XXVI Reunión Nacional de Mecánica de Suelos
e Ingeniería Geotécnica
Sociedad Mexicana de
Ingeniería Geotécnica, A.C.
Noviembre 14 a 16, 2012 – Cancún, Quintana Roo
Field Gmax relationships for Bay of Campeche clay
Relaciones del Gmax de campo para la arcilla de la Bahía de Campeche
Victor M. TABOADA1, Kuat C. GAN2, Diego CRUZ3, Procoro BARRERA3, Esteban ESPINOSA4 and Daulet
CARRASCO4
1NGI,
Inc., Houston, Texas, USA.
Marine Geosciences, Inc., Houston, Texas, USA.
3Instituto Mexicano del Petróleo, México, D.F., México.
4Petróleos Mexicanos, Ciudad del Carmen, Campeche, México.
2Fugro-McClelland
RESUMEN: Uno de los más importantes parámetros de suelo requeridos en el análisis de los pilotes de las plataformas
marinas fijas sometidas a carga lateral sísmica es la velocidad de onda cortante (V s) del suelo. Debido a que se realizan
mediciones in-situ de Vs en un número limitado de sitios de plataforma, existe la necesidad de desarrollar correlaciones
para estimar Vs basándose en propiedades básicas del suelo. Para cubrir esta necesidad se estableció una base de
datos con mediciones in-situ de Vs y propiedades básicas de la arcilla. Se recolectaron datos de 11 investigaciones
geotécnica costa afuera realizadas para PEMEX para el diseño e instalación de plataformas marinas fijas en la Bahía de
Campeche. La base de datos se diseño para desarrollar correlaciones empíricas entre el módulo de rigidez a pequeñas
deformaciones (10-4%) in-situ (Gmax) y la resistencia al corte no drenada, esfuerzo vertical efectivo, contenido de agua,
relación de vacíos y relación de preconsolidación, usando análisis de regresión simple y de regresión múltiple. Se
recomiendan las correlaciones empíricas desarrolladas mediante análisis de regresión múltiple para proporcionar un
medio de determinar la mejor estimación de Gmax o Vs de arcillas cuando no existen mediciones in-situ de Vs.
ABSTRACT: One of the most important soil parameters required in the analyses of the piles of oil platforms subjected to
lateral earthquake loading is the shear wave velocity (Vs) of the soil. Since in-situ measurements of Vs is part of the scope
of work of a limited amount of platform sites, there is the need to develop site specific correlations to estimate Vs based on
basic soil properties. To cover this need a database with in-situ measurements of Vs and basic soil properties of clay has
been established. Data were collected from 11 offshore geotechnical investigations performed on behalf of PEMEX for the
design and installation of fixed offshore platforms in the Bay of Campeche. The database was tailored to developed
empirical correlations between the in-situ small-strain (10-4%) shear modulus (Gmax) and undrained shear strength,
effective vertical stress, water content, void ratio and overconsolidation ratio, using simple regression analyses and
multiple regression analyses. The empirical correlations developed using multiple regression analyses are recommended
to provide a mean of determining the best estimate Gmax or Vs in clay when in-situ measurements of Vs are not available.
1 INTRODUCTION
1.1 Background
The Bay of Campeche is located in the large bay
comprising the southern portion of the Gulf of Mexico
between the Yucatan Peninsula to the east, the
Isthmus of Tehuantepec to the south, and the coast
of Mexico at Veracruz to the west. The Bay of
Campeche is limited to that section enclosed
approximately by 91o W. Longitude on the east to
95o W. Longitude to the west and 20o N. Latitude on
the north to the Mexican coast on the south, as
indicated by the rectangular area in Figure 1.
The Bay of Campeche covers an area of about
15,540 square kilometers, and is the largest oil field
in Mexico which has prompted an extensive
installation of shallow water fixed-pile platforms.
