Influencia del cam clay model modificado

Influencia del cam clay model en un pad de lixiviación

1. Proceedings of Tailings and Mine Waste 2025
November 2–5, 2025, Banff, AB, Canada

1
Influence of Modified Cam Clay and Hardening Soil
Models on Failure Prediction of Heap Leach Pad by 3D
Shear Strength Reduction Method
Jimmy Tapia, Universidad Nacional de Ingeniería, Lima, Perú
Laura Rojas, Ausenco, Lima, Perú
Jean Paul Minaya, Ausenco, Lima, Perú
Ignacio Mejia, Ausenco, Lima, Perú
Abstract
An advantage of the Shear Strength Reduction Method (SSRM) over the Limit Equilibrium Method (LEM)
is that it does not require assumptions about the shape or location of the failure surface, making it effective
for identifying critical failure zones. When performing SSRM analyses, the Mohr-Coulomb constitutive
model is the most commonly used due to its simplicity. However, other constitutive models—specifically
designed for different soil types—can better capture the non-linear and elasto-plastic behavior of materials.
Several studies highlight that the choice of constitutive model significantly influences failure predictions,
affecting slip surface geometry and the calculated safety factor (SF). This research analyzes the stability of
a heap leach pad in the Peruvian Andes, characterized by complex geometry (irregular stacked shape with
concave and convex zones in plan view) and soft fine soils in its foundation. The objective is to evaluate
how constitutive models influence predicted foundation failures using SSRM applied to a three-dimensional
finite element model with ten-noded tetrahedral elements under drained conditions. Comparisons are made
between the Modified Cam-Clay model (MCC, for soft soils), the Hardening Soil model (HS, for stacked
mineral), and the Mohr-Coulomb model, which is commonly applied to both stacked mineral and soft fine
soils. The results indicate that while slip surface geometry and SF vary only slightly among the constitutive
models evaluated, the HS and MCC models emerge as the most critical, as they predict larger failure
volumes and lower safety factors. These models should therefore be prioritized in slope stability
assessments of heap leach pads with complex geometries and soft foundations. This study focuses on global
failures rather than local ones and does not consider failure mechanisms that develop along the lining
system. Limitations include the sensitivity of outcomes to element type, finite element mesh density and
node count, which were not explicitly analyzed.

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Introduction
The prediction of failure mechanisms in geotechnical structures remains a fundamental challenge in
geotechnical engineering. Conventional approaches such as the Limit Equilibrium Method (LEM) are
widely employed due to their computational simplicity and the accessibility of commercial software.
However, as highlighted by (Tapia et al., 2025), a critical question persists: can the failure surfaces predicted
by LEM truly manifest in reality? Unlike LEM, the Shear Strength Reduction Method (SSRM) does not
rely on predefined failure geometries. Instead, it systematically reduces the shear strength parameters of
soils to identify failure mechanisms as they naturally emerge and to compute the corresponding safety
factor. Previous studies (Duncan, 1996; Griffiths & Lane, 1999) have investigated the theoretical
foundations of SSRM, supporting its validity in capturing realistic failure surfaces and serving as a robust
tool to validate results obtained from LEM.
Heap leach pads present particular challenges for stability analysis due to their geometric and
geotechnical complexity. These structures typically feature a heterogeneous distribution of foundation
materials (often including soft soils) and an irregular geometry marked by concave and convex slope
transitions. In such cases, the accurate identification of potential failure mechanisms requires advanced
numerical tools capable of realistically simulating site-specific conditions. A key component of this
modeling effort is the selection of an appropriate constitutive soil model, which governs the accuracy with
which soil behavior under loading is represented.
This study aims to quantify the influence of constitutive model selection on the prediction of failure
surfaces using the SSRM within a fully three-dimensional finite element framework. The use of a 3D model
is essential given the inherent complexity of heap leach pads, including transitions between convex and
concave geometries and localized weak zones in the foundation.
Despite the methodological advantages of SSRM (particularly its ability to identify failure
mechanisms without requiring prior assumptions about their location) the Mohr-Coulomb (MC) model
remains the default choice in many geotechnical analyses due to its simplicity. Nevertheless, SSRM is
sensitive to the selection of the constitutive model as well as mesh size and type, and convergence criteria
(Li & Shao 2011, Sun et al. 2017, Zhang et al. 2011). Tschuchnigg et al. 2019 have demonstrated that the
MC model may fail to capture the nonlinear and elasto-plastic behavior exhibited by many geomaterials,
potentially leading to unrealistic predictions of failure and unsafe design outcomes. This underscores the
importance of implementing more advanced constitutive models capable of reflecting complex soil
behavior and of evaluating their impact on calculated safety factors.
The present work focuses on assessing the effect of different constitutive models on failure prediction
for a heap leach pad located in the Peruvian Andes. A three-dimensional finite element model under drained
conditions is developed, and the predictive performance of two advanced constitutive models (Modified

