Assessing Slope Stability Hazards near Kingston Jamaica, with special emphasis on Port Royal
To be compiled as part of Master’s Thesis Report, required as partial fulfilment of Master’s
Candidacy in the MER Program.
Renee McDonald
Version 4.2, 9/25/2013
I. Intro
The 2010 Haiti Earthquake brought into sharp focus the reality of catastrophic earthquake
events in the Caribbean region. The Mw 7.0Haiti earthquake ruptured along the Enriquillo‐
Plantain Garden Fault (EPGF) system, and may have involved a previously unmapped north‐
dipping fault, now named the Léogâne fault (Calais et al. 2011). The earthquake was generated
by stress released near the eastern terminus of the EPGF, located along a segment of the
southern boundary of the Gonâve microplate(Mann, et al. 1995).The island of Jamaica extends
∼230 km along the Gonâve–Caribbean Plate boundary and straddles faults that accommodate
Gonâve–Caribbean Plate motion. Slip motion along these faults is left‐lateral, with the strike of
the fault approximately east‐west in the eastern half of Jamaica (Mann, et al. 1995)
Figure 1 Overview of Kingston Harbour and Regional Tectonics
200 km
In central Jamaica, just northeast of Kinston, however, the Wag‐water restraining bend striking
southeast results in a significant component of thrusting (DeMets and Wiggins‐Grandison
2007). This leaves the island and the city of Kingston in particular vulnerable to large strike‐slip
and thrust earthquakes. In the past there have been seismic events that have had calamitous
effects on the island, and the city of Kingston in particular. This includes among others, the now
infamous 1692 quake that devastated the pirate haven of Port Royal, and the 1907 Jamaica
earthquake.
Figure 2 Overview of Jamaica's Geology, Major Fault Systems and the location of the 1957 and 1993 events.
1957
1993
Kingston is the life‐blood of Jamaica. With a population of 937,700 (Jamaica Census 2011), it is
the most populous city in the English‐Speaking Caribbean. Many essential services are
headquartered in this vibrant capital. Like Port‐au‐Prince in Haiti, Kingston is located on a large
alluvial fan. The sediments are fairly stiff but unconsolidated (Wiggins‐Grandison 1994). This
leaves the city particularly susceptible to landslides and liquefaction. Liquefaction is a process
by which a liquid saturated soil loses its solid characteristics and for a short time acts like a
viscous fluid.
The term “liquefied” was first described in soil mechanics in Hazen, 1920. The author noted
that “If the pressure of the water in the pores is great enough to carry the entire load, it will
have the effect of holding the particles apart and of producing a condition that is practically
equivalent to that of quicksand.”This phenomenon played a central role in the devastation of
Port Royal during the 1692 and 1907 earthquakes. Field studies following past earthquakes
indicate that liquefaction tends to recur at many sites during successive earthquakes (Youd
1984), and understanding the probability of future events is therefore an important aspect of
geohazards analysis.
Located in an active seismic zone, Jamaica experiences more than 200 tremors annually,
according to the Earthquake Unit at The University of the West Indies. Former director of the
University of the West Indies (UWI) Seismic Research Centre in Trinidad, Dr. John B. Shepherd,
has noted that “From the seismologist’s point of view, the parishes of Kingston including Port
Royal, and lower St. Andrew were probably the worst possible locations to choose for the
capital city of Jamaica."It is not a matter of if a major earthquake will occur; it is simply a matter
of when.
Kingston has experienced several developments in recent times which also add to the hazard
risk. Both the physical and economic effects of an earthquake near Kingston could be
catastrophic. Researchers with the University of the West Indies suggest that if Jamaica were to
be hit by a quake similar in scale to the Haiti 2010 Earthquake, the island could suffer a
significant financial loss. Recent GPS studies on the island imply the island is due for just such a
sized earthquake (DeMets and Wiggins‐Grandison, 2007). Since the last significant earthquake
impacted Kingston more than a century ago (the 1907 Mw 6.5 Earthquake), more communities
have been built on coastal sands in earthquake‐prone areas. There has also been increased use
of reclaimed land for urban development.
Figure 3 Port Royal Features
During the next great earthquake in Jamaica, the fate of the Palisadoes, a strip of land, some 14
km long, that almost completely encloses Kingston Harbour is also of great concern (Figure
1).The Palisadoes isthmus is the only land‐access connecting the Norman Manley International
Airport to the rest of the city. Also located on this strip are the headquarters of the Jamaica
Defence Force Coast Guard (Figure 3).In order to achieve sustainable development in Kingston
and Jamaica that minimizes the impact of future natural hazards, it is important to recognize
and quantify the hazards posed by future earthquakes in Jamaica, and prepare accordingly. The
goal of this study is to quantify slope stability along the Kingston harbour waterfront, and in
particular, along southern edge of the Harbour near Port Royal and the Palisadoes, as this area
has been prone to frequent, sometimes devastating slope failure and liquefaction events
associated with earthquakes. This study combines sediment strength analysis with earthquake
probabilities to assess (1) the magnitude of past events that triggered slope failure in the
Harbour and (2) the likelihood and location of future slope failure events in and around the
southern edge of Kingston Harbour. Our hope is that this study will be used in Jamaica for
future hazard mitigation and city planning.