The oil platforms installed in the Bay of Campeche
must be designed against earthquake loading since
the piles can be subjected to large seismic lateral
loadings. The dynamic structural analyses of the oil
platforms require acceleration time histories or
acceleration spectra that already include the soil
amplification of the earthquake motions. One of the
most important input dynamic soil properties of the
seismic response analyses performed to evaluate
the soil amplification is the small-strain shear
modulus Gmax.
Although, there has been important advances in
laboratory testing to obtain the small-strain shear
modulus (less than 0.0001 percent) Gmax, the
adverse effect of unavoidable sample disturbance
and reconsolidation, as well as difficulty in
quantifying the aging effect on Gmax, renders in-situ
shear wave velocity measurements the currently
SOCIEDAD MEXICANA DE INGENIERÍA GEOTÉCNICA A.C.
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Field Gmax relationships for Bay of Campeche clay
preferred method for evaluating Gmax in-situ.
Unfortunately, it is not always possible to make insitu measurements of Gmax or shear wave velocity,
Vs, at all investigated locations, and the geotechnical
engineer is left to use empirical correlations
developed mainly for onshore soils with different
geological settings than those of the Bay of
Campeche clay. Thus, to take advantage of the
abundant basic soil properties and in-situ
measurements of shear wave velocity, correlations
between Gmax and basic soil properties are needed
for the Bay of Campeche clay soils.
Regional
correlation
studies
of
in-situ
measurements of shear wave velocity with other
index test or engineering properties of the soils have
been shown to be useful for estimating shear wave
velocity profiles at sites lacking direct in-situ
measurements of Vs. In an effort to establish a
database for the evaluation and modeling of shear
wave velocities of clay soil units in the Bay of
Campeche, data have been collected from offshore
soil investigation performed between 2004 and 2009.
The in-situ shear wave velocity data were
collected from measurements made with downhole
P-S suspension seismic velocity logger. Data from a
total of 22 boreholes at 11 sites in the Bay of
Campeche are incorporated in this study.
Figure 1. Location of the Bay of Campeche area.
1.2 Objectives and scope of work
Collect, analyze and develop a high quality
geotechnical engineering soil properties database
using available site investigation data from the
Bay of Campeche.
Use the database to determine correlations
between index and strength test parameters and
in-situ small-strain shear modulus to aid
geotechnical engineers in obtaining profiles of insitu Gmax specific for the Bay of Campeche clay.
2 GEOLOGY AND STRATIGRAPHY
The Bay of Campeche is an isthmian embayment
extending from the western edge of Campeche Bank
to the offshore regions just east of Veracruz (~96 o W.
Longitude). The Sierra Madre Oriental forms the
south-southwestern border, and the associated
coastal plain is similar to the Texas-Louisiana coast
in the northern Gulf. The bottom topography is
characterized by long ridges parallel to the exterior of
the basin. Salt domes are prevalent in the region,
and the upward migration of salt is theorized to be a
cause of the complex bottom profiles. Similar to the
northern Gulf, large quantities of oil are produced
here, and thick terrigenous sediments predominate.
The surface sediments of the Bay of Campeche
are terrigenous; predominantly clays and silts, which
are transported by abundant streams of the Grijalva,
Usumacinta and San Pedro rivers and the mouth of
the Laguna de Terminos. The terrigenous are
transported and distributed on the seafloor
accompanied with sand. From the mouth of the
Grijalva River, where the movements of the sea are
turbulent is the deposition of uniform fine sand.
Offshore flow behaves like laminated and low speed,
allowing the deposition of sediments from the size of
the clay.
In general, at the seafloor there is a layer of very
soft to soft olive gray clay, with shell fragments with a
thickness ranging from 5 to 25 m. However, there are
areas with presence of granular soil; these areas
almost always correspond to the mouths of the rivers
of the area and surfaces where coral formations
emerge or areas close to the coast where the waters
are shallow. An example of this is the coast located
in front of Ciudad del Carmen, where the seafloor
sediments consist of a dense layer of sand about
10 m thick overlaying a firm to hard clay soil. The
surficial clay layer reaches its largest thickness in the
southwestern part where it reaches 25 m. The
thickness of the clay layer reduces to the Northeast,
allowing the underlying sand to appear superficially
to the edge of the continental shelf.
