SEMINAR REPORT
TITLE: Effect of anchor geometry on uplift resistance of plate anchor
in sloping terrain
Under the guidance of Dr. Santhoshkumar G
Submitted by
SUJAN MAITY
24GE06004
GEOTECHNICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY BHUBANESWAR
2025
ABSTRACT
Plate anchors are used in various applications including geotechnical and offshore structures
such as floating wind turbines, transmission towers, and mooring systems to to resist uplift
forces. Majority of study was done on the performance of anchor plate in horizontal ground
, limited research is available on their behaviour in sloping terrains composed of purely
frictional soils. This study investigates the uplift resistance of horizontal plate anchors
embedded in purely frictional sloping terrain using three-dimensional finite element
modelling in PLAXIS 3D. The research focuses on how anchor geometry, slope inclination,
internal friction angle of the soil, and embedment depth influence the uplift capacity
horizontal plate anchor. The breakout factor (Nγ) is used as a dimensionless parameter to
represent uplift capacity. The results show that uplift resistance decreases with increasing
slope angle and length-to-width ratio (L/B), while it increases with higher embedment ratio
and friction angle. The failure mechanism changes notably with slope, which leads to
reduced yielding zones and lower resistance. In addition, the shape factor is introduced to
evaluate further how anchor geometry affects pullout capacity and two mathematical
model is establish for predicting the break out factor and shape factor.
Key words: Plate anchors, Uplift capacity, Sloping ground, Breakout factor, Soil failure
mechanism, PLAXIS 3D
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Table of Contents
Introduction ....................................................................................................................................................4
Problem Definition..........................................................................................................................................5
Finite Element Modelling (PLAXIS 3D) ............................................................................................................7
Model Validation ............................................................................................................................................7
Results and Discussion ....................................................................................................................................8
1.Breakout Factor vs. Slope Angle (I) ..........................................................................................................8
2.Breakout Factor vs. Length-Width Ratio (L/B) .........................................................................................9
3.Breakout Factor vs. Friction Angle (φ) ...................................................................................................11
4.Failure Mechanism ................................................................................................................................12
5.Shape Factor (S) .....................................................................................................................................14
summary .......................................................................................................................................................15
References ....................................................................................................................................................15
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Table of figures
Figure 1:Horizontal plate anchor _______________________________________________________________ 5
Figure 2:Plate anchor model in sandy slope. ______________________________________________________ 6
Figure 3.3D finite element mesh _______________________________________________________________ 7
Figure 4:Variation of breakout factor (Nγ ) with slope angle (I) at different embedment ratios for loose
sandloose sand (φ = 30) ______________________________________________________________________ 9
Figure 5: Variation of breakout factor with length-width ratio (L/B) for different slope angles, friction angles,
and embedment ratios for loose soil (φ=30),H/B=2 _______________________________________________ 10
Figure 6:Variation of breakout factor with length-width ratio (L/B) for different slope angles, friction angles,
and embedment ratios For loose soil (φ=30),H/B=5 _______________________________________________ 11
Figure 7:Variation of breakout factor with friction angle (φ). ________________________________________ 12
Figure 8Contours of displacement for a square anchor at H/B =5 and φ =40◦when (a) I =0◦ _______________ 13
Figure 9:Contours of displacement for a square anchor at H/B =5 and φ =40◦when (c) I =30◦. _____________ 14
Figure 10:Variation of a shape factor with slope inclination angle at H/B =5 and φ =40◦. _____________15
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Introduction
Plate anchors are the flat plate like structure used to resist uplift forces in various structures
such as offshore platforms, floating wind turbines, pipelines, and transmission towers.
These anchors are designed to counteract some kind long term load like earth pressure and
some short-term load like earth quake, also some load caused by waves, wind, buoyancy.
While considerable research has been conducted on plate anchors in horizontal soils, very
few studies are done on uplift resistance of plate anchor in purely frictional sloping terrains.
In this study, uplift capacity of horizontal plate anchor are determined on frictional sloping
terrain. Main aim is to evaluate how different factors such as anchor geometry, slope
inclination, internal friction angle of soil, and embedment depth affect the uplift capacity of
horizontal plate anchors using a three-dimensional finite element model in PLAXIS 3D.