Historical background
To give some perspective on the potential for slope failure along the southern edge of Kingston
Harbour, we begin this study by providing some historical perspective. The 1692, 1907, 1957,
and 1993 earthquakes all caused varying degrees of damage to the harbour, some of which was
catastrophic. For the two most recent events (1957 and 1993‐ Figure 2) we have robust
constraints on earthquake magnitude and location. Ultimately, we can use this information
combined with regional earthquake catalogues, region seismic measurements, and
geotechnical analysis to place constraints on the likely magnitude of older earthquake events in
the region and the probability of future slope failure in Kingston Harbour.
The 1692 Earthquake
The great Port Royal earthquake transpired on June 7, 1692. The entire quake probably lasted a
much as a few minutes and had a magnitude that could have been as high as Mw 8 (Clark
1995). By the time it was over, two thirds of the city had sunk into the sea and about 2,500
people, arguably a third of its population, had died (Clark 1995).According to one historical
source, at the time of the earthquake the town occupied an area of about 60 acres, but much of
this sank leaving only about 25 acres, of dry surface area (Porter 2002).Even though it was Port
Royal that sank, the intensity of the shock was perhaps felt even more in other parts of the
island(Clark 1995). It was reported that the earthquake “scarcely left a planter's house or sugar‐
work standing all over the island”(Sloane 1692). According to eyewitness accounts, strong
aftershocks continued to level damaged buildings for days, and troubled the island for months
afterwards (Sloane 1692). Taber also noted that “The earthquake was accompanied or followed
in some places by a great sea wave,” and several tsunamis were reported inside Kingston
Harbour both at Port Royal and present day Kingston according to historic accounts (e.g.
Sloane, 1692). There are varying reports about the actual intensity and magnitude of the quake,
and currently, it remains unclear how significant an earthquake the 1692 event truly was.
According to some, the earthquake was actually relatively small, but happened to trigger a
submarine landslide that carried the city of Port Royal into the sea (Clark, 1995). More recent
interpretations suggest that the earthquake had a maximum Intensity of X on Modified Mercalli
scale implying the 1692 earthquake had magnitude of at least 7 (Wiggins‐Grandison, 1994)
The 1907 Earthquake
The 1907earthquake occurred on the afternoon of January 14, 1907. The principal shock took
place at 3:33pm and lasted about 30 seconds(Taber 1920). Estimates for the magnitude of this
quake range as high as MM IX on the Mercali scale(Wiggins‐Grandison 1994), and 6‐ 6.5 on the
Richter scale (DeMets and Wiggins‐Grandison 2007) and Doser, Personal Communication). The
event occurred when only a handful of seismometers existed on earth (and only one on the
island of Jamaica, which broke during the earthquake), and as a result, the epicentre of this
earthquake remains poorly constrained. The earthquake caused a large fire in Kingston. US $30
million in damage was assessed and over 800 people lost their lives (Tortello 2002).The level of
destruction seen in Kingston was not only attributed to the earthquake itself, but also to the
conflagration which burned for days following.
The 1907 earthquake, although only a moderately sized event (Mw 6.5), caused significant
damage to Port Royal and the Palisadoes. It is clear from the literature that sediment failure
was widespread along the southern boundary of the Harbour as well as in deeper water
offshore. With regard to failure, “On the north side of the Palisadoes the sinking was such that
a lagoon formerly separated from the salt water by a beach was covered by the sea. Perhaps
the most conspicuous change of sea level was at the extreme south‐west point of the
Palisadoes at the entrance of the harbour, where a body of several hundred feet in length and
breadth sunk beneath the waters of the ocean”(Fuller 1907). This region of failure rest
immediately adjacent to the current location of the Jamaica Defence Force Headquarters.
Other damage included “Off the south coast the breaking, "bird‐caging," twisting, and burying
of the submarine cable from Bull bay to Yallahs point, indicating great sand‐slides along that
steep sub‐marine slope”(Cornish 1908).Also observed were the twisting of rails and tilting of
buildings such as the Victoria Battery (now known as The Giddy House) in Port Royal by
subsidence(Taber 1920).
The earthquake was followed, on the north coast at least, by a wave from the sea, but it caused
comparatively little damage.(Taber 1920). Tsunami were observed in Kingston Harbour, but
were described as “re relatively small, although large and powerful enough to throw one vessel
up into the mud alongside the dock” in Fuller, 1907.Taber noted that the 1907 event seemed
similar in its effects to the great disturbance of 1692, except with a somewhat lower intensity.
