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Hysteresis Behaviour and Energy Dissipation of Niger Delta Soil
under Cyclic Loading Conditions
Gamil M. S. Abdullah
1
, Charles Kennedy
2
, Gul Muhammad
3*
, Abdul Aziz Ansari
4
, Saeed Ahmed
5
,
Omrane Benjeddou
6
1
Department of Civil Engineering, College of Engineering, Najran University, Najran, Saudi Arabia.
2
Civil Engineering Department, School of Engineering, Kenule Beeson Saro-Wiwa Polytechnic, P.M.B.
20, Bori, Rivers State, Nigeria
3,4
Department of Civil Engineering, College of Engineering and Technology, Ziauddin University
Karachi, Pakistan
5
Department of Civil Engineering, DHA SUFFA University, Karachi, Sindh, Pakistan.
6
Department of Civil Engineering, College of Engineering, Prince Sattam Bin Abdul Aziz University,
Alkharj, 16273, Saudi Arabia
*Corresponding Author
DOI: https://doi.org/10.51244/IJRSI.2025.120800100
Received: 05 Aug 2025; Accepted: 10 Aug 2025; Published: 10 September 2025
ABSTRACT
The dynamic properties of soils influence seismic site response and liquefaction susceptibility. The previous
studies mostly worked on effect of natural fiber and synthetic fiber used in clayey soil to investigate its effect
on the dynamic properties of modified soil.This research deepens our understanding of the dynamic behaviour
of Niger Delta soils, which is important for evaluating the region's vulnerability to liquefaction and seismic
response. By combining experimental data with well-validated empirical models for small to medium-shear
strain behaviour in the area's common sandy soils.This study experimentally investigated the behavior of
damping ratio and shear modulus under the effects of confining pressure of sandy soils collected from
Igbogene Town in the Niger Delta region of Nigeria. Undisturbed samples were acquired from boreholes using
thin-walled tubes and consolidated anisotropically under effective stresses of 100, 200, 300, and 400kPa in a
cyclic direct simple shear apparatus as per standards. Shear modulus reduction curves were generated from
hysteretic stress-strain behavior at shear strains ranging from 0.001% to 2%. The data correlated well with
empirical exponential decay models, validating their applicability for Niger Delta region soils. The damping
ratio increased nonlinearly with strain, aligning with trends for liquefiable soils. Empirical equations tied the
pressure-dependent damping behavior to existing models. Results provided input parameters for seismic
ground response analyses. However, wider confining pressure testing would better characterize variability with
depth. This work enhances geotechnical seismic hazard evaluations through validated empirical
characterizations of small to medium-shear strain behavior for sandy deposits prevalent in the Niger Delta.The
findings can be directly used in seismic ground response analysis. These results are expected to improve
geotechnical seismic hazard assessments and provide more accurate evaluations of seismic risk in the region.
Keywords: Soil Dynamics; Shear Modulus; Damping Ratio; Confining Pressure; Liquefaction; Niger Delta
INTRODUCTION
The Niger Delta's complex geology presents unique challenges for soil mechanics, with Akpokodje [1]
emphasizing the importance of understanding sub-soil behavior for loss estimation. The study's focus on soil
hysteresis and energy dissipation under cyclic loads is particularly relevant given the region's seismic activity.
Amini [2] demonstrated the noteworthy impact of confining pressure on dynamic soil characteristics, which
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aligns with this study's approach. The dynamic properties of soils, like damping ratio and shear modulus, are
crucial parameters for evaluating site response during earthquakes [3]. Accurate characterization of these
properties is essential for predicting liquefaction potential and seismic ground motions. While many empirical
and semi-empirical models have been proposed [4], [5], site-specific measurements are still needed to validate
and refine existing models for diverse geological environments.
In Nigeria, the Niger Delta region faces seismic hazards due to active faults, yet limited research has been
conducted on the area's dynamic soil properties. This study addresses this gap by employing cyclic direct
simple shear tests, following best practices [6], to provide valuable data for seismic hazard assessment.