Another important feature of the stratigraphy of the
Bay of Campeche is that below the sand layer that
underlies the surface clay layer is an alternating
sequence of clays and sands. The former vary from
very firm to hard clays, and the latter are medium
dense to very dense sands.
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TABOADA V. et al.
3 BAY OF CAMPECHE DATABASE
3.1 Introduction
The database contains 11 sites in the Bay of
Campeche, Gulf of Mexico, Mexico where offshore
geotechnical investigations were performed on
behalf of PEMEX as part of geotechnical campaigns
conducted between 2004 and 2010. The water depth
in these sites varied between 14.0 m and 102.3 m.
An overview of the sampling and in-situ testing
performed at these sites is presented below.
The soil conditions at the 11 sites were
investigated by drilling and sampling to a termination
depth of 121.9 m below the seafloor. In addition to
drilling and sampling, piezocone penetration tests
(PCPTs), remote vane tests and P-S suspension
seismic velocity logging were performed.
At each site, the soil investigation was completed
in two combined borings. The first boring was drilled
to allow sampling at close intervals of about 0.9 m
from the mudline to 12.5-m penetration and about
1.5 m from 12.5- to 24.5-m penetration. A second
boring (primary) was drilled to perform sampling,
remote vane testing and piezocone penetration
testing from 3.0-m penetration to the termination
depth of the boring. Following completion of the
drilling, sampling and in-situ testing activities,
downhole P-S suspension seismic velocity logging
was performed in the primary boring from 3.0 m to
121.9 m below the seafloor. In addition, nearseafloor in situ vane tests were performed in the
immediate vicinity of the borings to a depth of 6.1 m
below seafloor.
The following three sections provide details
related to in-situ measurements of shear wave
velocity and a summary of the soil properties
included in the Bay of Campeche database.
3.2 In-situ measurements of shear wave velocity
The 11 sites in the Bay of Campeche contain in-situ
measurements of shear wave velocity every 0.5 m
over the depth interval of 3.0 to 121.9 m below
seafloor using downhole P-S suspension seismic
velocity logger.
The digital P-S Suspension Probe, roughly 8.5 m
in length, contains a seismic source and two
receivers. The receivers, or geophones, are spaced
1.0 m apart from each other and are separated from
the seismic source by a series of isolation tubes. The
whole probe is suspended by an armored, 4conductor cable that serves both to support the
probe and to convey data to and from the recording
device and the laptop, on the surface.
The probe is lowered into the borehole to a
specified depth (a rotary encoder on the winch
measures probe depth), where the source generates
a pressure wave in the borehole fluid. The pressure
wave is converted to seismic waves (P and S) at the
borehole wall. Along the wall at each receiver
location, the P and S waves are converted back to
3
pressure waves in the fluid and received by the
geophones, which send the data to the recorder on
the surface. The elapsed time between arrivals of the
waves at the receivers is used to determine the
average velocity of a 1-meter-high column of soil
around the borehole. A schematic of the P-S
Suspension Logging System is presented on
Figure 2.
Figure 2. P-S suspension logging system.
3.3 Soil properties included in the database
The compiled database contains index and
engineering properties obtained from classification
tests, strength tests and consolidation tests as
indicated below.
The database includes index properties such as
total unit weight, water content, specific gravity, void
ratio and Atterberg limits. And engineering properties
such as undrained shear strength derived from
unconsolidated-undrained (UU) triaxial compression
tests and in-situ remote vane tests, in-situ shear
wave velocity, in-situ small-strain shear modulus, insitu effective vertical stress or effective overburden
pressure estimated from the submerged unit weight,
preconsolidation pressure (or maximum past
pressures) interpreted from the consolidation test
results obtained from one-dimensional incremental
loading test or constant rate-of-strain consolidation
test using the Casagrande (1936) method and the
Work Per Unit Volume Method proposed by Becker
et al. (1987), and overconsilidation ratio (OCR).