The 1957 Earthquake
There is relatively little descriptive information readily available related to the 1957 event in
comparison to the 1907 and even the 1692 events. The quake shook the island on March 1 of
that year with a Richter magnitude of6.9 (Wiggins‐ Grandison and Atakan 2005). With the
epicentre attributed to a location in Hanover parish (Figure 2). The intensity of the quake was
greatly felt in this part of the island. Consequently, the city Montego Bay received the most
structural damage. However, the effects of the quake were also felt in other parts of the island.
Despite this earthquake occurring more than 100 km from Kingston and of relatively low
magnitude, it triggered sediment failure in Kingston Harbour. For example, The Office of
Disaster Preparedness and Emergency Management reported that a 180m strip of the coastline
subsided (Tortello 2002).
The 1993 Earthquake
In more recent times, a Mw5.4 earthquake rocked Kingston on January 13(Wiggins‐Grandison
1994). The epicentre was near the Wag Water Belt (WWB) (Figure 2), and was the first
indication that WWB may be a source zone for larger Jamaican earthquakes (Wiggins‐Grandison
1994). As such, the 1993 event shed new light on the risk posed by seismic activity (especially to
Kingston) generated on the island itself, rather than offshore or east along the EPGF (Wiggins‐
Grandison 1994).Similarities in damage patterns to the 1907 event include the generation of
submarine landslides resulting in cable breaks, as well as pattern of damage similar to, but less
severe than the 1907 earthquake (Wiggins‐Grandison 1994).
Summary of slope failure near Kingston associated with historical earthquakes
It is clear from historic accounts that slope failure events occur in Kingston Harbour during
large to moderate‐sized earthquakes near Jamaica. Understanding the depositional properties
of these sediments and their inherent strength provides key insight into if, how, and when
slope failure occurs in Kingston Harbour. Here we analyse sediments physical properties along
Port Royal and Palisadoes sand spit to assess the strength of sediments in this region, and the
probability of failure. We compare our results to historical studies and develop models to
assess the probability of failure at Port Royal and the surrounding area in the future.
II A Sediment Stability Study for Port Royal: Background Information.
Our analysis looks at sediment stability at the southern edge of Kingston Harbour, near the
town of Port Royal. We study this site because (1) it has a long (>300 year) history of repetitive
slope failure events, (2) it is of economic and strategic importance to Jamaica as the site rests at
the entrance to Kingston Harbour and is the location of the headquarters of the Jamaican
Defence Force Coast Guard, and (3) the sediment character and regional geology of Port Royal
are generally similar to the sediments found along the entire Palisadoes sand spit, so we can
apply our results near Port Royal to other locations across the southern edge of the Harbour.
The Palisadoes tombolo, on which is sited the town of Port Royal and the Norman Manley
International Airport, is made up of discontinuous coral reefs connected by sands and gravels
deposited by longshore drift from the estuaries of the Hope, Cane, Yallahs and Morant Rivers to
the east of Kingston(Burke and Goreau 1966) (Figure 1).Port Royal was an island in the middle
of the 17th century, the connection being completed prior to 1692 (Taber 1920). Modern
geologic investigations show that the spit beneath Port Royal is made of loose, water‐saturated
sand to a depth of about 20m; below this lie gravels and occasionally a buried reef (Burke
Reference). Due to the actions of the generally east‐west trending longshore drift in
combination with successive incidents of failure, the Port Royal coastline is quite dynamic. Since
1991, there has been sediment accretion of approximately 50m in some cases on the Port Royal
stretch (Figures 4 and 5). This new material is mostly unconsolidated and is therefore more
susceptible to failure.
Figure 4 Evolution of Port Royal since 1873
Port Royal Features Survey Lines
Roads
Figure 5 Sediment accretion in Port Royal since 1873
Data Collection
Determining the sediment strength and the conditions for failure to occur along Kingston
Harbour requires understanding the physical properties of sediments at the site. During January
2013 we spent 10 days collecting coastline sediment, marine sediment core, and single channel
active‐source seismic data to constrain the physical properties of sediment in and around the
harbour. The seismic survey consisted of collecting 4.0 kHz chirp data on 16 NW‐SE trending
cross lines in Kingston Harbour and around the Port Royal, Jamaica. We use the data to
constrain regional slope and subsurface sediment consistency and structure offshore.
Sediment collection/analysis on the beach
0 50 100 150 200 250 300 350
1
2
3
Sediment Accreted (m)
Survey Line
Sediment Accretion in Port Royal1873‐2012
1873‐1968
1968‐1991
1991‐2012
Beach sediments were analysed in order to obtain estimates for grain size, grain roughness,
level of sorting, and sediment angle of repose. The aim of this analysis was to gain an
understanding of the physical nature of the beach, the variation in the measured parameters,
and to constrain the strength of the sediments.