Undisturbed soil samples were acquired from boreholes representing various soil types in the Niger Delta.
Anisotropic consolidation was applied under diverse confining pressures [3], followed by cyclic torsional shear
tests to measure damping ratio and shear modulus at varying shear strain levels. Cyclic load-controlled triaxial
tests were conducted at effective confining pressures of 100-400 kPa [7], with a damping ratio computed using
Dobry et al.'s [8] equation. The study's findings on shear modulus reduction are consistent with established
theories [9] and extend to Niger Delta soil types. The nonlinear damping ratio-strain relationship aligns with
uchowski et al. [10] findings. Bender element tests [11] and resonant column tests offer comprehensive soil
characterization [12].
The focus on sandy soils is particularly relevant, with Thevanayagam [13] highlighting the importance of fines
content and confining stress. The study contributes to seismic risk understanding, supporting Anbazhagan et
al.'s [14] emphasis on site classification. However, it could benefit from examining environmental
implications, considering the oil and gas industry's presence [15].
To quantify the damping ratio, cyclic load-controlled triaxial tests were performed on the consolidated samples
under undrained conditions at effective confining pressures (σ′c) of 100, 200, 300, and 400 kPa. At each strain
level, four load cycles were applied with maximum shear strain (γ) ranging from 0.001% to 2%
logarithmically. Using equation [Eq. 1] from Dobry et al.,[8] damping ratio (ξ) was computed by the
developed hysteresis loop during each cycle.
ξ = (ΔW/4πWE) × 100 (1)
During each loading cycle, ΔW is the energy dissipated and is equivalent to the area bounded by the hysteresis
loop. WE is the energy dissipated during each loading cycle and can be derived from the maximum shear
modulus of soil. Santos et al. [16] developed mathematical models to predict the variation in damping ratios
for various soil types under variable confining pressures and shear stresses.
Shear modulus (G) was calculated by determining the stress-strain curve slope at each strain level for a given
loading cycle.
G = Δτ/γ. (2)
Where Δτ denotes the change in shear stress and γ represents shear strain. The nonlinear relationship between
shear modulus and strain, the data can be normalized using the maximum shear modulus (Gmax) measured at
0.001% strain. This normalization provided a clearer representation of the behavior of the shear modulus. The
normalized shear modulus (G/Gmax) was then adjusted to match the empirical nonlinear curves introduced by
Santos et al. [16]. The foundational equations for modeling how Gmax varies with effective confining pressure
were established by Dobry et al. [8].
The soil behavior at any location can be assessed by accurately determining the dynamic soil properties such
as shear modulus and damping ratio. The importance of these parameters can also be recognized as they help
predict the liquefaction potential and seismic ground motion. Several empirical and semi-empirical models
have been suggested [8], [16]to explain the variation of these properties with confining pressure and shear
strain. Nonetheless, due to the significant inconsistency of soil conditions, site-specific data remains crucial for
refining existing models and ensuring their applicability across diverse geological settings. Previously there are
fewer studies on the dynamic soil characteristics of the Niger Delta region. The present data is insufficient to
fully understand the variation of dynamic properties with depth and confining pressure. The Niger Delta region
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in Nigeria, characterized by active faults, is particularly vulnerable to earthquakes, yet a dearth of research
exists on the dynamic soil properties of its soils. This research study focuses on obtaining undisturbed soil
samples from Niger Delta and evaluating the dynamic properties of soil through cyclic torsional shear tests on
consolidated samples. The ultimate goal of the study is to geotechnical seismic hazard assessments in Nigeria
for the Niger Delta region by comparing the experimental data with the existing empirical models.