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Field Gmax relationships for Bay of Campeche clay
3.4 Summary of database soil properties
Figure 3 to Figure 9 present summary plots for the
combine data set from all sites in the database.
Natural water content (W) range is from 20 to 85%
with a majority of the values being between 40 to
60% (Figure 3). The liquid limit (W L) varies between
30 and 140% with most of the values being 80%
(Figure 4). The plastic index (Ip) falls between 15 and
110% with most of the values being in the range of
50 to 60% (Figure 5).
Figure 6 presents a Casagrande Plasticity Chart
for the data from all the sites. The data show a wide
range of values with most of the data plotting in a
fairly tight band above the A-line and close to the
U-line indicating predominantly high plasticity clay
type of soils. The OCR varies between 1 and 7 with
most of the values falling between 1 and 2.5
indicating that most of the soil samples are normally
consolidated to lightly over consolidated (Figure 7).
Figure 5. Histogram of plastic index of database content.
Figure 6. Casagrande plasticity chart of database content.
Figure 3. Histogram of water content of database content.
The in-situ shear wave velocity (Vs) is in the range
of 75 to 535 m/s with the majority of the values in the
range of 200 to 350 m/s (Figure 9).
Figure 4. Histogram of liquid limit of database content.
The shear strength data is concentrated in two
groups (Figure 8), one with shear strength from 5 to
40 kPa, with most of the values between 20 and 30
kPa, representing the soils near the seafloor,
corresponding to the first layer that occurs in virtually
all the Campeche Sound. In general, these soils are
normally consolidated. The other Group with shear
strength from 50 to 450 kPa, with concentration of
values between 100 and 300kPa, occur in deeper
strata.
Figure 7. Histogram of overconsolidation ratio of database
content.
SOCIEDAD MEXICANA DE INGENIERÍA GEOTÉCNICA A.C.
TABOADA V. et al.
Figure 8. Histogram of undrained shear strength of
database content.
5
where s’o and Gmax are in kPa. Increasing the void
ratio has two effects: (1) the density tot decreases,
which should tend to increase Vs; and (2) the
modulus Gmax decreases, which should tend to
decrease Vs. Their data showed that the decrease in
shear modulus outweighs the decrease in density
and that for fixed s’o, Vs decreases when the void
ratio gets larger.
Hardin and Black (1968) found that equation (2)
originally developed for sand, also gives reasonable
results for Gmax of normally consolidated clays having
void ratios up to 1.5. Hardin (1978) modified equation
(2) to consider clays of high surface activity and high
plasticity index having a void ratio greater than about
1 or 1.5, and also allowed for the stiffening effect of
overconsolidation ratio (OCR). The equation
proposed by Hardin is:
G max 
6,200
OCR k ( o' ) 0.5
0.3  0.7eo2
(3)
where s’o and Gmax are in kPa. The effect of the
plasticity is incorporated in equation (3) via the
exponent k which is a function of the plasticity index,
Ip (k = Ip0.72/50≤0.5). The final more general equation
is provided below (Vucetic and Dobry, 1991):
Figure 9. Histogram of in-situ shear wave velocity of
database content.
4 SIMPLE REGRESSION ANALYSIS
4.1 Background
The direct measurement of the in-situ shear wave
velocity provides the most reliable and certain means
of obtaining the shear modulus at low shear strains
(less than 10-4%) Gmax. It can be calculated as a
function of total mass density (tot) and shear wave
velocity as:
G max   totVs2
(1)
where rtot = gtot/g, gtot = total unit weight, and
g = gravitational acceleration constant = 9.80 m/s2.
Since the total mass density can be estimated with
reasonable accuracy, the shear wave velocity or
shear modulus at low shear strains can essentially
be used interchangeably.