3. CHAPTER NAME
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Cam Clay for soft fine-grained foundation soils, and Hardening Soil for the ore heap) is compared with that
of the conventional Mohr-Coulomb model.
Specifically, the study investigates how the failure surface geometry and the Safety Factor (SF) vary
according to the chosen constitutive model and examines the influence of mesh density in the finite element
discretization. The findings contribute to establishing sound criteria for the selection of constitutive models
in geotechnical stability analyses of complex structures such as heap leach pads.
Background
Understanding the stability of large geotechnical structures such as heap leach pads requires the integration
of advanced constitutive models and robust numerical techniques. Traditional limit equilibrium methods,
while useful, often fall short in capturing the complex interactions between soil behavior and stress
redistribution, especially in three-dimensional conditions.
The use of finite element analysis (FEA) in geotechnical engineering has become increasingly
essential for simulating realistic stress-strain responses, particularly when combined with constitutive
models that represent key features such as hardening, dilatancy, and stress-dependent stiffness (Brinkgreve
et al., 2019).
Moreover, the Shear Strength Reduction Method (SSRM) has emerged as a reliable approach for
assessing slope or foundation stability within FEA platforms, enabling the identification of potential failure
mechanisms under static or dynamic loading (Brinkgreve et al., 2019). The following sections describe the
theoretical basis and practical relevance of the constitutive models and 3D SSRM methodology adopted in
this study to evaluate the long-term stability of a heap leach pad.
Constitutive Models for Advanced Geotechnical Analysis
In advanced numerical modeling of geotechnical structures such as heap leach pads, selecting an
appropriate constitutive model is essential for accurately predicting both deformations and potential failure
mechanisms
The Modified Cam Clay (MCC) model is grounded in critical state soil mechanics and was originally
developed to describe the behavior of remolded clays. It is particularly effective for simulating the response
of normally consolidated and lightly overconsolidated clays (Wood, 1990; Roscoe & Burland, 1968). The
model features a single yield surface defined by an elliptical equation in p'-q space and incorporates
isotropic hardening governed by volumetric plastic strain. MCC offers a robust framework for simulating
elasto-plastic soil behavior, especially under undrained loading conditions. However, it tends to
overestimate stiffness at small strains and does not accurately represent stress-dependent stiffness or stress
path dependency (Wood, 1990).