EXPERIMENT METHODOLOGY
Site Description and Sample Preparation
The study took place in Igbogene Town, Bayelsa State, Nigeria, positioned between longitudes 15′E and
6°45′E, and latitudes 4°45′N and 5°15′N. Igbogene Town lies within the Niger Delta, a region characterized by
Tertiary and Quaternary clastic sediments, which have accumulated over millions of years through the
deposition of materials carried by the Niger River. These sediments rest unevenly on a bedrock made up of
Cretaceous sandstone and shale. The geological formations in the study area consist of intercalations of sand,
silt, and clay deposited in fluvio-deltaic environments [17]. Specifically, Igbogene Town is underlain by sand
and interlayered sand/silt/clay sediments of the Benin Formation, which covers most of the southern Niger
Delta.
Testing Procedure
Undisturbed soil samples were collected from the site using thin-walled tube samplers with an outer diameter
of 54 mm as per ASTM standard D1587. This sampling procedure preserves the natural on-field structure and
properties of cohesive soils. Samples were extracted at the total depth intervals of 1.50 m from the ground
surface down to a maximum depth of 30.0 m. Special precautions were taken during sampling and
transportation to the laboratory to minimize sample disturbance. The samples were visually classified and
representative samples were selected from each stratum for laboratory testing.
The site is underlain by a sequence of alternating sand, silt, and clay layers deposited in a fluvio-deltaic
environment typical of the Niger Delta. The detailed stratigraphy was not well defined due to the sampling
intervals. However, the soils can be broadly classified as silty soils, clayey soils, and sandy soils based on
visual classification and index property testing. This variety of soil types prevalent at the site makes it suitable
for investigating the effects of soil type and stress state on dynamic properties.
Experimental Setup
To perform the cyclic direct simple shear (DSS) test undisturbed soil samples were arranged to calculate the
dynamic properties of soil. The DSS test was chosen due to its ability to subject soil samples to full reversal
cyclic shear stresses and strains while maintaining constant normal stress, simulating field conditions during
earthquakes.The DSS testing was performed as per American standards (ASTM D6528) using the bender
element system for sample preparation and test execution. Bender elements consist of piezoceramic
transducers that generate and detect shear waves to monitor the shear modulus continuously during the test.
The samples were trimmed to a diameter of 50.0mm and a height of 20.0mm for testing. Porous stones and
filter paper sheets were used at the top and bottom of the sample for drainage.
The samples were first consolidated anisotropically under the desired confining pressures of 100-400kPa with
an increment of 100kPa, selected to represent overburden stresses at different depths. Confining pressure was
applied using a triaxial cell while allowing only vertical drainage. The consolidation duration was 24 hours to
allow complete dissipation of excess pore pressures.
After consolidation, the samples were subjected to cyclic shear loading under undrained conditions. The cyclic
stress-controlled DSS testing consisted of single amplitude load cycles applied at a frequency of 0.10Hz. The
shear stress amplitude was adjusted to achieve target shear strain amplitudes ranging from 10
-4
% to 10
-1
% in
logarithmic increments. At each strain level, at least 10 cycles were applied until a stable response was
achieved. The developed shear stresses and strains were recorded during testing to compute shear modulus and
damping ratio. From the shear stress-strain hysteresis loop during the loading phase, the shear modulus was
determined by calculating the secant modulus. Similarly, the energy dissipated within the loop represents the
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hysteresis energy used to quantify the damping ratio. Tests were terminated when the shear stress exceeded
0.1% to prevent sample failure. The output data of different shear strain levels were then utilized to develop
the shear modulus reduction and damping ratio curves.
RESULTS AND DISCUSSION
This study considered the effect of confining pressure on the dynamic characteristics of soil in the region of the
Nigerian Niger Delta using Bender Element (BE), and Resonant Column (RC) testing. Samples were prepared
carefully to ensure consistency in initial conditions. The results show a good relationship between maximum
shear modulus and confining pressure as studied by Dobry et al., [8]


󰇛
󰆒

󰆒
󰇜
(3)
Where G
ref
is the reference shear modulus at reference confining pressure σ'
ref
and k is the soil-dependent
exponent. All soil samples from the selected location exhibited the same behavior.