We acquired multiple sediment samples at 16 stations along the beach along the southern and
western edge of the Palisadoes sand spit (Figure 6). For our analysis, we define four zones (A,
B, C, and D), where noticeable changes exist in sediment character and geomorphology. The
beach face and swash zone were demarcated as Zone A. Zone B lay between the swash zone
and high‐tide mark, which included the berm crest‐coarse sediments. Zone C extended from
the high tide mark to the tree line. Zone D lay further inland beyond Zone C. The width of each
zone was measured at each stop and recorded. Grain size analysis cards were referenced in
order to characterize the zones based on the grain size, grain roughness and level of sorting.
Photos of each zone were also taken. Angles of repose were measured by slowly pouring the
sand by hand to form sand piles. The height and width of each pile was then noted in the field.
The results of the field analysis are shown in Appendix A. 12 of the samples were collected for
further angle of repose analysis and four were collected for density and porosity
measurements. The 4 density‐porosity samples were collected in Zone A in short (~6cm) long
sections of 6.67cm inside diameter core tubes. These samples were collected with push‐cores in
a manner best preserving the porosity structure of the sand. Specifically, after digging a pit into
the sand and applying the push core, the tube was then dug out and capped with a core cap.
Sand samples collected in the field were analysed in the lab for bulk density, grain density,
porosity, and error analysis for the angle of repose. The standard procedure for each analysis
can be found in Appendix B.
Figure 6 Location of Sediment sample collection sites and Survey Lines
Beach Slope Survey
To determine variations in beach slope along the western Palisadoes, we conducted a beach
survey along the coast near the town of Port Royal (Figure 6). This, combined with offshore
seismic imaging provided direct insight into the beach slope angle in this area of the Harbour.
Horizontal and vertical distances between points were measured using the Electronic Total
Station GTS‐220 (ETS). The ETS was used to automatically measure the distance between the
two by reflecting a laser off the prism on the meter stick and back to the ETS. Using the slope
distance (the hypotenuse), the horizontal distance and vertical distance were calculated and
recorded. GPS coordinates at each stop were also recorded. The ETS was positioned at a high
point from sea level and a marker was used to record changes in slope with lateral offsets every
5‐10 m on average. The slope of the coast was measured approximately every 250 meters along
the coast line. Sea level is typically within a half a meter of where the waves break at that time
of year.The ETS accuracy was determined to be within ±2mm, however, uncertainties in sea
level associated with tides and down‐slope positioning results in a vertical uncertainty of +/‐
0.25 m. GPS position uncertainty also averaged +/‐ 5 m. We account for these uncertainties in
our slope measurements for the beach and calculate slope angle using simple trigonometry
between points.
4. Sediment strength: Mohr Circle Analysis
We constrain the sediment strength and stresses necessary for failure at the western
Palisadoes sand spit using a simple sediment mechanics approach, based on mohr circle
analysis
We use Mohr circle analysis to determine the maximum stress the sediment can sustain before
mechanically failing. To assess whether failure occurs at a given site using Mohr circle analysis,
we need to know three things: the maximum principle stress (acting on a point, the
minimum principle stress ( acting on the same point, and the differential stress ( ‐ )
required to cause sediment failure. Experimental results by Byerlee demonstrate that we can
characterize the differential stress necessary for failure as a failure envelope defined by the
following mathematical formula:
τ = σ tan φ + c
Where τ= shear failure required for failure for a given friction angle and normal stress, σ=total
stress, tan φ= the coefficient of friction and c= cohesion.
We can calculate the coefficient of sliding friction directly from angle of repose measurements
(Fossen 2010). Mohr circles lying below the Mohr failure envelope represent a stable condition.
Failure occurs only when the combination of shear and normal stress is such that the Mohr
circle is tangent to the Mohr failure envelope.
With the consideration of possible pore fluids, the concept of effective stress comes into play.
Thus σ1 becomes:
σ ′
Where σ ′ is effective stress, density, ρ, acceleration due to gravity, g, and depth, d, and Pf pore fluid pressure.
For Sigma three we use the approach outlined in Engelder and Fischer (1994) such that:
′1
1 21
Where ν is the drained Poisson ratio, α is the Biot coefficient of effective stress and Pp is the
pore fluid pressure. Poisson’s ratio is the ratio of radial contraction to axial elongation. The Biot
coefficient describes how much a change of pore pressure also changes the bulk volume while
applied stress is held constant (source). A Biot coefficient of .86‐.93 was calculated using:
Ksat =Kframe +Kpore (Nolen‐Hoeksema 2000)
where K and¹are the bulk and shear moduli and the subscripts“sat,” “frame,” and “pore” refer
to the undrained saturatedrock, drained (dry or saturated) framework, and fluid‐filledpore
space. The termKpore is the difference between the undrained and drained bulkmoduli that
results from the presence of fluid with a nonzero bulk modulus. Kdry 50%‐4.9x108 Pa , Kdry
36%‐7.6x108 Pa, Ksat 50%‐ 4.81 x109 Pa, Ksat 36%‐ 6.35 x109 Pa, Ksolid ‐ 50x109 Pa.