Problem Definition
The study models can be represented as a horizontal plate anchor of width (B), length (L),
and thickness (t), embedded at a depth (H) in a cohesionless sloping terrain. To determine
uplift capacity anchors are buried horizontally with varying slope inclination angles (I=
0,5,10,15,20 degree), friction angles (φ = =30,35,40,45 degree), embedment ratios (H/B = 1
to 5), and length-to-width ratios (L/B = 1, 2, 5, 8, 10) .
Figure 1:Horizontal plate anchor
An anchor can have several orientations, including horizontal, inclined, and vertical, here in
this study horizontally oriented anchor are used.
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Figure 2:Plate anchor model in sandy slope.
Hassan et al(2024)
The uplift resistance is represented using the breakout factor (Nγ), a dimensionless
parameter defined as,
It is needed to generalise uplift capacity allowing for easy comparison of anchor
performance across different sizes, embedment depth and soil condition.
To further understand the influence of anchor shape, the shape factor (S) is introduced,
which compares the breakout factor of a rectangular anchor to that of a strip anchor (L/B ≥
10). This shape factor can be defined as
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Finite Element Modelling (PLAXIS 3D)
PLAXIS 3D was used to simulate the uplift behaviour of anchors. There are some built in soil
model like linear elastic, Mohr Coulomb, hardening soil, soft soil etc for replicating the
behaviour of soil in geotechnical applications. The Hardening Soil Model (HSM) was chosen
due to its ability to model nonlinear, stress-dependent soil behaviour more realistically than
the basic Mohr-Coulomb model. Four types of cohesionless sand with different unit weights
and friction angles were considered. The anchors were modelled as rigid plates with high
stiffness.
In element modelling soil dimensions are finite but in real world situation its boundary goes
infinite from the point of interest, dimensions are chosen such that influence of the
boundary on stress and displacement is minimal. The soil domain was extended at least 2H
beyond the anchor periphery and H above and below the anchor to minimize boundary
effects. So, anchor, dimensions become 4H + L in the length direction and 4H + B in the
width direction of the anchor.
The plaxis interface provides five distinct mesh densities. The optimum mesh density is
chosen to maximize the accuracy minimizing the computing time. Underestimated uplift we
can get from very fine mesh configuration, while it is overestimated by coarse mesh density.
Here fine mesh (30,641 elements) was selected to balance accuracy and computational
time.
Figure 3. 3D finite element mesh Hassan et al(2024)
Model Validation
The numerical model was validated through comparison with previous experimental and
numerical studies.
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For square anchors (L/B = 1), the results from the current model were compared with the
lower-bound solutions provided by Merifield et al. (2006) across different soil conditions.
The comparison showed good agreement, particularly for soil with friction angles φ = 30°,
35°, and 40°. Up to an embedment ratio of 4, the values matched closely. For deeper
embedment (H/B > 4), the current study slightly overestimated the uplift resistance, but the
difference remained within ±4%.
The results were also compared with experimental data from Murray and Geddes (1987)
and Dickin (1988). In these comparisons, the FEM model showed slightly higher uplift
capacities, especially for dense sands.
Minor overestimations were observed in the plaxis model, it is due to the assumption of
fully rough soil-anchor interfaces.
Results and Discussion
In this study, the uplift capacity is expressed using the dimensionless breakout factor (Nγ),
and the influence of various parameters—including slope inclination (I), anchor geometry
(L/B), embedment ratio (H/B), and soil friction angle (φ) are examined. Additionally, the
failure mechanism and the concept of shape factor (S) are analysed to see how it influence
the uplift performance.
1.Breakout Factor vs. Slope Angle (I)
Breakout factor decreases with increasing slope angle due to reduced soil confinement.
Slope inclination narrows the yielding zone, which reduces the anchor’s ability to resist
uplift. In the case of loose sand of friction angle 30 degree close for all length-width ratios at
all embedment depths.