As expressed by the eq.[4] because of the proportional relationship between shear velocity (Vs) and shear
modulus, the shear velocity increases with the rise in confining pressure.

(4)
where ρ is the soil's mass density.
The study observed that as confining pressure increased, the minimum damping ratio (Dmin) decreased, which
aligns with previous research by Darendeli [18] and Santos et al. [16]. This is because higher confinement
leads to stiffer soil, reducing its ability to dissipate energy. Empirical models developed in the study accurately
captured the effects of confining pressure on Gmax, Vs, and Dmin for silt samples, making them useful for
evaluating liquefaction potential and seismic analysis in the Niger Delta. Although this research focused on
silt, further studies are needed to explore the dynamic properties of sand and clay in the region for a more
comprehensive understanding of its seismic risks [17].
Impact of a Confining Pressure of 100 kPa on Shear Strain and Shear Modulus:
The effect of confining pressures on the dynamic response of sandy soils in Igbogene Town, Niger Delta was
investigated. DSS tests were performed on undisturbed soil samples collected from boreholes in Igbogene
Town under effective confining pressures (σ′c) of 100, 200, 300, and 400 kPa to represent pressure conditions
at different depths.
Fig. 1: Effect of 100kPa confining pressure on Shear Modulus
0
2
4
6
8
10
12
14
16
0 10 20 30 40 50
Shear Modulus (MPa)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
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The discrepancy of normalized shear modulus

with shear strain was determined from the stress-strain
hysteresis loops developed during DSS testing as per ASTM D6528 standards. As shown in Figure 1 explains
the decrease of shear modulus with increasing shear strain for sandy soil subjected to a confining pressure of
100 kPa. At very small strains < 0.001%), G remained relatively constant. With further increase in strain, G
reduced nonlinearly and followed an exponential decay trend consistent with the findings of Santos and
Correia [16].
The data obtained at 100 kPa was fitted to existing empirical models by Santos et al. [4] to quantify the shear
modulus reduction behavior. A good correlation was observed between the measured data and the model,
validating its applicability for soils in the Niger Delta region under the studied stress condition as suggested for
site-specific soils by Dobry et al. [8]. This confirms the impact of confining pressure and shear strain level on
the shear modulus highlighted in previous studies.
The results provide valuable input for developing shear modulus reduction curves needed in dynamic analyses
like liquefaction assessment and seismic ground response modeling for Igbogene Town [6]. However, testing
over a wider range of confining pressures would better characterize the pressure-dependent behavior, reflecting
field stress variability with depth as indicated by Cubrinovski et al. [19].
Impact of a confining pressure of 100 kPa on Damping ratio:
The damping behavior of sandy soil subjected to a confining pressure of 100 kPa was investigated based on the
energy dissipated per load cycle computed from hysteresis loops using Equation 1 recommended by Dobry et
al. [8]. Figure 2 shows the variation of damping ratio (ξ) with increasing shear strain levels from 0.001% to 2%
obtained from DSS testing.
Fig. 2: Damping Ratio variation at 100kPa.
The damping ratio increased nonlinearly with shear strain as observed in previous studies. At small strains (γ <
0.01%), ξ was minimal (<5%) but rose sharply beyond 0.01% strain. The trend is consistent with the trend
reported for liquefiable soils by Santos et al. [16]. An empirical equation was derived by fitting the 100 kPa
data to existing damping models discussed in Darendeli [18] to define the damping behavior for the sandy
soil.The experimentally validated damping variation with strain and effective confining pressure provide
crucial data for assessing seismic site response and liquefaction potential of sandy deposits in Igbogene Town.
However, additional testing under higher confining stresses is suggested to develop a more comprehensive
pressure-dependent damping characterization [19].