For our Biot Coefficient analysis, we assume porosity values range between 35 and 65%,
consistent with measurements and other regional studies of sands (Hamilton 1970).This value
corresponds with those presented in Gommeesen, et al. 2007, that found higher Biot
coefficients corresponded to low cementation factors. For all of this analysis, we assume
hydrostatic conditions since sediments are highly porous sands.
For this analysis we calculated the angle of repose using the premise that for a sand pile to fail,
the tangential stress across the pile (τ) must be greater than the forces holding the pile
together, which are the normal compressive stress due to gravity (σ) and the internal friction
coefficient between sand grains (κ) (see Appendix) This concept is expressed by the relationship
necessary for failure: τ>κσ. To find the point at which the sand pile would fail, it was necessary
to determine the τ that would overcome the calculated κ and σ. Additionally, we calculated κ
from direct measurements where κ=tanθc and θc is the critical angle of wet sand that we
measured directly using the methods of Mason et al., 1998 and Halsey et al. 1999.
Assessing the Factor of Safety at Port Royal:
A. Pseudostatic inertia slope stability analysis
As an initial, first‐order approach for analysis of slope stability, we use a pseudostatic inertial
method. This method assumes that material retain their shear strength during failure. Although
this is unlikely during failure at Port Royal since liquefaction frequently occurs at this site during
large earthquakes, this approach provides a strong‐case end‐member assessment for sediment
strength and failure probability at Port Royal. Later, we conduct a weak‐case end‐member
assessment for sediment strength and slope failure probability by accounting for the high
likelihood of liquefaction and shear loss during ground shaking and failure. Determining the
probability of slope failure at Port Royal using a pseudostatic inertia approach requires an
assessment of the factor of safety (FS) for the sediments at the site. The factor of safety for
simple pseudostatic analysis is defined as the following:
Where is the resisting force of the sediments to failure and is the driving force (this could
be gravity plus any other force, such as the force generated by an earthquake) along any given
failure plane. Note that an FS value greater than 1 implies a stable slope, whereas a value less
than one is unstable since driving forces exceed resisting forces. We use the 2D simplified
Bishop Method (Bishop, 1955) to calculate the Factor of Safety at Port Royal. This method
assumes failure occurs along a block rotating on a cylindrical slip surface. To calculate the
resisting and restraining forces on this block, the block is broken up into a series of vertical
slices. We calculate both the resisting and restrain forces for sediments at Port Royal using the
following Bishop’s Method equations:
, /
and
∑
Here, n is the slice number, is the effective cohesion of the sediments, W is the weight of
each slice, b is the width of each slice, u is the fluid pressure at the base of each slice, , is the
effective internal angle of friction, and is the angle between the horizontal and the base of
the slip plane surface. Note that the Simplified Bishop method assumes no interslice shear
forces. The factor of safety, FS, appears on both sides of the equation, and is therefore solved
iteratively, and ultimately converges on a single value.
Monte Carlo Simulations using the Simplified Bishop’s Method at Port Royal.
Given that a wide range of both (1) potential slope failure surfaces and (2) sediment physical
properties exist, we solve FS values with the Simplified Bishop’s Method using an iterative
Monte Carlo approach. From this, we assess what the lowest FS might be at Port Royal
assuming pseudostatic inertia slope stability conditions. We define the shape of the slope for
the Simplified Bishop’s Method analysis from regional land and sea surveys. Our analysis
indicates slopes ranging between 5‐15 degrees near Port Royal. To calculate FS values, we
therefore range the slope between these values. For determining weight, our analysis indicates
sediment grain densities average ~2700 kg/m3, sediment porosities ranging from 35‐55%, with
sediments consisting of at least 90% sand. The analysis includes three different sedimentary
zones: the upper unconsolidated sandy zone, a vadose zone where we assume an average
water content filling ~50% of the pore space, and a saturated zone where we assume water fills
100% of the pore space. For this analysis, we assume water is incompressible and maintains a
constant density of 1027 kg/m3. As a maximum (strong) end‐member case for FS, we assume
hydrostatic pressure conditions both before and during failure. Based on our observations, we
assume sediment cohesion is low, and typically ranges between 0 to 10 kPa for slightly
cemented sand.