Hardin and Richard (1963) using resonant column
tests on sand illustrated that the main parameters
controlling Gmax are void ratio (eo) and mean effective
stress [s’o=1/3 (s’1+s’2+s’3)] and proposed the
following expression for angular clean sands and
crushed quartz silt:
G max  3,200
2.97  eo 2
1  eo
 o'
(2)
G max  625Fe OCR k ( p a o' ) 0.5
(4)
where pa is the atmospheric pressure in the same
units as Gmax, and Fe is a void ratio function different
for different type of soils. More recently,
Jamiolkowski et al., (1991) have suggested
Fe = 1/e1.3.
The empirical equation (4) was developed based
on laboratory data. It is therefore of interest to
developed similar empirical correlations based on insitu measurements of Gmax (or Vs). Simple regression
analyses are used in this section to provide as a first
approximation expressions for Gmax in terms of one
variable including void ratio, effective vertical stress
and undrained shear strength. Expressions for Gmax
in terms of several variables are presented in the
next section.
4.2
Correlation with void ratio
The void ratio of a soil is related to the water content
by:
eo 
Gs  w 1  w
 tot
1
(5)
where Gs = specific gravity of soil solids, gw = unit
weight of the water, w = water content, and gtot =
total unit weight. The void ratio at a given depth was
computed using equation (5), the measured water
content at the depth of interest, and interpolated
values of Gs and gtot at the same depth, were
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Field Gmax relationships for Bay of Campeche clay
estimated from developed profiles of Gs and gtot
based on measurements made at selected depths.
The effect of void ratio on Gmax is presented on
Figure 10. It is observed that Gmax decreases as the
void ratio increases. The relationship between void
ratio and in-situ Gmax developed through least square
regression analyses to the 243 data pairs (G max
and eo) is:
G max 
1280
exp( 2.162eo )
(6)
where Gmax is in MPa, and the coefficient of
determination (r2) is 0.659. In the above equation
exp(x) is the function ex, where e = 2.718.
4.3 Correlation with in-situ effective vertical stress
The relationship between in-situ effective vertical
stress (s’vo) and in-situ Gmax for all the sites is
presented in Figure 11. The data follow a clear trend
with the Gmax increasing as the effective vertical
stress increases. The least square regression
analyses to the 243 data pairs (Gmax and s’vo) gave
the following relationship:
G max  870( vo' ) 0.832
(7)
where Gmax and s’vo are in kPa. The coefficient of
determination is 0.859, indicating that 85.9% of the
observed variability in Gmax is attributable to s’vo.
Figure 11. In-situ Gmax related to effective vertical stress
(s’vo).
A total of 183 data pairs (su and Gmax) were used
in the development of the correlation between s u and
Gmax. A simple regression analysis of this existing
data yielded the following relationship between su
and in-situ Gmax.
G max  1325S u0.881
(8)
where su and Gmax are in kPa, and the coefficient of
determination is 0.913. The Gmax versus su
relationship is shown in Figure 12.
Figure 10. In-situ Gmax as a function of void ratio (eo).
4.4 Correlation with undrained shear strength
The values of undrained shear strength (s u) used to
establish the correlation with Gmax have been
determined by unconsolidated-undrained (UU)
triaxial compression tests and in-situ vane tests.
Figure 12. In-situ Gmax as a function of undrained shear
strength (su).
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7
5 MULTIPLE REGRESSION ANALYSES
Multiple regression analyses were also conducted in
log-log format to provide power function expressions
for Gmax in terms of several variables. A summary of
the most prominent correlations derived using
multiple regression analyses is presented in this
section.
The relationship with the highest correlation using
three variables was:
G max 942S u0.377 (
 vo'
w
) 0.428
(9)
where Gmax, su and s’vo are in kPa, and water content
(w) in decimal form. The coefficient of determination
(r2) is 0.953, and a total of 183 datasets (Gmax, su,
s’vo and w) were used in the multiple regression
analyses. This equation is recommended to estimate
the in-situ Gmax due to its high correlation and
simplicity, and to the fact that when the
overconsolidation ratio was further added no
improvement in the correlation was attained.