Impact of a Confining Pressure of 200 kPa on Shear Strain and Shear Modulus:
The effects of 200 kPa confining pressure on the dynamic properties of sandy soils from Igbogene Town,
Niger Delta were investigated. Sandy soil samples that had not been disturbed and were taken from boreholes
0
5
10
15
20
25
30
0 10 20 30 40 50
Damping Ratio (%)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
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at effective confining pressures of 200 kPa were subjected to cyclic direct simple shear (DSS) testing
by ASTM D6528 guidelines.
Fig. 3: Shear Modulus of Sandy Soil at 200kPa of Igbogene Town
Figure 3 shows the variation of normalized shear modulus (G/Gmax) with shear strain obtained from DSS
tests. At very small strains < 0.001%), G remained relatively constant as reported in previous studies. With
increasing strain, G reduced nonlinearly and followed an exponential decay trend consistent with the findings
of Santos and Correia [16].The data was fitted to the empirical model proposed by Santos et al. [4] to quantify
the shear modulus reduction behavior. A good correlation between the measured data and the model was
observed, validating the model's applicability for soils in the study area under 200 kPa stress conditions. This
confirms that confining pressure and shear strain influence shear modulus as emphasized by Dobry et al. [5].
Impact of a confining pressure of 200 kPa on Damping ratio :
The damping behavior of sandy soil under 200 kPa pressure was also investigated. Figure 4 depicts the
variation of damping ratio (ξ) with shear strain obtained from DSS testing hysteresis loops using the energy
method recommended by Dobry et al. [5].
The damping ratio increased nonlinearly with strain remaining minimal (<5%) at small strains but rising
beyond 0.01% strain, consistent with trends for liquefiable soils reported by Santos et al. [16]. An empirical
equation was fitted to existing damping models [18] to define the soil's damping behavior, validating the
models.
Fig. 4: Damping Ratio of Sandy Soil at 200kPa of Igbogene Town
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50
Shear Modulus (MPa)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Damping Ratio (%)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
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The results provide input for seismic analyses as emphasized by Idriss and Boulanger [6]. However, testing
over a wider range of pressures is suggested to better characterize pressure-dependent behavior reflecting
variable field stresses with depth [19].
Impact of a Confining Pressure of 300 kPa on Shear Strain and Shear Modulus:
The impact of 300 kPa confining pressure on the dynamic properties of sandy soils from Igbogene Town was
investigated. Cyclic DSS tests following ASTM D6528 were performed on undisturbed samples under 300 kPa
effective stress.
Fig. 5: Shear Modulus of Sandy Soil at 300kPa of Igbogene Town
Figure 5 shows the change in normalized shear modulus (G/Gmax) with shear strain. At very small strains <
0.001%), G remained relatively constant as reported previously. G reduced nonlinearly with increasing strain,
consistent with an exponential decay trend observed by Santos and Correia [4]. The data was fitted to the
empirical model by Santos et al. [4] to quantify shear modulus reduction behavior. A good correlation between
measured and modeled data was observed, validating the model's applicability under 300 kPa stress conditions
as suggested for site-specific soils.
Impact of a confining pressure of 300 kPa on Damping ratio:
Figure 6 presents the damping ratio variation with the shear strain curve obtained from DSS hysteresis loops
using the energy method recommended by Dobry et al. [8]. ξ increased nonlinearly with strain remaining
minimal (<5%) at small strains but rising beyond 0.01% strain, consistent with trends for liquefiable soils
(Santos et al., 2012). An empirical equation fitted the 300 kPa data to existing damping models [18],
corroborating these models.
Fig. 6: Damping Ratio of Sandy Soil at 300kPa of Igbogene Town
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Damping Ratio (%)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
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The results aid seismic analyses as emphasized [6]. However, wider pressure testing would better characterize
pressure-dependent behavior reflecting variable field stresses with depth [19]. The 300 kPa analyses validate
empirical models and add to the understanding of dynamic soil behavior in Igbogene Town.
Impact of a Confining Pressure of 400 kPa on Shear Strain and Shear Modulus:
The impact of 400 kPa confining pressure on the dynamic properties of sandy soils from Igbogene Town was
analyzed. Cyclic DSS tests compliant with ASTM D6528 were conducted on undisturbed samples under 400
kPa effective normal stress.