The analysis using the Simplified Bishop’s method assumes a constant slice thickness of
0.125 m. For different failure plane solutions, the analysis (which we solve for iteratively using
numerical techniques) systematically sweeps through 3 million different failure plane solutions
where radii and associated circumference values increase at a given slide origin location. The
origin itself also varies, and iteratively moves at 0.25 m intervals. As a result, possible failure
planes are as small as 1 meter long and as large as 300 m long. We then use a Monte Carlo
approach to iterate through an additional 3 million FS solutions where we vary randomly
sediment characteristics above with depth, calculating a factor of safety for each iteration, and
ultimately, save the lowest 10 factor of safety values at the site for further evaluation.
Results from this strong‐case scenario analysis assuming pseudostatic inertial slope
stability conditions indicate a minimum FS of ~2.04 exists at Port Royal, implying the region is
very stable under normal gravitation conditions if sediments maintain their shear strength at
this site. Under the conditions described in the pseudostatic model, our analysis suggests
failure will preferentially occur in the shallowly buried, unsaturated sediments before failure
occurs in the submarine environment (Figure 7).
Figure 7 Port Royal Stability Model. The green lines on the cross‐section show likely failure plains at Port Royal during an earthquake. The analysis implies unsaturated sediments will likely fail first.
As we demonstrate below, this result is generally different than what we commonly
observe during failure at Port Royal in which sediment failure often occurs both along the shore
edge and in the submarine environment.
Defining the earthquake necessary to trigger pseudostatic slope failure at Port Royal.
The FS value of 2.04 is what we calculate assuming no ground shaking necessary for failure at
this site. Nonetheless, we can use this value to make a rough estimate of the earthquake
necessary to trigger failure at Port Royal assuming pseudostatic inertial slope failure conditions.
To estimate this value, we re‐arrange our factor of safety calculation and assume a FS value of
1—the critical value necessary for failure. For the resistive force, we assume the conditions that
yield our minimum factor of safety value of 2.04. We then solve for the driving force, ,
necessary to trigger failure. By dividing through by the slide mass, M, we then calculate the
approximate peak ground acceleration (PGA) necessary for an earthquake to trigger failure:
1 _ . / . /
./
./
Based on our Monte Carlo solution for the minimum FS value of 2.04 for , we calculate a PGA
value of ~0.25 g +/‐ 0.05g, where g is the gravitational acceleration of mass on earth (9.81
m/s2). This result implies that according the best‐case (strong‐case) scenario using the
pseudostatic inertia slope stability analysis, any earthquake capable of producing >0.25g
ground acceleration at Port Royal will trigger slope failure.
Whether an earthquake triggers ~0.25g of ground acceleration is dependent upon
multiple factors, including fault orientation, earthquake depth and location, fault type, and
regional geology. To first order, earthquake magnitude and earthquake distance are the two
most significant factors defining earthquake ground acceleration for shallow thrust or strike‐slip
earthquake events—the earthquakes we typically observe in Jamaica (e.g. Wiggins‐Grandison
2004; Campbell and Bozorgnia, 2008). Multiple studies provide first‐order estimates for the
amount of ground acceleration an earthquake generates for a given earthquake magnitude and
distance from the epicentre. Here, we use the analysis of Campbell and Bozorgnia (2008) to
assess what earthquake magnitudes and distances are required to trigger failure at Port Royal.
Results from this analysis imply that an earthquake moment magnitude as low as Mw 5,
if it occurs within three kilometre of the site, would trigger failure (Figure 8).
Figure 8. PGA required for failure at Port Royal‐ Area highlighted in green denote the strong‐case scenario
Larger earthquakes can occur at greater distances and still trigger failure. For example,
Mw 6 and 7 earthquakes could occur as far as ~10 km and ~14 km away respectively and trigger
failure. Importantly, we again note that these first‐order results represent a best‐case (strong
sediment) scenario, where sediments maintain shear strength during failure, and no
liquefaction occurs at the site. Even in this instance, the analysis indicates slope failure will
likely occur when moderately large earthquakes occur near Kingston.
Liquefaction slope stability analysis (The Weak‐Case).
Multiple historical accounts of liquefaction at Port Royal during historic earthquake
events indicate that sediment shear strength will not likely be maintained during failure and
that significantly smaller earthquakes at greater distances away than those expected for the
pseudostatic case can trigger failure. As a result, liquefaction slope stability analysis, as
opposed to Pseudostatic inertia slope stability analysis, represents arguably a more
accurate approach for assessing slope stability at Port Royal. We define the FS for
determining liquefaction as the following:
Where CRR is the cyclic resistance ratio of the in situ sediments at Port Royal and CSR is the
cyclic stress ratio caused by an anticipated earthquake at Port Royal. The CSR is dimensionless
number that represents an average maximum value of shear stress earthquake shaking
produces divided by the total vertical stress of the sediment column (e.g. Day et al., 2012). The
CRR is estimated from empirical relationships and experimental studies that determine the
typical resistance of different sediment types at different depths to a given shear stresses.
