0.36 and the calculated compression indices ranged from 0.18 to 0.32. Some of the calculated values were greater than the measured values and some of the calculated values were less than the measured values. The largest discrepancy was on the order of 34 percent less than the measured value, but there was no apparent pattern to the variation.
The poor degree of reproducibility of liquid limits for silt soils may be largely responsible for the large 40. discrepancies and the random variability of the calculated vs. the measured values of the compression indices. The natural moisture content, which is a measured physical property of the soil not particularly dependent upon test procedures, should have a high degree of reproducibility.
For a normally consolidated alluvial soil the natural moisture content should bear some relationship to the liquid limit even at great depths. This leads to speculation that the natural moisture content of the predominantly silty banks' sediments may provide a means of making first order settle• ment estimates. In order to evaluate this possibility the measured C ,/1+e values were plotted vs. the corresponding liquid limits and natural moisture contents on semi-log paper, as shown in Fig. 8. The solid line on Fig. 8 represents the relationship obtained by substituting the natural moisture content, w, for the liquid limit, L , in equation (4-4); combining the resulting relationship with equation (4-2); setting G=2.70 and S=100 percent and solving for C /1+e. The relationship derived by this process is
Cc/l+e = 0.239 log1Q w -0.253. ... (4-5)
The measured values of Cc/l+e plotted vs. the liquid limits have completely random distribution, with some points above and some points below the solid line. The points
which represent the plotting of the measured Cc/l+e values vs. the natural moisture content lie consistently above the solid line. This suggests that a relationship similar to
(4-5), such as the relationship represented by the heavy dashed line in Fig. 8, may in fact provide a reasonable means Fig. 8 Possible relationship between the ratio of the Compression Index over
the Void Ratio plus one (Cc/l+e), and the measured water contents - liquid limit and natural moisture content. of making first, order estimates of potential settlements for
the banks' sediments. The relationship represented by the heavy dashed line can be expressed as
Cc/l+e = 0.239 log1() W -0.235. ... (4-6)
This relationship is proposed as a possible means of making first order approximations of settlement potentials
for a specific deposit of sediments based on the test results
available and this relationship should not be used unless
the user is fully aware of its severe limitations. If it were deemed desirable to verify or refine this relationship,
it is reasonable to assume that the soils of the delta
proper, at depth, are very similar to the soils of the banks,
and that the results of tests on these soils should satisfy the
same relationship if such a relationship exists. The sur-
ficial delta deposits have more clays and organics than the
banks sedimenrs and would not be expected to conform to the
same relationship. With all the development which has taken
place on the delta there should be a wealth of information
available which could be plotted to assess the usefulness
of the relationship.
SETTLEMENT CASE HISTORY
The Westshore Terminals Bulk Loading Facility is
located on Roberts Bank about midway between Canoe Passage
and the Tsawwassen Ferry Terminal. It is shown in Fig. 3 and
as can be seen it consists of a large man-made area connected
to the mainland by a long causeway. The site provides open
storage for very large windrows of coal, has conveyor systems 43. for moving and handling the coal, and has bulk loading facilities for loading deep sea shipping.
The dredging to create the fill for the bulk loading facility was begun on July 1, 1968 and continued to the end of May - early June of 1969. The site grade was raised from an average of -10 ft. to an average of +22.5 ft. giving an average total depth of 32.5 feet of fill. There were 12 settlement gauges placed around the terminal area during the commencement of dredging. Swan Wooster Engineering Co. Ltd., who did the overall engineering for this project, have made available the settlement records of the settlement gauges
and of some of the installations which were constructed on the
fill after the completion of dredging.
During the course of the dredging the settlement gauges were often bent and even broken. Whenever this happened the survey crew attempted to re-establish the gauge at its proper elevation. The resulting records reflect the extreme difficulty of accomplishing this task, especially if a number of days passed between the breaking of a gauge and the discovery of the broken gauge. Fig. 9 shows the location of gauges 7 and 12, the settlement records of which have been chosen as representative of all the settlement records. The predicted settlement due to the site fill is 3.5 to 4.0 feet. For the purposes of plotting and comparison, the settlement records for gauges 7 and 12 were "normalized" by dividing the settlements by 3.5. Fig. 10 shows plots of the percent of predicted settlements as recorded along with the predicted settlement curve. 44.
Fig. 9 Terminal of the Westshore Terminals Bulk Loading Facility showing the location of settlement Gauges 7 and 12 and the initial location of the coal stockpiles. TIME - DAYS
Fig. 10 Settlement at gauges 7 and 12. The solid lines show the actual data and the predicted settlement. The dashed lines represent the rationalized settlement curves.
Cn The predicted settlement curve is based on one dimensional consolidation theory and instantaneous loading. Working' on the assumption that during continuous loading there should be continuous settlement, and that the major discontinuities in the curves are due to gauge damage, the curves were "rationalized" by connecting together all reasonably continuous segments in such a manner as to produce a single continuous smooth curve. The rationalized curve is represented by the dashed lines and any symbols which appear on the dashed curves are for identification only and do not represent plotted points. The rationalized curves do not allow for changes in slope due to changes in rates of loading during the dredging operation and thus may be oversimplified.
Conversations with Swan Wooster personnel have indicated that the initial fill placement was taking place much nearer to gauge 12 than gauge 7 and the filling advanced on gauge 7 gradually, which would account for the differences in slope between gauges 7 and. 12 over the first 200 days. The first reading for gauge 7 is July 26, 1968 and for gauge 12 is August 1, 1968. It has been assumed that these dates represent day zero for these gauges. There is little to be learned from further discussion of the individual gauge records since the gauge damage has rendered the interpretation subject to personal judgements.
After the completion of dredging, construction of the facilities was begun and the rails for the large moving stacker which travels between the coal stockpiles were soon laid. Settlement records were kept for each joint of each rail from the time of installation up to September 1973, at reasonable time intervals. To get an extended time - settle• ment curve the settlement record for the rail joint nearest gauge 7 was added onto the rationalized settlement curve for gauge 7. The resulting settlement curve is shown in Fig. 11. along with the time placement of the events which would be expected to influence the settlements.
If one can accept the rationalized curve for gauge 7 as being somewhat reasonable, then the extended settlement curve presented in Fig. 11 is very reasonable and interest• ing. The settlement due to the site fill alone was virtually complete when the stockpiling of coal was started, which initiated further settlements. The settlement due to the site fill appears to have, been within the range predicted by Cook (1968). The stockpiling of the coal was started
675 days after day zero for gauge 7 and the extended settle• ment curve shows an immediate response to the additional loads. Although the settlement due to this loading was probably not complete at the time of the next major loading, the settlement curve suggests that the additional settlement at this point would have been about 2 ft. The predicted settlement was 3 to 4 ft. under the center of a coal pile and
1.5 ft. between the coal piles. The stacker rail from which this part of the settlement record is taken is located between the piles and hence it appears that the actual
settlement between the piles is slightly in excess of the predicted settlement. In February of 1972 the terminal area
layout was expanded to accommodate two additional stockpiles Approximate time of Expansion of terminal Stockpiling of coal to include 2 additional Dredging on 2 initial piles coal piles
r TTOTT l- - - 1 : hi: .Iii: • :t: j::: r pjx :!" ftM- • : i!:|: : j: : i f: •1 1 '1' : X '.BI i T -" I-I-" r W\+1 I - X -' IIT TI t 1 ! J-l • :: :j 1- - . : 1. if T j;; - . 1. T 1; "::F Ti :| i :i.. -(• - : :::ji i r-;.t• \ };.•: i: 1' l! 1 ' TI PI Ll •rt : if i; Ur - 1 -r :.!: -Li - -ii •IM' \u 1 gto j; ; ilT- "If 1 • j Iff I- it j. JHi TJTJ.'" lf-i .... ; j- •iii W'| 1 T :| i-i 1 1. X T|ft -. I T f' :| i Ii r fit - • • -If- H- ::| 1 •i ;j±b- :i :::::[: - ";| ;|; T j r f M il: r ft -•}• - 1 ! U:: :::"]+ ::::|- I. lit - -i if" ll | I.- 1•1: I _™ t| j- •i •I- ii J. }.L xxtt x+^: -1 : i . r i 1 ii ll 1; :::••! TJ-i if J : x: f " r :.| r |i i- : J:. i: x: \ |f t fM •+ Tix t" "if If xt •.: -;| ': -T IF JLLLm"- -H-- f . . |. ; •!•! ir -i- 4:|±f: i.t JX x.xi !•'• n - rf "±. i 1 f; ii".- a ma ii 2 " • ;r' & "~-'Xif !-r j ll- t ic - • 11 s< i- - - ""1 1 if - -i : 4 : : S i h xl: : it - j: : " i if 1 g au g< ]?' If iii - 1 |.y.f l"l; -i j-t- ii M ! : ; X -H- -F T • -i 1 ; rl - i J •H.rr s- (X 111:]. ?et h 1- ;i. jl|; »'-!f 1 : m : •i- t -I- p tf L! -I- Lj4 i t o tPF u -:|:': i-l- 1 :":[, •'!• J:: Ii mf cer ••.I- : x TIX s i ; :-"l rf "1 If Wt 1- fi 1 :a' f'j il ii •Id l III i-i- m : : II f . J- .1 T:: HI i j i if rr • :| -\ '• f : X: : j:: :i. -' '-f ':} i : aoc- m ' \'\ -;| i; : .j:' E:ff 1 1 .: - -i- ;t -t i l"!i Tt 1 f! o igs ;7.:r ll- jx' -i4t fjj gp II: -i: I- - - I; j. ' -1 i ; . -Ti -; i •I-i. . • -! •F 111 'I'l'F!-T ::: T f:; -H- -Ti- - - •lr : x: ; 1 JJ y •-! ] if .] j •i -$; : :: -i. j!.li :[:;!! : | |: r - - - •i T" •iii -i Tf If -F #: -HTff- - r -1- i ! .i -i.. . i- $ • -M- - ;i •F| .44 :jl" j:::: -1 ll-i :x:f-t r "-T nT : •$: ll' m Th ' 1 TP 1 T 1 - I-: T: tbl fiI f-•ti \ . . . .l.j- .)... FI - 1 "!T :± jj:jx : ::. .!:;•. : -i i-i:| : :l: |il ±i. |: "hr j' • | .::(: :!l -fel ;i- -i- 1 : : -DJ i fi ' "it :i ij f Xi: mv 1460 1600 3 2oo 40O Boo (000 \ZOO leoo
TIME - DAYS
Fig. 11 Extended Settlement record related to significant events, formed by combining, the rationalized settlement curve for gauge 7 with the settlement record of the joint on the Stacker Rail closest to the location of gauge 7. •49.
of coal. This development is clearly reflected by the accelerated settlement occurring after that time.
The extended settlement record correlates very well with the loading history of the terminal area. Because the loading was not instantaneous, but v/as spread over a. long period of time, it is not possible to make accurate estimates of the time to 90 percent consolidation. The settlement record does indicate that the settlement due to the fill was about 90 percent complete by 450 days after the installation of settlement gauge 7. Installation, maintenance and monitoring of settlement gauges is the only reliable method of determining the settlement history. Any project on the banks which involves any type of preload should be very carefully monitored and the decision to remove the preload should be based primarily on the settlement vs. time curves derived from the settlement gauge readings.