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Figure 4: Variation of breakout factor (Nγ ) with slope angle (I) at different embedment
ratios for loose sandloose sand (φ = 30)
Hassan et al(2024)
2.Breakout Factor vs. Length-Width Ratio (L/B)
As the L/B ratio increases, the breakout factor decreases. For Square anchors (L/B = 1) the
highest resistance are observed, while strip anchors (L/B ≥ 10) show the lowest. This
confirms that shorter anchors mobilize more resistance from surrounding soil. A
mathematical expression was developed to predict Nγ using φ, I, H/B, and L/B
where, φ = friction angle (in radians), I = slope inclination angle, H/B = embedment ratio,
and L/B = length-width ratio.
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Figure 5 Variation of breakout factor with length-width ratio (L/B) for different slope angles,
friction angles, and embedment ratios For loose soil (φ=30),H/B=2
Hassan et al(2024)
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Figure 6:Variation of breakout factor with length-width ratio (L/B) for different slope angles,
friction angles, and embedment ratios For loose soil (φ=30),H/B=5
Hassan et al(2024)
3 Breakout Factor vs. Friction Angle (φ)
The breakout factor increases with increasing friction angle due to higher shear strength of
the soil. Dense sand (higher φ) provides more resistance, especially for deeper anchors.
Results are consistent with past studies however, a slight variance is noticed at higher
embedment ratios and friction angles, ranging from 1 to 2 percent.
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Figure 7:Variation of breakout factor with friction angle (φ).
Hassan et al(2024)
4 Failure Mechanism
In this section yielding zone or failure pattern of anchor plate embedded in horizontal
ground and slopy ground. In horizontal terrain, the failure zone forms a frustum shape
extending to the ground surface. The soil above anchor moves upward creating a failure
zone that extends to the surface. In sloping ground failure mechanism changes significantly
due to influence of slope inclinations. The size of yielding zone is decreased when slope is
introduced. The dimensions of yielding zone significantly influence the anchor’s capacity.
This decrease in yielding zone leads to lower breakout factor which signifies the influence of
the self-weight of the soil mass inside the yielding zone in counteracting uplift pressures.
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Figure 8:Contours of displacement for a square anchor at H/B =5 and φ =40◦when (a) I =0◦
Hassan et al(2024)
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Figure 9:Contours of displacement for a square anchor at H/B =5 and φ =40◦when (c) I =30◦.
Hassan et al(2024)
5. Shape Factor (S)
The shape factor increases with embedment ratio and friction angle but decreases with
increasing slope angle and L/B ratio. So lower aspect ratio shows more decrease in shape
factor. Anchors with L/B ≥ 5 behave similarly to strip anchors. The shape factor of an anchor
exhibits a more significant decrease with increasing slope angle for lower length-width
ratios, in contrast to anchors characterized by higher length-width ratios. Denser soils (high
φ) enhance the shape effect. And a mathematical modelling was also proposed to predict
shape factor.
where, φ = friction angle (in radians), I = slope inclination angle, H/B = embedment ratio,
and L/B = length-width ratio.
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Figure10: Variation of a shape factor with slope inclination angle at H/B =5 and φ =40◦.
Hassan et al(2024
summary
• So, anchor geometry and slope inclination has great influence on uplift resistance of
the horizontal plate anchor. Regardless of the embedment ratio and friction angle, a
consistent pattern emerges: higher length-width ratios are associated with smaller
breakout factors.
• In horizontal ground, the anchor failure zone forms a wide frustum shape failure
zone which extends to the surface, allowing greater uplift resistance. In sloping
terrain, the yielding zone becomes smaller due to slope inclination, which reduces
the breakout factor which means less resisting uplift capacity.
• To evaluate the effect of shape variations and slope inclinations, the study provides
mathematical equations that allow precise predictions of anchor uplift capability.
References
1. Hassan, Mirza Mahamudul, et al. "Effect of anchor geometry on uplift resistance of
plate anchor in sloping terrain." Ocean Engineering 292 (2024): 116498.
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2. Kumar, Jyant, and K. M. Kouzer. "Vertical uplift capacity of horizontal anchors using
upper bound limit analysis and finite elements." Canadian geotechnical journal 45.5
(2008): 698-704.
3. Murray, E. J., and James D. Geddes. "Uplift of anchor plates in sand." Journal of
Geotechnical Engineering 113.3 (1987): 202-215.
4. Merifield, Richard S., and Scott W. Sloan. "The ultimate pullout capacity of anchors in
frictional soils." Canadian geotechnical journal 43.8 (2006): 852-868.
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