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In the case of the mineral ore deposited in the heap leach pad, the Hardening Soil Model (HSM)
provides an advanced empirical approach to capture nonlinear and stress-dependent soil stiffness. It
incorporates both shear and volumetric hardening laws, and is capable of simulating the dependency of
stiffness on the current stress state and strain level (Schanz et al., 1999). Unlike MCC, the HSM
distinguishes between primary loading and unloading-reloading paths and includes three different stiffness
moduli: the secant stiffness in primary loading (E₅₀), the tangent stiffness for unloading/reloading (Eᵤᵣ), and
the oedometer stiffness (Eₒₑd), all of which vary with confining pressure.
Comparing both models allows for a deeper understanding of how the assumed soil behavior
influences predicted failure mechanisms and safety margins when using the shear strength reduction method
in 3D slope stability analyses. For example, HSM tends to predict more realistic deformations and failure
surfaces in granular or overconsolidated materials, while MCC may be more appropriate in clays close to
critical state (Schanz et al., 1999; Wood, 1990).
3D Numerical Modeling Using Shear Strength Reduction
Three-dimensional numerical modeling using the Shear Strength Reduction Method (SSRM) has become
an essential tool in advanced geotechnical engineering practice. SSRM works by progressively reducing
the shear strength parameters of the soil—typically cohesion (c) and internal friction angle (φ)—until failure
occurs, thereby identifying the safety factor for a given slope or structure (Griffiths & Lane, 1999).
In 3D, this method offers significant advantages over traditional 2D analyses. It enables a more
realistic representation of complex geometries, such as those found in heap leach pads, where geometry,
stratigraphy, and loading conditions often vary spatially. This spatial variability can influence failure
mechanisms and cannot be fully captured in two-dimensional models (Itasca, 2021).
Moreover, 3D SSRM accounts for stress redistribution in all directions, providing a better
understanding of how localized weaknesses or heterogeneities affect global stability. It also allows the
simulation of anisotropic behavior and irregular boundary conditions, which are common in real-world
projects (Brinkgreve et al., 2019).
Overall, three-dimensional SSRM-based modeling enhances the accuracy of failure prediction and
supports more informed decision-making for the design, monitoring, and mitigation of complex
geotechnical systems.
Methodology
In a previous study (Tapia et al., 2025), a three-dimensional analysis was conducted using the Shear
Strength Reduction Method (SSRM) via the finite element method, applying a mesh composed of four-
node tetrahedral elements. The Mohr-Coulomb constitutive model was used for both the heap leach pad

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body and the foundation material. The primary goal was to validate the failure surfaces identified in the
numerical model and compare them with results obtained through the limit equilibrium method using Slide3
software.
In the current study, the SSRM approach is extended using Plaxis 3D, with a three-dimensional model
based on ten-noded tetrahedral elements under drained conditions. Modified Cam Clay (MCC) model is
adopted to represent the soft clay layer within the foundation, while the Hardening Soil Model (HSM) is
applied to simulate the behavior of the mineral ore deposited in the heap leach pad. Additionally, the Mohr-
Coulomb (MC) model is used for both the foundation's soft clay and the ore body, allowing for a
comparative evaluation. This approach enables the assessment of four different modeling combinations,
providing insights into how the choice of constitutive model influences the predicted failure surfaces and
stability outcomes.
This research focuses on global failure mechanisms rather than local ones and does not consider failure
modes involving the geomembrane liner system. Limitations include the sensitivity of the results to the
element type and node count, which were not explicitly analyzed in this study.

Figure 1: Three-dimensional model generated in Plaxis 3D, representing the local geology
Case Study
Geology
The heap leach pad evaluated in this study is located in the Andean region of Peru. The local geology of the
foundation area primarily consists of residual soils derived from the weathering of andesitic tuffs. Field
inspections identified localized deposits of materials classified as fat clay and elastic silt (CH, MH), as well
as silt and lean clay (ML, CL), according to the Unified Soil Classification System (USCS). These materials
are predominantly found at the toe of the heap leach pad.
Tuff
CH