PROBABLE EARTHQUAKE ACCELERATIONS
The National Building Code of Canada divides Canada
into seismic zones based on the acceleration amplitude which has a 1 in 100 probability of being exceeded in any
given year. There are four zones defined, ranging from zone
0, for acceleration amplitudes less than 1 percent of gravity,
to zone 3 for acceleration amplitudes greater than 6 percent
of gravity. Roberts Bank and Sturgeon Bank are located in
a zone 3 region and possible seismic activity must be one of the
design parameters for a project on the banks.
Dr. W. Milne of the Victoria Geophysical Observatory prepared, on request, an estimate of expected accelerations with certain return periods for a site near Roberts Bank.
The earthquake catalogue for this region lists 2443 earth• quakes for the period 1899 to 1970 inclusive. Calculations indicate that 42 of these earthquakes could have been felt at Roberts Bank. Table 2 lists the date, epicentral distance, magnitvide and expected maximum acceleration at the banks for each of the 42 earthquakes. An extreme value statistical analysis was applied to the 42 events listed in Table 2, and
Table 2 Historical Earthquakes Max. Expected Date Distance Magnitude Acceleration . Day/Month/Year miles Richter Percent G
4/ 9/1899 1063 8.2 0 10/ 9/1899 1010 8.6 0 9/10/1900 1063 8.2 0 17/ 3/1904 111 6.0 0 11/ 1/1909 20 5.6 4 29/ 9/1911 25 4.3 0 18/ 8/1915 85 5.5 0 3/10/1915 649 7.75 0 22/ 2/1916 29 4.3 0 1/ 7/1917 227 6.4 0 23/12/1917 227 6.5 0 6/12/1918 158 7.0 1 10/10/1919 72 5.5 0 24/ 1/1920 22 5.0 2 12/ 2/1923 20 4.3 1 7/ 9/1926 38 5.5 1 1/11/1926 243 6.6 0 4/12/1926 39 4.3 0 8/ 5/1927 38 5.5 1 26/ 5/1929 380 7.0 0 18/ 4/1931 44 4.3 0 13/11/1939 110 5.75 0 29/11/1943 44 5.0 0 15/ 2/1946 119 5.75 0 23/ 6/1946 99 7.30 4 17/ 7/1946 270 6.50 0 13/ 4/1949 128 7.0 1 22/ 8/1949 543 8.0 0 30/ 3/1954 8 3.0 0 5/ 8/1954 13 3.0 0 20/11/1954 12 3.0 0 51.
Max. Expected Date Distance Magnitude Acceleration Day/Month/Year miles Richter Percent G
26/ 4/1955 13 3.0 0 26/ 1/1956 57 5.0 0 21/12/1956 328 6.75 0 10/ 7/1958 869 7.9 0 4/ 9/1959 18 3.4 0 14/ 7/196 4 24 4.6 1 29/ 4/1965 118 6.5 1 1/11/1966 21 3.5 0 25/ 5/1967 27 4.1 0 20/ 6/1967 8 3.6 1 14/ 2/1969 8 4.2 2 the analysis yielded the maximum probable ground surface accelerations for certain return periods along with the 99 and 95 percent confidence limits for the same return periods. The return period is the inverse of the statistical probab• ility that the given maximum probable ground surface acceleration will be exceeded in any given year. The results of the analysis for the site near Roberts Bank are given in Table 3.
Table 3 Earthquake Probability Analysis
rn Period Acceleration 95% Conf. Limits 99% Conf .Limits Years Percent G Percent G Perc ent G
3. 0.30 0 .28 0.34 0.27 0.35 10. 1.03 0 .90 1.18 0.85 1.25 30. 3.36 2 .80 4.02 2.60 4.34 50. 5.86 4 .79 7.18 4.40 7.81 100. 12.54 9 .93 15.83 9.01 17.46 200. 26.90 20 .66 35.04 18.48 .39.17 300. 42.08 31 .71 55.83 28.15 62.88 1000. 158.98 113 .34 223.01 98.29 257.14
Fig. 12 shows the information contained in Table 3 plotted on Log-Log paper. An inspection of the accelerations and the confidence limits reveals that the confidence limits Fig. 12 Predicted Maximum Ground Surface Accelerations for Various Return Periods for Roberts Bank, from an analysis by Dr. Milne. became fairly divergent as the Return Period approaches and exceeds the period of record (72) years. This is to be expected in a statistical analysis when the behavior of a natural event is being extrapolated beyond the time span of the input data. As the period of record becomes longer, improvement can be made to both the acceleration predictions and the 95 and 99 percent confidence limits; however, it will take substantial increases in the period of record to produce a significant change in the analysis.
LIQUEFACTION POTENTIAL OF THE BANKS
Liquefaction
In the laboratory and in the field, saturated granular soils from medium sands to fine sandy silts have been observed to lose their shear strength when subjected to cyclic shear stresses under conditions where the drainage is impeded or prevented. The equation for the shear strength of a cohesionless soil is:
T = («r- u) tan 0 ... (6-1) where f = shear strength, cr = total normal (confining), stress, u = pore water pressure, 0 = angle of internal friction of the soil. If the drainage is impeded the cyclic shear stresses cause a rise in pore water pressure, and the pore water pressure may continue to rise with each cycle of stress until the pore water pressure equals the total confin• ing stress. From equation (6-1) it can be seen that at this point the soil will have zero shear strength, and it is this condition of zero shear strength which is known as liquefaction. The classic example of liquefaction in the field under cyclic loading occurred in Niigata, Japan, during the 1964 earthquake. Niigata is located on an alluvial flood plain and delta on the North West coast of Honshu Island. The city is founded on geologically recent fluvial deposits which include extensive deposits of loose sand with standard penet• ration test blow counts of less than 10 (Kishida, 1965) . The water table is very near the surface throughout this area, resulting in saturated deposits.
On June 16, 1964 an earthquake of magnitude M=7.5 occurred, at an epicentral distance of approximately 32 miles from
Niigata, and this earthquake had a recorded maximum ground surface acceleration of 0.16g and a duration of 40 seconds
(Seedand Idriss, 1971). There were many reports of phenomena occurring during the Niigata earthquake which can be related to liquefaction of the foundation soils. Some of the reported phenomena were the appearance of geysers spouting water and sand into the air and forming sand cones (sudden release of built up pore water pressure); buried tanks, pipe• lines and other buried objects floating to the ground surface
(soil behaving as a dense liquid); and buildings settling and rotating into the soil although suffering little structural damage (loss of bearing capacity from reduced shear strength)
(Kishida, 1965; Evans, 1964).
It was observed that some areas of Niigata had exten• sive liquefaction and foundation failures while other areas had little or no evidence of liquefaction. Ohsaki (1970),
Kishida (1965) and others conducted investigations of the in situ soil conditions before and after the earthquake in an attempt to explain the difference in liquefaction potential.
On the basis of their studies they proposed a number of empirical liquefaction criteria. Standard penetration test blow counts represented the most abundant source of sub• surface information and the empirical criteria proposed were based on the N-value.
Empirical Liquefaction Criteria
Of the numerous empirical criteria proposed after the
Niigata earthquake as indications of whether a site will or will not liquefy during earthquake loading, the criterion proposed by Ohsaki (1970) is perhaps the simplest. Ohsaki's observations of sites which did and did not liquefy at
Niigata, and the N-values of the soils at these sites, led him to propose that the relationship N-2z (where N = standard penetration test blow count and z = depth in meters) repres•
ents a critical condition and that liquefaction of the soils
is possible "during an earthquake of a considerable intensity"
if the N-values are less than this critical value. This criterion is shown in Fig. 13 as a solid line from 0 to 15 meters depth and as a dashed line from 15 to 20 meters depth.
Ohsaki proposed his criterion for deposits of 15 to 20 meters depth; and it has been shown dashed from 15 to 20 meters to indicate that this is the extreme limit for which
it was proposed. The Ohsaki criterion was used in evaluating
the site of a paper manufacturing plant at Hachinohe as a
guide to the necessary densification of the foundation soils. Fig. 13 Comparison of the Ohsaki and Kishida liquefaction criteria The soils in question were very loose, clean, saturated medium and fine sands from the surface to 5 meters depth.
Vibroflotation was used to densify the soil, at the location of important buildings and installations, to meet.the Ohsaki criterion. One and a half years after construction was completed, the May 16, 1968 Tokachioki earthquake occurred.
The earthquake had a magnitude of M=7-8; had an epicenter approximately 112 miles from the site; and a reported maxi• mum ground surface acceleration of 0.21g with a duration of
45 seconds (Seed and Idriss, 1971). There was extensive liquefaction of the untreated areas but only minor settle• ments and damage of the treated areas, which indicated that the Ohsaki criterion had some merit.
Using pre-earthquake and post-earthquake subsurface test data, Kishida (1965) studied the soils conditions under structures which had no damage, light damage and heavy damage during the Niigata earthquake. Kishida concluded that the boundary between light and heavy damage was an
N-value of 15 from 0-5 meters, an N-value of 25 from 10-15 meters and a linear increase of N-value from 15 to 25 between depths 5 and 10 meters. The Kishida criterion is also shown in Fig. 13 and it. terminates at 15 meters depth since Kishida has not proposed a criterion for soils below
15 meters.
The available subsurface data for Roberts and
Sturgeon Banks consist primarily of the results of standard penetration tests made in 37 boreholes which were chosen to be broadly representative of the subsurface soil conditions of the entire banks area. The test results are plotted in
Pig.l4 with Depth (in feet) as the ordinate and N-value as
the abscissa. The column on the extreme left of the N-value
axis, labeled P (for push), represented attempted SPT tests
for which the weight of the drill rods was sufficient to
cause 1 foot of penetration with no blows of the hammer,
which indicates very loose soil. The numbers located on
the graph represent the total number of SPT tests made at
that particular depth which had that N-value. The Ohsaki
and Kishida criteria illustrated in Fig. 13 have been
superimposed on Fig. 14.
It is evident that virtually all the banks sediments
lie on the heavy damage side of the Kishida criterion.
Inspection of the Ohsaki criterion indicates that below 20
feet depth almost all the soils have N-values less than the
critical N-values and above 20 feet depth more than half
the soils have N-values. less than the critical N-values.
From this one can conclude that if the banks were subjected
to 40 to 45 seconds of earthquake loading v/ith maximum ground
surface accelerations in the range of 0.16g to 0.21g then
extensive liquefaction is indicated.
Analytical Liquefaction Potential
In 1971 Seed and Idriss proposed a simplified analy•
tical procedure for evaluating the liquefaction potential of
a saturated cohesionless soil. The proposed method approxi•
mates the cyclic shear stresses induced in the soil by earth•
quake loading and compares those stresses to the results of 59.
-p
Q)
EH PM W Q
N-VALUE
Fig. 14 Cumulative results of Standard Penetration Tests from 37 bore holes on the banks. 60. laboratory cyclic shear tests to obtain an approximate estimate of the liquefaction potential of the in situ soil.
The approximation of the cyclic shear stresses induced in the soil involves converting an earthquake acceleration record, which is characterized by its maximum acceleration and magnitude, into an equivalent number of cycles of aver• age cyclic shear stress for any point in the soil column.
This average shear stress,Zav, is defined as:
Tav^0.65 Xh a 'r, • ' ... (6-2) g where a = maximum ground surface acceleration, 0.65 = max ^ factor to approximate equivalent average acceleration, y
= total unit weight of soil, h = depth, g = acceleration of gravity, and r^ = reduction factor to account for the deform- able nature of the soil column.