Figure 13 present a comparison between in-situ
Gmax measured in the field with suspension logging
and the expression given by equation (9). In general,
all the predicted values are between the bands of
±50% of the measured Gmax, with most of them
falling in the narrower bands of ±25%.
The following expression was obtained when the
overconsolidation ratio (OCR) was introduced:
G max 815S
0.272
u
(
 vo'
w
) 0.506 OCR 0.181
1183( vo' ) 0.745 OCR 0.360
eo0.613
The trend between measured Gmax and the
expression given by equation (11) is illustrated by
Figure 14. The graph shows most of the predicted
values of Gmax are within ±50% of the measured
Gmax.
(10)
where Gmax, su and s’vo are in kPa, and water content
(w) in decimal form. The coefficient of determination
is 0.959, and a total of 183 datasets (Gmax, su, s’vo, w
and OCR) were used in the multiple regression
analyses.
As observed by comparing the multiple coefficient
of determination between equations (9) and (10),
0.953 versus 0.959, respectively, no improvement or
only marginal improvement is attained if stress
history, in terms of OCR, is included as independent
variable in the multiple regression analysis because
the apparent effect of OCR has already been utilized
to quantify the values of su, s’vo and w.
The expression with the highest correlation
derived without involving the undrained shear
strength was:
G max 
Figure 13. Comparison of measured and predicted Gmax as
a function of undrained shear strength and effective
vertical stress normalized with water content.
(11)
where both Gmax and s’vo are in kPa. The coefficient
of determination is 0.933 and a total of 243 datasets
were used in the analyses. The above expression is
very similar to that obtained by Mayne and Rix
(1993).
Figure 14. Comparison of measure and predicted in-situ
Gmax as a function of effective vertical stress (s’vo),
overconsolidation ratio (OCR) and void ratio (eo).
Multiple regression analyses were also conducted
to provide power function expressions for G max in
terms of cone net resistance obtained from
piezocone penetration tests, and soil properties. The
expressions are presented elsewhere (Taboada et
al., 2013).
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Field Gmax relationships for Bay of Campeche clay
6 APPLICATION OF EMPIRICAL CORRELATIONS
A comparison between measured and predicted Vs
profiles using equations (9) and (11) is presented in
Figure 15 for one site included in the database of the
Bay of Campeche. A good correlation between
measured and predicted Vs in clay is observed
despite the fact that at the site the clay strata are
interbedded with relative thick layers of silty sand.
The second relationship for field Gmax in terms of
s’vo, stress history (OCR) and (eo) is consistent with
the factors known to affect laboratory resonant
column tests.
8 ACKNOWLEDGEMENTS
The
authors
gratefully
acknowledge
the
authorization provided by PEMEX to access the data
collected in the Bay of Campeche and published the
results of this research. Additionally, the support
provided by NGI, Inc. to work on this investigation is
greatly appreciated by Victor Taboada.
9 REFERENCES
measured shear wave velocity profiles for a site with clay
strata interbedded with four layers of dense to very dense
silty sand.
7 CONCLUSIONS AND RECOMMENDATIONS
A database of in-situ Vs measurements with P-S
suspension seismic velocity logger and standard
geotechnical engineering material properties for the
Bay of Campeche clay has been established. The
database allowed the development of several
empirical correlations between field Gmax and basic
soil properties. Two of them are recommended to be
used to determine the best estimate field Gmax or Vs
of the Bay of Campeche clay when in-situ
measurements of Vs at the site are not available.
The first equation presents the relationship
between Gmax and undrained shear strength (su),
effective vertical stress (s’vo) and water content (w).
It is recommended for its simplicity, high coefficient
of determination of 0.953, and because it could not
be improved when introducing the overconsolidation
ratio (OCR).
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