Fig. 7: Shear Modulus of Sandy Soil at 400kPa of Igbogene Town
Figure 7 depicts a variation of normalized shear modulus (G/Gmax) with shear strain. At very small strains
< 0.001%), G remained relatively constant. G decreased nonlinearly with increasing strain, consistent with an
exponential decay observed by Santos and Correia [16].
The data was fitted to the empirical model of Santos et al. [16] to quantify shear modulus reduction behavior.
A good fit between measured and modeled data validated the model under 400 kPa stress, consistent with
Dobry et al.'s [8] recommendation for site-specific soils.
Impact of a Confining Pressure of 400 kPa on Damping ratio:
Figure 8 shows damping ratio variation with strain from DSS loops using the energy approach of Dobry et al.
[8]. ξ rose nonlinearly with strain, remaining minimal (<5%) at small strains but exceeding 0.01% strain,
aligning with trends for liquefiable soils reported by Santos et al.[16]. The 400 kPa data correlated well to
existing damping models [18], corroborating these relationships.
Fig. 8: Damping Ratio of Sandy Soil at 400kPa of Igbogene Town
0
5
10
15
20
25
30
0 10 20 30 40 50
Shear Modulus (MPa)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50
Damping Ratio (%)
No of Cycles
0.01% Strain
0.1% Strain
1% Strain
2.5% Strain
5% Strain
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The results inform seismic analyses as emphasized by Idriss and Boulanger [6]. Testing over a wider pressure
range would better define pressure-dependent responses reflecting varying field stresses with depth. Analyses
under 400 kPa stress extend understanding of Igbogene Town soil dynamics.
CONCLUSION
The study experimentally characterized the dynamic properties of sandy soils collected from Igbogene Town
in the Niger Delta region of Nigeria under varying effective confining pressures up to 400 kPa. Cyclic direct
simple shear tests were performed on undisturbed samples as per ASTM standards to investigate the influence
of confining stress and shear strain levels on shear modulus and damping ratio.
The shear modulus was found to reduce nonlinearly with increasing shear strain, according by empirical
exponential decay models proposed by Santos et al. (2012). The measured data correlated well with existing
modulus reduction relationships, validating their suitability for the characterization of Niger Delta region soils
at the studied confining stress levels of 100, 200, 300, and 400 kPa. This confirmed the crucial role of
confining pressure and shear strain in controlling shear stiffness, in line with previous research findings.
The damping ratio exhibited an upward nonlinear trend with shear strain, remaining below 5% at small strains
but rising beyond 0.01% strain levels. The damping behavior followed patterns documented for liquefiable
soils. Empirical equations fitted the experimental data and corroborated existing damping models by Darendeli
(2001).
The research provided valuable input for developing shear modulus degradation and damping variation curves
needed in seismic site response and liquefaction evaluations of sandy sequences in the Igbogene Town area.
However, additional testing under a wider confining stress range would better define the pressure dependency
of dynamic properties reflecting varying in-situ stresses with depth.
Overall, the study successfully characterized the small to medium shear strain behavior of sandy soils from the
Niger Delta through cyclic lab testing. The experimentally validated empirical models enhance understanding
of dynamic soil response in the region and aid geotechnical seismic hazard assessments. Further research
incorporating larger samples and a wider range of parameters would build upon these findings.
Credit authorship contribution statement
GMSA: Conceptualization, Methodology, Funding Acquisitions, Writingoriginal draft, Writingreview and
editing.
CK: Conceptualization, Investigation, Data curation, Methodology, Writingoriginal draft.
GM: Formal Analysis, Writingoriginal draft, Writingreview and editing.
MAS: Formal Analysis; Data curation, Writingreview and editing.
ACKNOWLEDGMENTS
The researchers express gratitude to the Deanship of Scientific Research at Najran University for funding this
project.
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