It has been shown (Finn, Pickering and Bransby, 1971) that there is a unique relationship between the initial effect• ive stress ratio (ratio of the cyclic shear stress to the in• itial vertical effective stress) and the number of cycles of stress to initial liquefaction for a given soil at a given relative density, regardless of the magnitude of the stresses.
The second part of the Seed and Idriss simplified analysis involves determining the initial effective stress ratio which will cause initial liquefaction in the same number of cycles by comparing the in situ soil to laboratory tested soils and applying appropriate correction factors.
There are two basic corrections which must be made to
the laboratory data, providing the number of cycles of stress
to failure for the laboratory specimen are the same as for
the in situ analysis, and the soils themselves are similar. 61.
The most important correction to make is to allow for the
different initial stress conditions which may exist between
the laboratory specimen and the in situ soil. If the lab• oratory tests were conducted in a simple shear apparatus
then the initial confining stresses were analogous to the
initial in situ stresses and no correction is necessary. If,
however, the laboratory tests were conducted in a triaxial
compression apparatus then the initial confining stresses of
the laboratory specimen were significantly different than
those of the in situ soil. In the triaxial cell the initial
confining stress is the same for any orientation whereas for
the in situ soil the initial horizontal confining stress is
usually only a fraction (about 0.3) of the initial vertical
confining stress. Seed and Idriss indicate that the appro•
priate correction factor varies with the relative density and
they have suggested correction factors of 0.55 to 0.68 for
relative densities of 30 to 80 percent, respectively.
The other major correction which may be necessary is;
a correction for any difference between the in situ relative
density and the relative density at which the laboratory
tests were performed. Seed and Idriss suggest that the
appropriate correction factor is the ratio of the in situ
relative density over the relative density of the laboratory
specimen. By following the outlined procedure a relationship
between the maximum ground surface acceleration and relative
density can be obtained for initial liquefaction in the
number of cycles for which the analysis is performed. Seed
and Idriss included plots of representative values of the correction factors and cyclic triaxial test data to facilitate the use of their method.
The only factor necessary to perform this analysis for the banks sediments which has not yet been discussed is the number of significant stress cycles to use. An inspection of the earthquake data in Table 2 indicates that earthquakes in excess of magnitude M=8.0 have occurred close enough to have been felt at the banks, and that the highest recorded acceleration, .04g, was reached twice during the 72 year period from earthquakes of magnitude M=5-6 and M=7.3- Table 4 shows the number of significant stress cycles associated with different magnitudes of earthquake presented by Seed and Idriss (1971). Comparing the magnitudes of the earthquakes
Table 4 Earthquake Duration Number of Earthquake Magnitude Significant Stress Cycles Richter Nc
7.0 10
7.5 20
8.0 30 which have previously occurred close enough to have been felt at the banks with the corresponding number of significant stress cycles indicates that from 10 to 30 cycles of signifi• cant stress could be expected in the event of an earthquake which could affect the banks.
The Seed and Idriss simplified procedure was used to evaluate the liquefaction potential of the banks sediments.
The grain size distribution curves presented in Fig. 4 indicate that a mean grain size, Drn, of 0.2 mm. would be J u representative of the banks sediments. From the data presented by Seed and Idriss, the corresponding values of initial stress ratio of 0.24 and 0.21, for 10 and 30 cycles to initial liquefaction respectively, where chosen. The water table was assumed to be at the surface and the analysis was performed for a depth of 20 feet, which is approximately the critical depth when the water table is near the surface. Values for the correction factors were taken from the plots presented by Seed and Idriss. Fig. 15 shows the calculated initial liquefaction lines for 10 cycles and 30 cycles of stress, based on the above conditions, plotted on a graph of maximum ground surface acceleration vs. relative density. Also shown are the N-values corresponding to 40, 60 and 80 percent relative density as determined by the Gibbs and Holtz and the Baazara correlation curves. The borehole data has indicated that there are extensive areas of the banks sediments which have a relative density on the order of 40 percent. The Seed and Idriss simplified procedure indicates that 10 cycles of stress with a maximum ground surface acceleration of 0.075g or 30 cycles of stress with a maximum ground surface acceleration of 0.065g would be sufficient to cause initial liquefaction of these soils at 20 feet depth.
It is common practice to use the earthquake accelera• tion which has a 1 in 100 annual probability of being exceeded as the design acceleration for engineering works.
The extreme value statistical analysis prepared by Dr. Milne I
O H EH a w u
a s
JO 20 30 ""46 SO 60 TO So" loo RELATIVE DENSITY - percent SPT Gibbs & —i HoltZg to 18 .SPT-Bazaraa ~so_ 21 38
Fig. 15 Results of the Seed and Idriss Simplified liquefaction analysis. Assumptions - Depth =20 ft., D^Q = 0.2 mm, water table at surface. ov gave a value of 0.125g as the maximum ground surface
acceleration for rock or firm soil with a 1 in 100 annual probability of being exceeded. The response of the sediment column to the bedrock motions can modify those motions in
such a manner that the ground surface accelerations can either be amplified or diminished (Seed,1969). It is necessary to be aware that amplification is possible since
this represents the most dangerous situations; however, since
this analysis is based on generalized soil conditions and generalized test results from numerous sources and soils,
the results of the Seed and Idriss simplified procedure will be discussed in terms of the accelerations predicted by Dr.
Milne. Fig. 15 indicates that a relative density of greater
than 61 percent would be necessary to withstand 10 cycles and greater than 67 percent to withstand 30 cycles of stress with
a maximum ground surface acceleration of 0.125g without
liquefying.
The Seed and Idriss simplified procedure indicates
that extensive areas of the banks could liquefy if subjected
to 10 cycles of stress with a maximum ground surface
acceleration of 0.125g. Based on the Baazara interpretation
of the N-values, some areas of Sturgeon Bank have sufficient
relative density to withstand 10 and possibly even 30 cycles
of the stress described. However, when the possibility of
amplification is considered then even those areas have some
probability of liquefying.
If a development is contemplated for the banks then a
liquefaction potential analysis should be undertaken for the 66. specific site chosen. The first step is to undertake a detailed subsurface investigation and sampling program which would provide a reasonable estimate of the existing in situ relative density and would yield samples suitable for testing in triaxial cells, or other apparatus suitable for controlled cyclic loading tests. The object of the testing program is to produce a family of curves which relate the shear stress ratio (ratio of shear stress to confining stress), the cycles of stress to liquefaction and the relative density.
The testing program could consist of running tests to
liquefaction for various relative densities at a chosen shear stress ratio, and repeating the series at enough shear stress ratios to produce the family of curves desired. A preferable
form of presentation would be as a plot with cyclic shear stress ratio as the ordinate and relative density as the abscissa
and showing the curves for different chosen cycles of stress to initial liquefaction. The basic laboratory data must then be modified to account for the difference in the initial mean
confining stress between the test apparatus and the in situ
soil. If the tests were performed in a simple shear device
then this step is not necessary. Finn, Pickering and Bransby
(1971) presented a precise relationship between the stress
ratios of the cyclic triaxial test and the cyclic simple
shear test (which is analagous to in situ soil under earth•
quake loading); however, as certain approximations and
assumptions enter into the other portions of the liquefaction
potential analysis, the correction factors, C^, presented by
Seed and Idriss would be adequate for data conversion. Once the basic data has been plotted in the desired form, an analysis similar to the basic steps of the Seed and Idriss simplified procedure can be carried out, or a more rigorous analysis possibly using computer programs can be run. For the
simplified approach the equivalent average shear stress, "2"av is calculated (as per equation (6-2) ) from the maximum design acceleration. Inclusion of the factor r^ is not recommended because a value for r, is rather uncertain since the actual response of the soil column to earthquake accelerations is uncertain. It is conservative to exclude r^,. For any depth of interest, and knowing the position of the water table, the equivalent average shear stress ratio, ^V^, can be calculated ^o and the plots of stress ratio vs. relative density can be entered directly for an estimate of the liquefaction potential.
One form of more rigorous analysis pointed out by Seed (1969), is to model the soil column in a computer simulation, feed in various earthquake records at the base of the soil, and observe the soil response at various depths of interest. The shear stress vs. time record at any point can then be converted into cycles of equivalent average shear stress, and again the shear stress ratio can be calculated and the data plots
entered directly.
The above detailed testing program and subsequent analysis would be expensive to perform, however the apparent liquefaction potential of the banks' sediments is high enough that, for a project which represents a substantial capital investment and has a long projected life-span, this form of analysis should be considered. 68.
SUBAQUEOUS SLOPE STABILITY
The two basic forms of instability which can affect subaqueous slopes are erosional instability and mass wasting or slumping. These processes can act independently of one another or can be interrelated. A mass wasting can erode (turbidity currents) or it can create conditions which are more susceptible to erosion than the conditions which existed prior to the mass wasting. Erosion can alter an initially stable slope to the point where mass wasting is suddenly triggered»
Erosional Instability Fig. 3 shows a number of areas of the foreslope which
recent surveys have indicated are retreating. There is one area near the center of Sturgeon Bank, one area near the center
of Roberts Bank and one area just north of Westshore Terminals
bulk loading facility. These areas of retreat represent areas
where erosion is in excess of deposition; creating a net loss
of sediments at these points. Luternauer and Murray (1973) 6 estimate a volume loss of 294 x 10 cubic feet of sediments
for the retreating sections of Roberts Bank between October
1968 to April 1972. This estimate is based on hyposgraphic
profiles taken at the times stated, 3 1/2 years apart. Reliable sounding records do not cover a long enough time span to indicate whether or not areas of retreat have been associated with the delta for a long period of time. If erosion had been active at specific locations along the fore- slope of the delta for a longer period of time then the leading edge of the delta would have developed a configuration which 69. would reflect this condition. The leading edge, as expressed
by the subaqueous depth, contour, would be indented at
locations of consistent, erosion. The subaqueous contours of
the Fraser River Delta are remarkably smooth and regular,
other than off the mouth of major distributaries, with no inden•
tations consistent with long term erosion.
There are two plausible explanations of the above
observations which are worth mentioning. One explanation is
that the erosion is a long term process, the location of which
is constantly shifting in such a manner that the net effect
over long periods of time is to maintain, the regular, smooth
advance of the delta. The other explanation is that the
erosion could be a very recent event which has not yet been
reflected by noticable changes in the depth contours. If it
is a recent event it could be related to some natural
geomorphic phenomenon but is more probably related to the
influence of man. In very recent geologic time man has
stabilized the main channels of the river and built a number
of causeways out onto the banks. Such activity may have
upset the balance of some previously stable geomorphic
process(es), triggering the present erosion*
It is of vital interest to obtain a detailed under•
standing of the erosion and the controlling parameters which
determine where the erosion will occur and at what rate.
There is insufficient data available at this time to allow
any conclusions beyond the conclusion that erosion is
presently taking place. A project can be protected from
erosion by placing an erosion resistant material over the 70.
erodable materials. When the only information available is
that erosion is taking place then the erosion resistant material must be placed by intuition and a large factor of safety may
still be inadequate. With a knowledge of the parameters cont•
rolling the erosion, the factor of safety can be reduced and
alternate possibilities such as actually controlling the
location of erosion can be considered.