We constrain the Cyclic Resistance Ratio from our understanding of shear wave
velocities in unconsolidated, high permeability marine sands. Specifically, we use the results
from Hamilton (1979) in saturated sands and the results of Bachrach et al. (2000) to constrain
shear wave velocity in unsaturated to partially saturated beach sands with depth at Port Royal.
We follow the approach of Sykora (1987) and Roberson et al. (1992) to calculate the corrected
shear wave velocity with depth for sediment strength analysis. Finally, we use standard
empirical relationships (Andrus and Stokoe 2000) to estimate the CRR for a given corrected
shear wave velocity with depth at the site. For a detailed description of the empirical method
used to solve for CRR, I refer the reader to Chapter 6 of Day’s Geotechnical Earthquake
Engineering Handbook, Second Edition, and in particular, figure 6.10 that shows the
relationship between measured CRR values and shear wave velocity in sediments.
CSR, the shear generated by specific ground acceleration from an earthquake, is
dependent on several parameters, including the depth of the sediments, sediment effective
stress, confining pressure, and the amount of ground acceleration generated by a specific
earthquake ground motion. CSR can be solved directly via the following empirical equation
(Seed and Idriss, 1971; Kayen et al., 1992):
0.65 1 0.12
Where, z is the depth of the, is the total vertical stress, , is the vertical effective
stress, is gravitational acceleration, and PGA is the peak ground acceleration experienced at
the site. For our analysis, we calculate vertical stress assumes hydrostatic fluid pressure
conditions, and measured densities combined with standard density‐depth profiles sandy
marine environments (Hamilton et al., 1979).
Results for the Liquefaction Factor of Safety Analysis at Port Royal.
We calculate the Liquefaction factor of safety (FS) in 1D by running the model for a
series of different ground acceleration values ranging from 0.05 g to 0.3 g. Results of this
analysis indicate that liquefaction will occur at this site for ground acceleration values as low as
0.09 g (Figure 8), where liquefaction is expected to occur at 6 to 12 m below the surface. The
higher the PGA, the more significant the liquefaction, with nearly the entire sediment column
liquefying to limestone bedrock ~18 m below sea level when PGA exceeds 0.2 g. It is important
to note that these results are likely conservative estimates because they are 1D and fail to
account for the 5‐15 degree slope that exists along the coast line near Port Royal. The slope will
further reduce the stability of the system by several per cent (Seed and Harder, 1990).Future
2D analysis should incorporate these effects.
Figure 9 Factor of safety for liquefaction for sediments near Port Royal.
Implications for liquefaction at Port Royal.
The liquefaction Factor of Safety analysis at Port Royal suggests relatively minor ground shaking
can cause potentially significant liquefaction at this site. Applying results of the 1D study to
projected PGA values generated by earthquakes at a given distance indicates magnitude >7
earthquakes as far as ~40‐50 km away could trigger failure at port royal. The Wag Water and
EPGF system, however, are located only 20‐30 km from Kingston. Therefore, a large earthquake
in this region will likely trigger significant liquefaction in Port Royal. The analysis also suggests
that Mw 5‐6 event within 10s of kilometres could also trigger significant liquefaction at this site.
Addressing the probability of future liquefaction at Port Royal.
Distribution of earthquakes with respect to magnitudes exhibits scale invariability (Gutenberg
and Richter 1954). This distribution is described in the Gutenberg‐Richter relationship. The
Gutenberg‐Richter Law (GR) is an empirical relation between the magnitude x of some seismic
event, and N(x), the number of events with magnitudes higher than x. Ishimoto and Iida (1939)
and Gutenberg and Richter (1944) proposed the following linear relation:
log10 N(x) = a – bx
Which is also referred to as the Gutenberg‐Richter (G‐R) magnitude‐frequency relationship
(MFR). The constant b, which is typically close to 1, is a tectonic parameter describing the
relative abundance of large to smaller shocks(Bhattacharya, et al., 2011).As an example of the
Gutenberg‐Richter magnitude‐frequency relationship, in general, for every one magnitude 4.0
earthquake event, there will be 10 magnitude 3.0 quakes and 100 magnitude 2.0 quakes. A b‐
value significantly different from 1.0 may suggest a problem with the data set; e.g. it is
incomplete or contains errors in calculating magnitude (Bhattacharya, et al., 2011).The constant
‘a’, the intercept of the line equation above, is a measure of the regional level of seismicity.
The dataset used for this Gutenberg‐Richter analysis incorporates recorded seismicity in
Jamaica over the period from 2000‐ 2011.Though the time span of the catalogue was not larger
than the return period of the largest expected event (> Mw 7), the results determined from
graphing the data available provide a record of 1073 earthquakes, and these earthquakes
provide a large number of events that we can use to asses regional earthquake probabilities. A
threshold magnitude of at least Richter Mw 3 was decided on in order to minimize any skew in
the analysis. Earthquakes below a Mw 3 threshold did not follow the standard MFR, and this is
primarily due to limited detection thresholds of the seismic instruments below this magnitude).