Mass Wasting
Mass wasting is the downslope movement of a mass of material as opposed to erosion which is a grain by grain type
of process. The volume of material involved in mass wasting
ranges from a few cubic yards of material to in excess of a
billion cubic yards of material. The movement of the material
can be a sudden accelerating downslope rush, or it can be a
slow gradual and even intermittent downslope creeping of the
material. In some instances a single event can be identified
as triggering the mass wasting and in other cases a number
of phenomena can be shown to have gradualy created an unstable
condition leading to a mass wasting. In many cases the cause
of the mass wasting can only be guessed at.
There are a number of phenomena which have been shown
to contribute to instability and even to trigger subaqueous
mass wasting. In the absence of any forces other than gravity
then the stability of the subaqueous slopes for a granular
material would be controlled by the angle of repose of that
material. The effect of other forces, such as wave pressures,
current action and earthquake loading is to reduce the stable 71. slope angle; therefore the angle of repose is the upper bound for the angle of the subaqueous slopes.
Carrigy (1970)presented the results of a study cn tha angles of repose of various granular materials. He defines two angles of repose for each material. The "critical angle
of repose", ac, is the maximum slope which a material can have before it slides and the "angle of rest", a^, is the angle at which the material comes to rest when the sliding finishes. The critical angle of repose is always greater than the angle of rest. The angles of rest measured by Carrigy for three sands in water were 32.1, 32.4 and 31.4 degrees.
As previously stated in the geology section, the subaqueous slopes average 1 1/2 degrees but exceed 23 degrees in a few places. Fig. 16 shows two sections (the locations of which are shown on Fig. 17) each plotted from the 1967 Swan Wooster survey and the 1974 Canadian Hydro- graphic survey chart No. 34 80 "Active Pass to Burrard Inlet."
These sections were chosen to represent the steepest condit• ions existing other than at the mouths of major channels.
The plots from the two sources were superimposed for the purposes of comparison; and although reasonable care was taken in attempting to locate the sections identically on the two source charts, which were drawn to very different scales, the two sets of profiles do not coincide. Some of the discrepancy may be due to deposition and erosion in the seven years between the two surveys but it is felt that most of the discrepancy is due to the difficulty of getting an exact locational match for the plotted sections. ! i i i : •' • ' i 1 i ! M i ! I.ij j. ! | .1. I..L.L!..,. ._. .. .., ,-• .• I Profile plotted If r.OmjSw^ 1967 ;•;; : Profile plotted from ; Canadian Hydrographic Survey chart #3480
-I._L.i_I.'llli. i ! i •••l-l- -!-•-•!• ; . i .. . Fig.16 Two Sections of the 'subaqueous Slope i I ;. Plotted to natural scale to 73.
Fig. 17 Location of cross sections S and R. The line used for the leading edge of the banks on this drawing is the lowest normal tide level. The surveys which have thus far been carried out on the subaqueous slopes have found no evidence of mass wasting other than the previously discussed slump structures. Based on the data available up to 1962, Mathews and Shepard (196 2) discussed the possibility that the deep gullies found off the mouths of the major distributaries might be related to mass wasting. The gullies, and in particular the system of gullies and canyons off the mouth of the main channel, run downslope to a maximum depth of 90 fathoms.
Mathews and Shepard compared these gullies to land• slide gullies off the Mississippi Delta and contrasted them with the turbidity current gully in the Rhone Delta in Lake Geneva, leaving the impression that they favor landsliding as the geomorphic process involved in the formation of the gullies. To illustrate their argument they presented charts showing subaqueous contours of the Mississippi and Rhone deltas. The chart of the Mississippi Delta shows numerous well developed gullies along with a great confusion of irregular topography throughout the same area as the gullies. The subaqueous topography of the Rhone River Delta shows prominent levees on the sides of the turbidity current gully and it is stated that the gully bottom sediments are sand and the levees are mud (presumably clay and silt).
The irregular topography of the Mississippi Delta is consistent with mass wasting, as the slides will develop wherever the factor of safety drops below 1.0. Slide material
travelling downslope is probably often diverted into the slide scar of a previous slide and certain preferential gullies 75. become established and.deepened. On the Fraser Delta we find . a few well developed gullies, but the confusion of irregular topography is missing.
The surveys made up to 1962 did not indicate the presence of any levees on Fraser Delta gullies and the lone sample obtained from the bottom of a gully has less sand than did samples from the adjacent slopes. Echo-sounding records from a 197^ Canadian Hydrographic Service survey of the Fraser
Delta slope (Luternauer, 1976) show what appear to be subdued levees adjacent to the gullies crossed by the survey. The
Strait of Georgia, is tidal, as opposed to non-tidal Lake
Geneva, and if the geomorphic process operating on the slopes of the Fraser Delta was attempting to form levees, the tidal currents would probably interfere with this process.
It is conceivable that when the river is in flood the salt water wedge could be splitting the flow such that that portion which.is denser than the sea water flows down- slope, and that portion which is less dense flows out on the surface of the salt water. The portion flowing downslope would flow in the established gullies, much like turbidity currents, but it could also involve sliding of the accumulated gully bottom sediments (Terzaghi, 1962). The composition of the sediment samples previously mentioned could be a function of the time of sampling and the seasonal variation of the Fraser
River sedimentation.
Effect of Surface Waves
Surface waves create moving zones of pressure which are alternately higher and lower than the mean pressure at the 76. seabed. Henkel (1970) discussed a number of the possible effects of surface wave pressure zones on the stability of underwater slopes. The most readily apparent effect is illus• trated by Fig. 18, which depicts a freebody diagram of the forces acting on a circular arc slice of a subaqueous slope.
The forces have been depicted at the precise time when the transitory wave pressure is aligned such as to minimize the stability of the. sliding mass against failure. The shearing resistance of the soil, which acts tangential to the arc base such as to resist any unbalanced forces, has not been shown on the freebody diagram. If the stability of the freebody slice is considered by summing the moments around the center of rotation, C, it can be seen that the non-hydrostatic wave pressure at this instant in time contributes to the clockwise
(overturning) moment.
The other effects of the transitory non-hydrostatic wave pressures are associated with the response of the seabed material to the transitory wave pressures. . The moving pressure zones, regularly alternating higher and lower than the mean seabed water pressure, in effect, subject the seabed to a cyclic pressure loading. Two possible effects of the cyclic pressure loading are a buildup of non-hydrostatic pore water pressures in the seabed, and a gradual remoulding of soft cohesive sediments reducing the shear strength of those sedi• ments. Investigation of these two possible effects is beyond the scope of this thesis, and they will not be further pursued.
A simple computer program for analysing the stability of circular arc potential failure surfaces by the method of NOTE: The soil shear stresses acting around the slip arc are not shown on this freebody.
C = Center of slip arc and rotation R = Radius of slip arc W = Weight of freebody 6 = Angle of slope with horizontal p = Sinusoidal non-hydrostatic water pressure
Fig. 18 Freebody diagram of circular slip arc showing non-hydrostatic water pressure from wave loading. 78. slices, with non-hydrostatic pressure loadings and pore pressure responses, prepared by Neil Wedge of the University of British Columbia, was modified and used for a series of analyses of the assumed maximum slope of the banks. A Fortran listing of the program used has been Included as Appendix 2.
The program makes a static analysis of stability using a sinu• soidal pressure distribution for the wave pressures, which is strictly appropriate for deep water waves only (depth of still water greater than one-fifth the wave length). The use of a static analysis gives an upper bound solution for the stability, as the dynamic effect - if any - would be to reduce the stability.
The program centers the sinusoidal wave pressure distri• bution over the midpoint of the segment of slope being analysed, with the greater pressure on the upslope half of the surface, thus maximizing the effect of the wave pressure. The non- hydrostatic pressure changes at the surface of the seabed result in changes in the sediment pore pressures. Sleath (1970) presented the results of a laboratory study, wherein the pres• sure distribution in a bed of sand being subjected to wave pressure loading was measured. This study indicated that the sediment pore pressures respond in phase with the passing wave pressures, and that the magnitude of the response is dampened with depth in the seabed. The program includes the damping effect reported by Sleath (1970) as well as the damping of the wave pressures which occur with depth in the water column.
Profiles of the foreslope indicate a maximum slope of on the order of 23 degrees, therefore, a slope of 25 degrees 79- was analysed as the assumed maximum slope using the modified program. In order to determine the appropriate wave loading
to apply to the analysis, data from wave-rider, buoys (which is
discussed in another section) was studied. The maximum recorded
peak to trough wave height at the banks was on the order of
9 feet and this wave had a period of approximately 7 seconds.
By applying the approximate deep water relationships
C = 3T and X = CT ... (7-1,7-2)
where C = velocity in knots, T = period in seconds and A = wave
length, It was calculated that this wave would have been approx•
imately 250 feet long. The mean still water depth at the mid•
point of all sections being analysed was chosen to be 100 feet
primarily to ensure deep water conditions even at the upslope
edge of the assumed failure surfaces.
A review of all the available data on the banks' sedi•
ments (reported and discussed elsewhere in this thesis) indica•
ted that the stability analysis should be performed for a
purely frictional material. The cohesion was assigned a value
of zero, the angle of internal friction was given a value of
30 degrees and the material was assumed to have a bouyant unit
weight of 59 lb/ft3.
A series of potential failure arcs with horizontal lengths
ranging from 125 feet to 250 feet was analysed. The depth of
the potential failure arc was varied from 5 feet to 55 feet
for each chosen failure length. The lowest factor of safety,
for any of the potential failure surfaces computed by the
program, was 1.2 for the shortest, shallowest potential failure
surface (1.25 feet, 5 feet). In all cases, the factor of safety 80. increased as the depth of failure increased and as the length of failure increased.
This analysis indicates that even the steepest slope found on the banks is stable during loading by non-hydrostatic pressures induced by water waves. The analysis also indicates that, if there are any failures, they will be very shallow failures and should not constitute a catastrophic danger to engineering installations except as a form of progressive
erosion. If this problem is recognized it can be dealt with
in much the same manner as ordinary erosion. The sediments on the slopes of Roberts Bank and Sturgeon Bank are considered to be sufficiently coarse that with the relatively large periods
of oscillation involved (7 seconds and greater) dissipation of
pore pressures will be rapid and excess pore pressures due to
cyclic wave loading will not be likely to build up.
Effect of Earthquake Motions
There are two basic effects of earthquake motions which
must be discussed with respect to slope stability considera•
tions. First, the accelerations of the earthquake motion
creates inertial forces in the slope sediments and any com•
ponents of these forces acting outward from the slope become
part of the driving force attempting to cause failure. Second,
the oscillatory nature of the earthquake motions subject the
sediments to reversing shear stresses which, as was discussed
elsewhere, can lead to a buildup of excess pore water pressures.
This can have a significant effect on the strength of primarily
granular soils.
Sarma (1973) presented a method of slope stability 81. analysis which incorporates a horizontal acceleration in the analysis. Although this method uses the concept of a horizon• tal acceleration. It is a static analysis in which the hori• zontal acceleration is converted into an inertial driving force and dynamic effects are not considered. Sarma (1973) uses the symbol K to represent the horizontal acceleration'as a decimal fraction of gravity in his analysis. Equations are then set up for the condition of limit equilibrium (factor of safety exactly equal to 1.0) and the value of K which satisfies these equations is the critical acceleration, K . Sarma
suggests that the value of Kc can be used directly as an indica• tion of the static factor of safety or the normal static factor of safety can be arrived at by an alternate procedure. The alternate procedure involves reducing the strength parameters of the material along the slip surface such that the calculated critical acceleration is just equal to zero. The factor by which the strength parameters must be reduced to achieve this condition is the static factor of safety.
To incorporate the possible dynamic effects of earth•
quake loading into the analysis, Sarma .(internal report written
for a project while working as a Research Associate at U.B.C.)
included a pore pressure factor in the analysis which he
related to increases in pore pressure due to cyclic loading.
He defined the change in pore pressure, Au, as
Au = AnKYh ... (7-3)
where A^ = the pore pressure parameter, K = the horizontal
inertia coefficient, y = the saturated unit weight of the soil
and h = the depth of the point from the surface of the slope. 82.
This definition of the change in pore pressure, Au, requires the adoption of the assumption that the change in pore pressure at any point is proportional to the total stress at that point, which is probably a reasonable assumption.
In the section on liquefaction potential, it was shown-' that a complex earthquake motion can be approximated by two parameters, K and N, where K is the magnitude of acceleration and N is the number of cycles of stress. The change in pore pressure, Au, also depends on both these factors. K enters directly into equation (7-3), therefore, the pore pressure
parameter An must bear a relationship to' the number of cycles of stress, N. From formulae proposed by Martin, Finn and Seed
(1975), Sarma plotted curves of U/G^Q VS. T/O^Q (where u = excess pore pressure, x = shear stress, and a' = initial ver- ' 3 vo tical effective stress) for different numbers of cycles of stress. These curves are reproduced in Fig. 19 and the deri• vation of the" initial failure line, shown as a dashed line in
Fig. 19, is shown in Fig. 20. To.relate the curves to the slope stability analysis the portion of each curve from zero out to the initial failure line is approximated by a straight line. A straight line approximation to these curves gives the equation
u/a' = A x/o' ... (7-4) vo n vo where A^ is a constant for a fixed number of cycles of stress, and is equated to the pore pressure parameter, A , of the slope stability analysis.
The linearization of the u/a' vs. x/a' curves creates vo vo a unique relationship between the pore pressure parameter, A, I 1 • i-i- 'Fig. jigjj Relationship1 between excess Pore 'Pressure Jand -applied shear (stress for i !-; ; ^various numbers of cycles of stress. \ U...Ld--l'''' CO •!- •!- i- t-j- XLJ LO 84.
Fig. 20 Derivation of the failure criterion used to place the failure line on Fig. 19. 85. . in the slope stability analysis and the number of cycles to initial failure, N, for laboratory cyclic loading tests. There are two reasonable ways to perform the linearization, the re• sults of which have been plotted in Pig. 21. The upper curve
shows the An values derived by joining the origin to the inter• section of the failure line with the curves for the various
numbers of cycles 3, N. The lower curve is the A values obtained ° n by approximating the average slopes of the Fig. 19 curves. The upper curve is favoured by this writer because it leads to higher pore water pressures and is, therefore, to be considered more conservative.
The derivation of the initial failure line is based on an initial principal stress ratio, Ko, of 0.5 and the assumption that this ratio remains constant during the cyclic loading.
The curves presented in Fig. 19 are based on the results of various cyclic loading tests on a soil described as "crystal silica sand" at relative densities ranging from 45 to 60 percent.
Although the composition of the banks' sediments is not the same as the material tested, the A vs. N curves derived from ' n the test results should provide a reasonable first order approxi• mation of the number of cycles to failure. If refinement of the A vs. N curves was felt to be desirable then a testing pro- gram could be undertaken using the banks' sediments, with the tests conducted under conditions which matched the in situ conditions.
Sarma further modified, his method of analysis to include non-hydrostatic wave pressure loadings in conjunction with the earthquake loading. A series of potential failure surfaces
37. on the steeper portions of the subaqueous slopes, as repre• sented by the upper portion of profile S in Fig. 16, were analysed for stability using the Sarma method. The analyses were performed for a soil with zero cohesion, an angle of internal friction of 30 degrees and a total unit weight of
124.8 p.c.f. Wave pressure loading corresponding to a sinu• soidal wave with a wave height of 9 feet and a wave length of
250 feet was inserted Into the analyses. The section analysed and the input wave loading are shown In Fig. 22.
To illustrate the procedure and the kind of results that may be obtained, five potential failure surfaces were analysed, for a fixed chord length, and the two surfaces which gave the lowest critical acceleration, K , for factors of safety,
FS .= 1, are shown in Fig. 22. The analyses were performed with the aid of a computer program which Is limited to the case of a homogeneous material. This limitation is not considered to be restrictive in this instance, since the field data available indicates that a homogeneous representation of the upper sedi• ments is reasonable. A Fortran listing of the program used is presented in Appendix 3-
The lowest critical acceleration, K , obtained from the analyses was 0.124g for surface 5. and the critical accelera• tion increased as the depth of the potential failure surface
Increased. This is consistent with the previous analysis where the factor of safety increased as the depth of the surface increased.
Fig. 23 shows the Kc vs. A curves developed for surfaces
4 and 5- Potential failure surface 5 gives a K of 0.019g when ; 88. •
Fig. 22 Slope analysed by Sarma program,, showing ::Zfailure:.sur,f ac.es:^Zandl5_iaM:_the::::;:^ri;;::.. non-hydrostatic wave data.
-—i~
, ,1 ; Fig.23 Relationship between critical Acceleration and Pore Pressure Parameter for surfaces 4 and 5. 90.
A = 10 and this corresponds to 8 to 10 cycles of stress accord• ing to Fig. 21. Thus, this analysis indicates that a condition of limit equilibrium will be reached for the shallow potential failure surface on the assumed steepest subaqueous slopes on the banks, with a single horizontal acceleration directed out• ward from the slope of 0.124g, when combined with the 9 foot wave loading. In conjunction with this same wave loading 8 to
10 cycles of stress, with a horizontal acceleration into and out of the slope of 0.02g, are sufficient to achieve the condi• tion of limit equilibrium. Somewhat greater magnitudes of horizontal acceleration would be necessary to achieve the condi• tion of limit equilibrium in conjunction with lesser wave load• ings or in the absence of wave loading.
The results of these analyses, in. agreement with the results of the circular arc analyses, indicate that the steepest
of the subaqueous slopes are stable even during storm magnitude wave loading, in the absence of dynamic loading. A significant
seismic event is indicated as necessary to produce slope insta•
bilities, which would tend to be of a shallow nature.
To obtain an estimate of the magnitude of horizontal
acceleration which would be necessary to trigger a mass wasting
on the scale of the slump structures previously discussed, a
very large potential failure section 200 feet deep, as shown
in Fig. 24, was analysed. No non-hydrostatic wave pressure
loading was used in this analysis since the section being analy•
sed was much too massive and extensive to be affected by wave
loading. The analysis yields a critical acceleration, Kc, of
0.24g to produce the condition of limit equilibrium for the section analysed neglecting cyclic loading effects. Fig. 12 . indicates that a maximum horizontal acceleration of 0.24g would be associated with a seismic event with a return period of about 180 years. Such an event could be classified as a rare event, which is in agreement with the previous discussion.
The earthquake stability analysis indicates that the banks' sediments could be liquefied by an earthquake of a magni• tude and duration which is within the range of possible seismic activity of the area. There are a number of ways to reduce
the liquefaction potential of a particular site of finite size,
however, the expense and the consequences of these methods must
be carefully considered. The two methods which seem to offer
the greatest potential for successful application are. the place•
ment of a fill loading and the densification of the in situ
deposits. Documented evidence of the success of the latter
procedure is contained in the study by Ohsaki (1970) following
the Tokachioki earthquake.
Densification is the most direct and positive method of
reducing liquefaction potential. The addition of site fill
increases the overburden effective stress but it also increases
the shear stress ratio during the earthquake excitation, which
offsets the advantages of increased effective stress and may
result in only a minimal reduction in earthquake resistance.
Luternauer (1976) speculated that the undulating surface
of the foreslope below -70 meters, in the area between a point
opposite Canoe Passage and the Westshore Terminals bulk loading
facility, could be related to mass wasting. The undulations in
question appear on three (H, I and J) of a series of hypsographic 93. profiles of the foreslope taken by the Canadian Hydrographic
Service in 197*1 • The undulations appear to have a somewhat regular wave-like profile, with a wavelength of about 300 feet and a peak to trough wave height of about 5 to 10 feet measured in the plane of the slope; which averages 1.4 to 1.5 degrees at this depth and location. Tracings of the surface of the recorded echo signals of hypsographic profiles H, I and J, between 60 and 100 meters depth, have been presented in Fig. 25
and the locations of the profiles is shown In Fig. 26. No
scale was put on Fig. 25 since the horizontal scale is dependent
upon the actual horizontal motion of the- survey ship; however,
navigational positioning indicates that the horizontal scale
for these profiles is approximately 1 inch to 300 meters. The
distortion created by the very large ratio of horizontal to
vertical scale tends to mask the wave-like nature of the undu•
lations but close inspection reveals that these long shallow
wave forms appear to be asymetrical with the long gentle slope
running downslope and the shorter steeper slope running.out
from the general slope.
In the latter part of July, 1976, the Geological Survey
of Canada did some side-scan sonar of the foreslope of Roberts
Bank. The track lines followed by the survey ship were sub-
parallel to the strike of the slope when making side-scan sonar
records, and a number of the track lines passed through the
area covered by profiles H, I and J. Although the analysis of
the survey results is not complete, Dr. Luternauer made the
side-scan sonar records available for inspection. The records
show many areas with orderly rows of mega-ripples with remarkably Fig. 25 Tracing of Hypsographic Profiles H, I and J from 60 to 100 meters below sea level. ROBERTS •' i BANK
STRAIT OF GEORGIA'
CANADA .U.S.A.
Galiano Island Active Pass r Mayne Island SCALE 1:98,842
H, I, J - Hypsographic profile lines Mean Low Tide Depth Contour in Fathoms
Fig. 26 Location of hypsographic profile lines H, I and J. 96. regular size, shape and spacing on the foreslope of central
Roberts Bank. These mega-ripples are of an asymetric shape similar to the shape of sand dunes.
The mega-ripples are prevalent on all the records taken on the foreslope of central Roberts Bank. No records were taken south of the bulk loading facility, but some records were taken on north Roberts Bank, right to the main channel of the
Fraser, which show subdued by still recognizable mega-ripples.
By plotting the track line of the ship on a chart the Geological
Survey of Canada has been able to transfer the orientation of
the mega-ripples to the chart. In some places the mega-ripples
appeared disturbed or jumbled but there was always an overall
recognizable orientation to the ripples. The orientation of
the ripples as transferred to the chart is parallel to sub-
parallel to the dip of the slope, and the steep slopes of these
asymetric wave forms are facing westward.
From the plotted ships positions and the time marks placed
on the side-scan records the Geological Survey of Canada has made
an initial estimate (verbal communication) of the spacing of
the mega-ripples on the order of 40 meters. Precise echo sound•
ing run simultaneously with the side-scan sonar Indicates a
peak to trough wave height for the mega-ripples on the order
of 2 meters. These mega-ripples are sub-parallel to hyposo-
graphic profiles H, I and J and the intersection of the mega-
ripples and the profiles would be at a small angle. The ripples
as seen on the profiles would appear to have a much greater
spacing than 40 meters and It is quite clear that the undulating
features noted in profiles H, I and J and the mega-ripples 97. revealed by the side-scan sonar are identical features.