Thus, In order to guarantee the best completeness of data possible, only earthquakes of greater
than or equal value to the threshold were used from the dataset.
Figure 10. 25 km buffer delimited around Port Royal for EQ analysis
Our results correlate well with the Gutenberg Richter model. According to the data available,
there have been 42 earthquakes between magnitudes 3‐3.9 and 3 earthquakes between
magnitudes 4 and 5 within a 25 km radius of Port Royal over the time span (Figure 10). The
WWT, BMB and Kingston area account for the vast majority (approximately 48%) of this activity
over the time span investigated. This gives a Gutenberg‐Richter b‐value of 1.15, very close to
the expected value of unity (Figure 10).
Figure 11Gutenberg‐Richter plot for BMB/WWT Kingston area
For the probability analysis, the data was further sub‐catalogued by regions. The areas of the
Wag Water Trough (WWT), the Blue Mountain Belt (BMB) and the Kingston area (~10km
around the capital) were considered most relevant. In addition, all earthquakes within a general
25km perimeter of Port Royal itself were examined. The WWT, BMB and Kingston areas are the
most prone earthquake activity on the island. In recent times, the strongest events have also
been generated in this region. It is likely therefore that an earthquake that would trigger failure
in Port Royal would originate in this region.
Within the BMB/WWT/ Kingston zone 67 events above the Mw 3 threshold were recorded over
the time span. This averages at 5.58 events per year. Applying the Gutenberg‐Richter law we
can then estimate that the return period for Mw 5 events is approximately 18years, with 180
years for Mw 6 events. The most recent magnitude 5 event generated in this zone was recorded
in the 1993 Mw 5.5 event. When applied to the 25km sub‐ zone around Port Royal, results show
a return period of approximately 29 years for Mw 5 events and 286 years for Mw 6.The most
recent magnitude 5 event generated in this zone was recorded in 1993.
This would suggest that the Kingston/Port Royal area is due for an earthquake in the Mw 5
range in the near future (based on averages, it was expected to occur around 2011). The reality
is that typical 2‐sigma uncertainty in earthquake recurrence interval is large‐‐ nearly 50% of the
y = ‐1.146x + 5.061
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
log
10N(x)
Earthquake Magnitude Mg
Gutenberg‐Richter plot for BMB/WWT Kingston area
recurrence interval itself (Savage et al., 1992)‐‐so we can say with greater (95% confidence) that
moderate Mw 5 earthquake, capable of causing potential liquefaction and moderate
destruction near Kingston is probable within the next decade. The probability of a much larger
Mw 6 earthquake is significantly lower, since the recurrence interval is ~286 years, and the last
event in this region may have been only 106 years ago. My analysis indicates events like the
1692 and 1907 earthquake should occur again near Kingston sometime within the next ~180
yrs, but the uncertainty in this timing is high(+/‐150 years for 2 sigma).
8. Final Summary and Conclusions.
Jamaica and the city of Kingston in particular vulnerable to large strike‐slip and thrust
earthquakes. The city is also particularly susceptible to landslides and liquefaction due to its
positioning on an alluvial fan. Based on our Monte Carlo solution for the minimum FS value of
2.04 for , we calculate a PGA value of ~0.25 g +/‐ 0.05g. This result implies that according the
best‐case (strong) pseudostatic inertia slope stability analysis, any earthquake capable of
producing >0.25g ground acceleration at Port Royal will trigger slope failure. Results from this
analysis imply that an earthquake moment magnitude as low as Mw 5, if it occurs within three
kilometre of the site, would trigger failure. The liquefaction Factor of Safety analysis at Port
Royal suggests relatively minor ground shaking can cause potentially significant liquefaction at
this site. Therefore, a large earthquake in this region will likely trigger significant liquefaction in
Port Royal. Probability analysis indicates a return period of 18‐29 years for the area for Mw 5
events. This would suggest that the Kingston/Port Royal area is due for an earthquake in the Mg
5 range in the near future. This study indicates such moderate earthquake events will cause
liquefaction and associated damage along the Palisadoes on human time scales (with an
occurrence rate of perhaps 2‐3 times per century).Our hope is that this study will be used in
Jamaica for future hazard mitigation and city planning.
9. Acknowledgements
This work was funded fully through gracious support of the Society of Exploration Geophysics’
Geoscientists without Borders program. Matching support for additional data collection and
travel was kindly provided by Southern Methodist University’s Institute for the Study of Earth
and Man. Data collection was completed by several SMU and UWI students who worked
tirelessly in the field during the winter of 2010. The study was lead and supervised by Drs. Matt
Hornbach (SMU) and Lyndon Brown (UWI).