The mega-ripples have all the characteristics of being a current related phenomenon. Dr. Luternauer has indicated
(personal comment) that the flood tide has the strongest effect on the foreslope of the banks and that the orientation and asymetry of the mega-ripples appear to be consistent with the direction of the flood tide currents. Some of the records were taken during a flood tide and some during an ebb tide but the orientation and the direction of the asymetry of the mega- ripples appears to have remained unchanged. Whatever the rela• tionships between the mega-ripples, the tides and the currents are, it is clear that these features are not related to mass wasting and, hence, the question of slope stability can now be resolved. Some erosional instability is indicated by the areas
of retreat but there appears to be no instability with respect to mass wasting under static loading and full storm wave loading.
ADDITIONAL DESIGN CRITERIA
The remaining factors which must be considered to provide
a complete data base for an engineering investigation of the
banks are primarily environmental. There are two basically
distinct aspects of the environment which must be considered.
One aspect is the physical forces of the environment which will
be acting on any engineering structure on the banks. The major
physical forces of the environment to be considered are wind and
wave. Temperatures can also play an important role at many
locations, but do not do so here as the average January tempera•
ture is about 36°F and the average July temperature is about 98.
62°F (Hoos and Packman, 1974). The other aspect of the environ• ment is the biological environment, which has come to be known as the ecology.
Wind
Hoos and Packman (1974) list the maximum observed wind speeds in the banks area as N..W. 55 miles per hour at Vancouver International Airport and S.E. 64 miles per.hour at Tsawwassen Ferry Terminal and they present a wind rose of the cumulative winds from 1953 to 1971- Table 5 is a summary of the informa• tion on that wind rose.
Table 5 Cumulative Winds - 1953 to 1971 Direction Frequency % Mean Wind Speed mph
N. 2.3 4.1 N.E. 12.3 7-3 E. 31.6 7-4 S.E. 10.5 8.9 S. 6.8 8.7 S.W. 7-0 7-9 W. 15.8 10.8 N.W. 5.6 7.8 Calm 8.1%
Swan Wooster (1967) presented monthly wind roses of winds in excess of 20 miles per hour in terms of hours per month averaged over a 10 year period. The Swan Wooster (1967) data also Included the average number of hours of wind per month in excess of 30 miles per hour. January, October, November and
December each have at least 1 hour per month of 30+ m.p.h.- winds from the N.W. with January having the most at 2.1 hours per month. November and December also have winds in excess of 30 m.p.h. from S. and S.W. for less than 1 hour per month for each direction. The only other months with winds in excess of 99.
30 m.p.h. are May and June with 1.1 and 1.5 hours per month, respectively, from the West. August has the lowest total hours of wind in excess of 20 m.p.h. at 13-7 and March has the highest at 44.
Wave
The Marine Environmental Data Service collects and com• piles wave records from such sources as Waverider Accelerometer
Buoys, two of which were located off the banks. Station 102 was a buoy located off Sturgeon Bank from February 7. 1974 to
August 9, 1975 and Station 108 was a buoy located off Roberts
Bank from February 7, 1974 to July 31, 1975- The Roberts Bank
buoy (Station 108) was out of commission from the end of October
1974 to the end of April 1975 and thus did not record through
the winter months, which have the greatest periods of the strong•
est winds and therefore potentially the largest waves. For the
few months when both buoys were operating simultaneously, the
records produced in the form of the Characteristic Wave Height
vs. the Time in Days plots are very similar. This indicates
that for the purposes of choosing design parameters the Sturgeon
Bank data should be applicable to the whole Delta front.
When functioning properly the Waverider buoys make a
20 minute wave record every three hours. The significant Wave
Height is defined as four times the square root of the area
under the variance spectrum of the water elevation. To form a
continuous plot of significant wave height with time when the
wave record interval is the standard three hours, the plots
are joined by linear interpolation. Gaps in these records
indicate malfunctions which caused missing readings. Environment 100.
Canada compiles all the wave data on computers which produce detailed listings of the Individual wave records, monthly curves of Characteristic Height vs. Time, Percentage Exceedence vs. Wave Height for the observation period, Percentage Occur• rence vs. Peak Period for the observation period and a scatter
diagram of significant Wave Height vs. Peak Period during the period of observation.
The largest significant wave height recorded off Sturgeon
Bank was between 9 and 10 feet with a peak period between 6 and
7 seconds and off Roberts Bank was between 7 and 8 feet with a
peak period between 5 and 6 seconds. Sturgeon Bank recorded
the maximum wave height with zero percentage exceedence as
13 feet and Roberts Bank recorded 10 feet. The fact that the
Roberts Bank buoy did not record during the winter months
explains why the Sturgeon Bank buoy recorded significantly lar•
ger waves.
The approximate relationship -
H = 1.4 /fetch ... (8-1)
where H = wave height in feet and fetch = the stretch of open
water over which a wave can build up, in miles, was used to
estimate the maximum wave height which could be built up during
gale force winds (winds in excess of 35 miles per hour). The
maximum fetch length In the Strait of Georgia terminating on
the banks is just over 72 miles (from Hornby Island), which
indicates a maximum wave height on the order of 12 feet. At
least one wave of this magnitude was recorded during the 1.5
year observation period, indicating that waves of this magni•
tude would not be a rare event on the banks.
For design purposes the wave data, wind data and geography 101. must be considered together. Winds from the North West have the most hours per year in excess of 30 miles per hour, and the longest fetch is provided from the North West. From this
it is clear that the most frequent large waves, and potentially
the largest waves, will come from the North West. . This infor• mation can guide the orientation of structures, breakwaters and
causeways and aid the design of slopewash protection for such
structures.
Ecology
Mention of the biological environment has been left to
last not because it is of less importance than the forces of
the physical environment but because it cannot be as readily
defined as can the physical environment. The interaction of
the physical environment and the engineering project are fairly
well understood and, in most cases, the engineer is designing
for the estimated worst probable conditions of the physical
environment acting against the engineering structure. There is
no parallel when discussing the biological environment because,
in most cases, the biological environment does not act against
the engineering structure, it is affected by it and reacts to
its presence.
A detailed look at the biological environment is outside
the scope of this thesis, however, it is necessary to discuss
it very briefly since the environmental impact of a project '
must be one of the factors governing implementation and design.
The much referred to work by Hoos and Packman (1974) contains a
wealth of information on all the various forms of life found in
the Fraser River Estuary. There are two aspects of the 102. biological environment of the banks which could potentially be fairly sensitive to changes on the banks, and which are of major importance. Portions of the banks are critical feeding, growth and shelter areas for the Fraser River salmon as they make the transition from river to ocean. The banks are adjacent to, and form part of, a very important feeding, rest• ing and wintering area for the migratory waterfowl which follow the Pacific Flyway. The banks are, of course, important to many other aspects of the biological environment (for example, they are an important feeding and spawning area for the Pacific
Herring which is a major source of food for the salmon) and it is the importance of the banks to the biological environment which necessitates the inclusion of the environment as a design parameter.
CONCLUSIONS
Roberts Bank and Sturgeon Bank are composed of geologi• cally recent, normally consolidated, sediments. These sediments are many hundreds of feet thick. The surface 80 feet of sedi• ment is primarily granular in nature, exhibiting no significant
cohesive properties. The granular sediments are remarkably uni•
form in gradation for any specific sample, however, there is no noticeable lateral continuity to the sediment layering even at
700 foot spacing. The sediment column has many layers with a
high silt content which are moderately compressible; and poten•
tial settlements must be one of the governing design considera•
tions for any proposed development.
The banks' sediments are of loose to medium density and
have a significant liquefaction potential based on a number of 103- different analyses. Although there is no proven evidence of previous liquefaction on the banks or on the Fraser Delta, the banks are located in an area which has a reasonably high pro• bability of, at some time, experiencing an earthquake of sufficient magnitude and duration to cause liquefaction of the sediments. The predicted 1 in 100 annual probability earthquake appears to be sufficient to cause the liquefaction of some areas on Roberts Bank and Sturgeon Bank.
The subaqueous slopes are at least nominally stable with respect to mass wasting. Any mass wasting, other than a catas• trophic event triggered by an external force, would be of a
shallow small volume nature. Studies conducted, so far, indi•
cate that erosion of the subaqueous slopes is presently occur•
ring at a number of points. Further studies are recommended to
locate and quantify any erosion and determine the controlling
parameters and the active agents. .
Winds, waves and temperatures experienced on the banks
are far from the extremes found, and dealt with in many other
parts of the world. These factors are reasonably well quanti•
fied for most design purposes. There is, however, one - factor
which is not very well quantified and of which a better under•
standing is needed; the ecology of Roberts and Sturgeon Banks.
Sufficient data were available from various sources to
allow a general overall appraisal of the engineering parameters
and.related factors for Roberts Bank and Sturgeon Bank. Some
factors, such as subaqueous slope erosion and the ecology,
require further study to define the significant factors at
work.
o 104.
BIBLIOGRAPHY
Bazaraa, A., 1967, "Use of the Standard Penetration Test for Estimating Settlements of Shallow Foundations on Sand," Ph.D. Dissertation, University of Illinois, Civil Engineering. Carrigy, M.A., 1970, "Experiments on the Angles of Repose of Granular Materials," Sedimentology, Vol. 14.
Cook, P.M., 1967, "Preliminary Soil Report, Sturgeon and Roberts Banks," prepared for SWAN WOOSTER Eng. Co.
Cook, P.M., 1968, "Soils and Foundation Report, Roberts Bank Development," prepared for SWAN WOOSTER Eng. Co. •
Cook, Pickering, and Doyle Ltd., 1974. "Soil Report, Vancouver Airport Extension, April 1974," prepared for the Department of Public Works. de Mello, V., 1971. "The Standard Penetration Test — A State-ofr-the-Art Report," 4th Pan Am Conf. on SM and FE, Puerto Rico, Vol. 1. Finn, W.D.L., D.J. Pickering and P.L. Bransby, "Sand Lique• faction in Triaxial and Simple Shear Tests," Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 92, SM 6, 1966.
Gargett, A.E., 1976, "Generation of Internal Waves in the Strait of Georgia, British Columbia," Deep-Sea Research and Oceanographic Abstracts, Vol. 23, No. 1.
GIbbs, H.J. and W.H. Holtz, 1957. "Research on Determining the Density of Sands by Spoon Penetration Testing," 4th ICSMFE, London, Vol. 1.
Henkel, D.J., 1970, "The Role of Waves in Causing Submarine Landslides," Geotechnique, Vol. 20, No. 1.
Hoos, L.M. and G.A. Packman, 1974, "The Fraser River Estuary, Status of Environmental Knowledge to 1974," Report of the Estuary Working Group, Department of Environ• ment, Regional Board, Pacific Region.
Johnston, W.A., 1921, "The Age of the Recent Delta of Fraser River, British Columbia, Canada," American Journal of Science (1).
Kishida, H-, 1965. "Damage of Reinforced Concrete Buildings in Niigata City with Special Reference to Foundation Engineering," Soils and Foundations, Vol. 6, No. 1. 105.
Lambe, T.W. and R.V. Whitman, 1969, "Soil Mechanics," Series in Soil Engineering, John Wiley & Sons, Inc.
Lee, K.L. and J.A. Pitton, 1969, "Factors Affecting the Cyclic Loading Strength of Soils," Vibration Effects of Earthquakes on Soils and Foundations, ASTM STP-450, American Society for Testing and Materials, 1969.
Luternauer, J.L. and J.W. Murray, 1973, "Sedimentation on the Western Delta-Front of the Fraser River, British Columbia," Can. Journal Earth Science 10_ (11).
Luternauer, J.L., 1974, "The Fraser Ri'ver Estuary, Status of Environmental Knowledge to 1974, Geology," Report of the Estuary Working Group, Department of Environment, Regional. Board, Pacific Region.
Luternauer, J.L., 1976, "Fraser Delta Sedimentation, Vancouver, British Columbia," Report of Activities, Part A, Geological Survey of Canada, Paper 76-1A, pp. 213-219-
Martin, G.R., W.D.L. Finn and H.B. Seed, 1975, "Fundamentals of Liquefaction Under Cyclic Loading," Journal of the Geotechnical Division, ASCE, Vol. 101, No. GT5, May 1975.
Mathews, W.H. and F.P. Shepard, 1962, "Sedimentation of the Fraser River Delta, British Columbia," Bull. Amer. Assoc. Petrol. Geol. 4i5 (8).
Mathews, Fyles and Nasmith, 1970, "Postglacial Crustal Move• ments in Southwestern British Columbia and Adjacent Washington State," Canadian Journal of Earth Science, V. 7, PP. 690-702.
Mayers, I.R., 1968, "Analysis of the Form and Origin of the Fraser River Delta's Subaqueous Slump Deposits," B.Sc. Thesis, Dept. of Geophysics, University of British Columbia. Milne, W.G., I963, "Seismicity of Western Canada," Contribu• tions from Dominion Observatory, Ottawa, V. 5, No. 13-
Ohsaki, Y., 1970, "Effects of Sand Compaction on Liquefaction During the Tokachioki Earthquake," Soils and Foundations, Vol. X, No. 2. Sarma, S.K., 1973, "Stability Analysis of Embankments and Slopes," Geotechnique, Vol. 23, No. 3.
Schmertmann, J.H., 1975, "The Measurement of Insitu Shear Strength," a State-of-the-Art presentation at the ASCE Specialty Conference on Insitu Measurement of Soil Pro• perties, Raleigh, N. Carolina. 106.
Seed, H.B., I.M. Idrlss and Kiefer, 1969. "Characteristics of Rock Motions During Earthquakes," Journal of the S.M. and P.D., ASCE, Vol. 95, No. SM5, September 1969.
Seed, H.B. and I.M. Idriss, 1971, "Simplified Procedure for Evaluating Soil Liquefaction Potential," Journal of the SM and FD, Proceedings, ASCE, September 1971.
Sleath, J.F.A., 1970, "Wave Induced Pressures in Beds of Sand," Journal of the Hydraulics Division, ASCE, Vol. 96, No. HY2, February 1970.
SWAN WOOSTER ENGINEERING CO.. LTD., 19.67, "Planning Study for Outer Port Development at Vancouver, B.C."
Taylor, D.W., 1948, "Fundamentals of Soil Mechanics," John Wiley & Sons, Inc.
Terzaghi, K. and R.B. Peck, 1948, "Soil Mechanics in Engineer• ing Practice," Second Edition, John Wiley & Sons, Inc.
Terzaghi, K., 1962, "Discussion, Sedimentation of the Fraser River Delta, British Columbia," Bull. Amer. Assoc. Petrol. Geol. 4(5 (8).
Tiffin, D.L., 1969, "Continuous Seismic Profiling in the Strait of Georgia, B.C.," Ph.D. Thesis, University of British Columbia.
Tiffin, D.L., J.W. Murray, I.R. Mayers, and R.E. Garrison, 1971, "Structure and Origin of Foreslope Hills, Fraser Delta, British Columbia," Bull. Can. Petrol. Geol. 19 (3). APPENDIX 1
Location Plan of Continuous Seismic Profiles, Bathymetric Profiles, North Continuous Seismic Profile, South Continuous Seismic Profile, Transverse Continuous Seismic Profile. 108.
LOCATIONS OF THE CONTINUOUS SEISMIC PROFILES TAKEN ACROSS THE SLUMP STRUCTURES BATHYMETRIC PROFILES IN AREA OF SLUMP STRUCTURES no. NORTH PROFILE
SOUTH PROFILE •03S TRANSVERSE PROFILE
117.
APPENDIX 2
Fortran Listing of computer program for analysing circular arc potential failure surfaces. $LIST UWSLOPES • 1 C IFIT=NO. FAILURE ARCS ; E= FA I LURE ARC SLOPE LENGTH/2 2 C D=INITIAL FAILURE DEPTH;DMAX=MAX FAILURE DEPTH 3 ri^OUYANT WEIGHT ;B=SLCPE ANGLE ; F= IN I Ti AL TRY F OF S 4 C PHI=FRICTICN ANGLE;C=COHESION 5 C N=NO. SLICES;J=N+1;ITMAX=MAX. U ITERATIONS 6 C IFPR=1 FOR NONHYDRQSTATIC; GW=UN IT WEIGHT WATER.
7 REAL DX.50)fTANT(50) ,T(50) ,XM{50)W(50),F1(50),F2(50),F3C50) 8 REAL PP(50).X150) ,TM(50).DEPI50)»HW(50),UT{50) ,UB(50) 9 REAL UX.LX:', R . DMAX ,DD
10 INTEGER N,K,JtITMAX»PR»IFDA,IFIT 11 707 CCNTINUE 12 10 FORMAT(8F10.3. 13 READ(5,20) I FIT 14 READ. 5,10) E,D,DMAX,G,B,F,PHI,C 15 READ.5, 20) N.J, it"NAX,IFPR,GW 16 20 FORMAT.415,F10.3 ) 17 WRITE (6,100) CtPHItG
18 100 FORMAT.'1*,«CGHESICN=» vF7o3,'PHI=»,F7.3BOUYANT UNIT WT. = »,F7.3) 19 WRITE(6.200) B 20 200 FORMAT { 11 SLOPE ANGLE=' .F7.3» 9 DEGREES'. 21 IF( IFIT.LT.1.00) IFIT= 1 22 B=B/57.28 23 PHI=PHIZ57.28 24 Z = TAN(B ) ...... 25 Y=CCS 29 WRITE(6?30C) R.D 30 300 FORMAT (//•RA'D". "in- FT_T_T~CTKUL'E="•, F9 . 3, ! DEP TH 0 F PfcNE IR AI I UN-' , F /. J J 31 'lFiN.LT.0.00) GOTO 1 32 A-FLOAT{N ) E = SORT(R*R-(R-D)*KR-D) ) 34 DXS=2.D0*E*C0S.B)/A 35 Xll)=-E*COS.B) + (R-D.)*SIN.B) 36 X(N-H)=E*COS(B) + CR-DJ* SIN-IB) 37 DX{15=DXS 38 C GET END POINTS AND WIDTH OF SLICES IF THEY ARE TO BE GENERATED ""DO 2 I = 2,N ~ —- A-FLO AT ( I ) X ( I ) = X ( 1) + (A- 1 ,.D0_)*pXS_ _ , a| DX{ I )=OXS 2 CONTINUE GOTO 17 : 1 CONTINUE IF(II.GTol.O) GOTO 17 IF SLICE ENDPOINTS ARE TO BE READ IN, READ THEM DO 3 1=1,J PEAD(5,30) XU) 30 FORMAT IF10.3) 3CCNTINUE IF SLICE ENDPOINTS HERE READ IN, GET SLICE WIDTHS N=-N DO 4 I=1,N DX{I)=X(I+1)-XU) 4 CCNTINUE 17CCNTINUE CO 5 1=1,N UX=X{1+1) Lx=xm XMi I )=(UX+LX)/2.DQ CALCULATE THE SLOPE OF THE FAILURE SURFACE AT SLICE MIDPOINT TANT(I ) =XM 11 ) *1 oDO/SQRT(R*"R-XM I I )"*XM( I ) ) T„„„T„T CALCULATE THE SLOPE ANGLE OF THE FAILURE SURFACE AT SLICE MIDPOINT Td ) =AT AN J TANT { I ) J "CTTCULATE THE WEIGHTS OF THE SLICES ,nj„ , , nni UXP={UX*UX/2.D0)*Z-(R-D)*UX/Y+(UX/2.D0)*{SQRT{R*R-UX*UX))+lR*R/2.D0) * f l^'i'L X> 10 \~. TfH^Z^~DT^ X7Yf TIX7 2.D 0j * IS QRT { R*R-LX* L X > ) + R* R / 2 .DO **ARSINlLX/R) \il I ,=G*IUXP-LXP) CONTINUE DO 8 1=1»N it j DEP { I ) IS THE HEIGHT OF THE SLICE AT ITS MIDPOINT « UTII)=03D0 UE(I)=0.DO '•»MM*WJ.wJ,A'{JI"lt(. 78 PPU)=0.D0 \ 79 8 CONTINUE 1 80 IFUFPR.EQ.OJGOTO 70 . . 81 IFfll.Gf.l.OJ GOTO 7 71 j 82 C PR=1 FOR AUTOMATIC PRESS. GENERATION i 83 C I FDA = 1 FOR DAMPING,0 FOR NO DAMPING ANYWHERE 84 C IFBT =1 FOR DAMPING IN SOIL,0 FOR NONE 85 READ(5,90Q0) PR, I FDA,IF8T 1 86 9000 F0RMAT13I5) i £7 IFiPR.NE.0) GOTO 600 i 88 DO 80 I=ltN 3 89 C UTC1)^PRESSURE TOP OF SLICE;U8{I)=PRESS. BOTTOM i 90 P. F A D ( 5, 500) UT(I ) , UB(I ) ••!i 91 500 FCRMAT(2F10.3I 92 80 CONTINUE i 93 GOTO 7 0 •] 94 C WN=WAVE NG. (2*PI/L);DC=MEAN STILL WATER DEPTH 95 C WL = WAVE LENGTH*,WH = WAVE HEIGHT — 'j 96 C DSB= THICKNESS PERMEABLE SEABED I 97 600 REA0(5,90> WN,DC,WL,WH,DSB 1 98 90 FCRMATi5Fl0.3) 99 771 CCNTINUE 100 1 UTE(6 ,1000) F'r RMAT ( ******* WAVE DATA ******«) 101 1000 ,~ .-.a 102 V.f I TE (6,2000) WN 103 2000 FCRMAT{»WAVE NUMBER = »,F10.3) 104 WRITE I 6, 3000) WL .' 105 3000 FORMATI * WAVE LENGTH = ' ,F10.3) 106 WRITE16.40CO) WH 1G7 4000 FCRMAT{'WAVE HEIGHT = »,F10.3) 1C8 WRITE(6,5000) DC 109 5000 FORMAT('ME AN STILL WATER DEPTH = *,F10.3) 110 FORMAT('THICKNESS OF PERMEABLE SEA BED - «,F10.3) 111 6000 112 "WRITE (6,400) ^ o_o , FORMAT!*********** SLICE INFORMATION *************) 113 4<.:0 114 WRITEt6*40 S „w „-r.K,-r, % 8 115 40 FORMAT I'SLICE',8 X » OX',6X,'WEIGHT',5X,*UT*,7X,'UB*,8X,'TANT«) 116 117 XPM=XP( I )-(R-0)*SIN(B) 1 118 H=DC-XPM*Z 1 119 DP=GW*(WH/2.0)*C0SI1.571-XPM*WN. 120 IFUFDA.EQ.O) GOTO 8500 i 121 UT{I)=DP/COSH< WN*H) 122 IF{IFBT .EO.0) GOTO 8000 123 WNO=COSH.WN*DS8) 124 WNC=WN*(DSB-DEP(I)) 125 UBCIl=UT(I|*COSHCWNC./WND I 126 GOTO 7000 127 8500 UT< I .=DP '< 128 8000 U6(i)=uun 129 7000 CONTINUE 1 130 70 CONTINUE j 131 DO 6 1 = 1 VN 13 2 WRITE I 6 ,50) I,DX(I),W(I) ,UT(I),UB{I), TANT. I ) i 133 50 FORMAT(• •,I6,5F10,3) 134 6 CONTINUE i 135 DO 9 1=1,N 136 .< XM { I )= { XM!I )/Y )-(R-D)*Z : 137 Fill )=C*DX{I) 138 F2(I )=(W(I)+UT(I )*DX(I J-UBlI)*DX( I) »*V 139 f 3(I) = W(I)*SIN{TI I))*R+UT{I)*DX(I)*XM(I)/ < > APPENDIX 3 Fortran Listing of Sarma slope stability program. SLIST SARMAS 1 DIMENSION XSC50),YS(50),YL{50),UT(50),U6(50),XKBAR(50),W(50> , 2 lWBARt 50 3 ,H(50) ,0(50) , AH50 ) ,A2(50 ) ,A3_ 50) , A4l 50 ) , A5{ 50) , A6( 5"0T7~" 3 2A7<50)»0D{50),A8(50),AAC20) 3.2 GO TO 191 4 111 CONTINUE , 4.2 PRINT 192 4.4 192 FORMAT(//»*#** NEW PROBLEM ***•,//) 4.6 191 CONTINUE 5 READ 2,NS 6 C NS=NO. OF SLICES +1,XS=SURFACE X-COORD.YS=SURFACE Y-COORD 7 READ 1, (XSU) ,1 = 1,NS3 8 READ 1, .YS i I ) , 1=1, NS 3 i 8. 2 GO TO 193 9 112 CONTINUE i 9.2 PRINT 194 9.4 194 FORMAT.//,1*** NEW SURFACE ***»,//) 9.6" 193 CONTINUE 10 READ 1, (YH I 3 , 1 = 1 ,NS3 11 READ 1,CUT{I),1=1,NS) 12 READ 1, (UB(I) ,1 = 1,NS3 13 READ 1,(XKBAR{13 ,1=1,NS) 14 READ 1,PHI,C,GAMMA,GAMWTWL 15 READ 2,JJ 16 READ 1,(AA{I 3,1 = 1 , JJ) 17 c YL=BASE Y-COORD,UT=NGN HYDROSTATIC TOP,UB=NON HYDROSTATIC BOTTOM 18 c XKB AR= ASSUMED SHAPE OF FUNCTION FOR DETERMINING INTERSLICE 19 c FORCES,PHI=ANGLE OF FRICTI ON,C=COHESI ON,GAMMA=SATURATED DENSITY 20 ~ c GAMW=UNIT WEIGHT WAT ER,AA = PORE WATER PRESSURE FACTORf EARTHQUAKE) 21 c WL=WATER LEVEL 22 2 FORMAT(1216) 23 1 FORMAT{12F6.33 24 PRINT 12 25 PRINT 4»PHI,C,GAMMA,GAMW,WL 8 26 4 FORMAT(4X,•PHI=«,F6.3,2X,«C=•,F7.3,2X,*GAMMA=',F7.3,2X,*GAMW= 27 1,F7.3,2X^* WL=« ,F7'.3) 28 PRINT 12 29 PRINT 101 8 1 8 30 101 FORMAT (3X, I ' ,8X, 'XSVIBXT VS"' , iiXT^YL' , I3X, U T' . 13 X , « UB • , 13 X , 31 1'XKBAR') s J,XKBAR III 1 32 PRINT 3,(1 ,XS(I ) , YSU ) ,YLU ) ,UT( I ) ,UB{ I , I = 1,NS) 1 3 FORMAT{16,6 F15.3) • 33 j 34 PRPHI=PHI i 1i 35 DO 44 J=1,JJ 1 36 SUMl=0o 1 37 SUM2=0. 3 8 SUM3=0. 39 SUM4=0. 40 SUM5=0. 41 SUM6=0„ 1 42 0(11=0. j 43 H(l)=0c I 44 PH=0. 45 HH = 0. 46 A=AA(J) 47 PRINT 121,A 48 121 FGRMAT(//,2X,'PORE PRESSURE PARAMETER A=«,F6.3) 49 PHI=PRPHI 50 PHI=PHI*3.1415 926/180. 51 TANPHI=TAN(PHI) 52 PRINT 12 53 DO 5 1=2,NS ; t 54 B=XS( I )-XS ( 1-1 ) 55 H( I )=YS(I)-YL(I) 56 AREA=(H(I)+H(1-1))*0.5*B 57 i: { I ) = ARE A* (GAMMA-GAMW ) 58 WBAR(I)=AREA#GAMMA 59 I F ( YS ( I ) . L E . WL.) GO TO 6 60 HH=YS(I)-WL 61 AREA1={HH+PH)*0*5*B 62 AR EA2=AR EA-ARE A1 63 MlI )=AREA1*GAMMA+AREA2*(GAMMA-GAMW) 64 PH=HH 65 6 CCNTINUE 66 IF(YLU) .GT. WL) W(I5=WBAR(I) 67 ALPH=ATAN( (YL( I ) - Y L ( I- 1 ) )/B) 68 BET A= AT AN { (YS I I ) -YS I I- 11 )/B ) 69 PfOP=0« 5*(UT{I)+ 0T tI—l)) *B*GAMW/C'OS(BET A) -—J 70 PBGT=0.5*(UB( I )+U8(1-1) )*B*GAMW/COS(ALPH) 71 G(I)=XKBAR(I)*{ GAMMA-GAMW )*H(I)*H ( I ) *0 • 5+C*H'l I ) 72 FF=Q( I )-Q( 1-1 ) 73 T A N A = T A N ( P H I - A L P H ) 74 XG=XS<1-1)+B*B/6.*((GAMMA—GAMW)*{H(1-1)+2.*H(I } )+GAMW*(PH+2,*HH))/ j 75 1W( I > i 76 1 I F ( YL( I ) .GT. WL . CR. YS(I) .LE. WL ) i 77 1XG=XS{I-1)+B/3.*(HU-1)+2.*H(I))/(H(I)+H(I~1) } 78 YG={YL(1-1)+0.5*H(1-1) )*(l.-(XG-XS(I-1) )/B )+ ( Y Ll I) +H< I j *0. 5) * S 79 11XG-XS( 1-1)J/B i 80 XB=XG i 1J 81 YB = YL (1-1) +(XB-XS( I-in*(YL( I j-YLl I-lH/B 82 DIV=UT(I)+UT(I-1) J 83 XT=(XS( I ) + XS( I-1»J*0.5 IFIABSIDIVI .LE. 1.0E-6) GO TO 14 i 84 \ i 85 XT = XS(I — l)+B/3.*(UT(I-1)+2.*UT(I))/(UT(I)+UT{ 1-1)) 86 14 CONTINUE i 87 YT=YSi I-i) + IYSI I)-YS( I-I J)*(XT-XS'( 1-1) )/B 88 Z=COS(PHI)/COS(ALPH) 89 0=W!I)*TANA+(C*B*Z-PBOT*SIN(PHI)*PTOP*SIN(PHI-ALPH+BETA))/ • 90 ICOS(PHI-ALPH) 91 DD(I)=D 92 A 11 I ) = FF*TANA 93 SUMl=SUMi+Ai(I) 94 A2( I 1 = XB-YB*TANA 95 A31 I)= F F*A 2(1) • 96 SUM3=SUM34-A3( I ) l 97 A4(I) = A*SIN(PHI )*YB/(COS(ALPH)*COS(PHI-ALPH)) i 98 A5(I)=WBAR(I)*(YG+A4(I)) 99 SUM4=SUM4+A5(I) 1 100 A8(I)=A4(I)/YB 101 SUM2=SUM2+WBAR(I)*ll. + A8( I ) ) 102 SUM5=SUM5+D i 103 A6( I ) =PTOP*COS(BETA)*(XB-XT + (YB-YT)*TAN(BET A) ) i 104 A7(I)=D*YB 105 SUM6=SUM6+A6(!j-D*YB 106 ALPH=ALPH*180./3.14159 26 107 BETA=BETA*180./3.1415926 108 IF(I oGT. 2J GO TO 102 109 PRINT 1G3 8 8 110 103 FORMAT(2X? « I , 5X » H',7X,*W• ,5X,•WBAR',4X,'PTOP«,4X,'P8GT»,4X, 111 1 8 1 1 1 "I A_ PHI • "", 4X7 '•BETA 6 X, Q * »6X i •FF % 5X » • T ANA • t 5X1 X6 t 6X» ' YG* t 6Xt C 8 112 2'XB°,6X, YB«,6X,«XT',6X, YT») 113 102 CCNTINUE 114 PRINT 10, I ,HU 3 ,W( 13 ,WBAR{ I ),PTOP,PBOT,ALPH,BETA,Q{I3,FF , TANA , 115 1XG,YG,XB,YB,XT,YT 116 10 FCRMATU4,16F8.1) 117 5 CCNTINUE 118 DIV=SUM1*SUM4+SUM2*SUM3 119 ALAM=t SUM2*SUM6*-SUM4*SUM5)/DIV 120 XKC=(SUM5*SUM3—SUM6*SUMl)/DIV 121 PRINT 12 122 12 FORMAT( 1H0 , //9H CONTINUE///) , _ 123 PRINT 104 4 124 104 F0RMAK6X, «A1» ,12X,'A2« , 12X, A3',12X,«A4•,12X, »A5« ,12X,»A6', 8 125 112X,«A7',12X, DD* ,12X,*A8» 3 i 126 PRINT 11, (Al ( I J7X2TIT,"A 3TD7 "A 4(1), A5(IJ,A6{1), A/113 ,Ul)(l),A8tU 127 1,I=2,NS) 128 11 F0RMAT(9F14.3) „ i 129 PRINT 12 130 PRINT 105 131 105 FORMAT(5X,«SUM1«,10X,»SUM2« , 10X,•SUM3',10X,• SU N4' ,10X,«SUM5* , 132 110X,•SUN6') 133 PRINT 11,SUM1,SUM2,SUM3,SUM4,SUM5,SUM6 134 PRINT 13,ALAM,XKC 13 FORMAT ( 1H0, 6HLAMDA=,F10 .4 , 5X, 12HCR I T. A'CCLN.-,F 10.4 ) 135 136 44 CONTINUE 137 C CHECK FOP FURTHER FAILURE SURFACES 138 READ 88,NN 139 88 FORMAT{14) 140 IF(NN .GE. 1) GO TO 112 . 141 C CHECK FOP NEW PROBLEM 142 READ 88,MM 143 IF(MM .GE. 1) GO TO 111 144 STOP 145 END END OF i