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Their consistency ranges from soft to stiff, depending on the degree of weathering and prolonged
exposure to climatic conditions, particularly rainfall, which has contributed to cohesion loss in the upper
soil horizons. Figure 1 presents the geological view of the study area, highlighting the presence of tuffs and
localized deposits of soft clayey soils (CH) near the base of the heap leach pad.
Geometry
The importance of a three-dimensional analysis grows significantly when the nature of the slope is more
complex and therefore it is difficult to execute a two-dimensional analysis (Chakraborty & Goswami 2018).
One aspect contributing to this complexity involves the variation of the radius of curvature, classifying
slopes as concave and convex. A concave slope is more stable than a convex slope and both are more stable
than a straight slope (Kang et al. 2022), this could be explained because the lateral pressure of a concave
slope offers a higher level of confinement or additional lateral support that a convex slope does not have
(Wines 2016).
Additionally, the three-dimensional analysis enables the assessment of potential foundation failures,
particularly considering the complexity introduced by the irregular distribution of soft residual soils and the
site's variable topography. Figure 2 shows the three-dimensional model of the heap leach pad founded on a
base composed of tuff and localized zones of soft clayey soil.

Figure 2: Three-dimensional model generated in Plaxis 3D, representing the Heap leach pad
Geotechnical parameters
The mechanical strength parameters for foundation soil and leached mineral were calculated from
consolidated undrained (ASTM D4767) and consolidated drained (ASTM D7181) triaxial compression
tests and specialized literature, considering post-peak values. Table 1 provides a summary of the
geotechnical parameters of the materials comprising the heap leach pad and its foundation, evaluated
according to the Mohr-Coulomb failure criterion. Table 2 and Table 3, in turn, present the geotechnical
parameters based on the Cam Clay model for the foundation clays and the Hardening Soil model for the
Mesh

7. CHAPTER NAME
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ore material of the pad, respectively.
Table 1: Geotechnical parameters - Mohr-Coulumb
Material Color
UW
(kN/m
3
)
c’ (kPa) ’ (°)
Young Modulus
(MPa)
Poisson´s
ratio
Mineral 18 5 38 40 0.3
Residual soil (CH) 17 0 19.5 10 0.2

Table 2: Geotechnical parameters of the soft clay – Modified Cam Clay
Parameter Symbol Value
Slope of the critical state line M 0.75
Cam-Clay compression index λ 0.2
Cam-Clay swelling index κ 0.04
Initial void ratio e0 1.0
Poisson´s ratio v 0.2
Coefficient of lateral stress in
normal consolidation
??????
0
��
0.82

Table 3: Geotechnical parameters of the mineral ore– Hardening Soil Model
Parameter Symbol Value
Friction angle  38°
Cohesion c’ 5
Angle of dilatancy y 0
Secant stiffness in standard drained triaxial test ??????
50
??????��
40 MPa
Tangent stiffness for primary oedometer loading ??????
���
??????��
40 MPa
Unloading / reloading stiffness ??????
????????????
??????��
120 MPa
Power for stress-level dependency of stiffness m 0.5
Poisson´s ratio for unloading-reloading vur 0.3
Reference stress for stiffnesses ??????
??????��
100 kPa
K0-value for normal consolidation ??????
0
��
0.3843
Failure ratio qf/qa ??????
� 0.9

The mechanical strength parameters of the foundation rock were obtained from unconfined compressive
strength tests (ASTM D7012) and geomechanical stations. Table 4 presents the parameters of the bedrock
according to the generalized Hoek Brown failure criterion.

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Table 4: Geotechnical parameters of the bedrock
Material Color
UW
(kN/m
3
)
UCS
(MPa)
GSI mi D
Young Modulus
(MPa)
Poisson’s
ratio
Tuff 24 50 45 13 0 2000 0.25
Results
Table 5 presents the results of the 3D-SSRM analysis, considering the mesh density in the residual soil area
and part of the heap leach pad, where the size of the element in each refinement region has been varied,
resulting in an increased number of elements.
Table 5: Results
Constitutive
Model
SRF Isometric view Section
MC - MC 1.35


MC (stacked mineral) y MC (soft soils)
HS - MC 1.36


HS (stacked mineral) y MC (soft soils)
MC - MCC 1.35


MC (stacked mineral) y MCC (soft soils)
HS - MCC 1.32


HS (stacked mineral) y MCC (soft soils)

The numerical results obtained using the Modified Cam-Clay model (for soft soils) and the Hardening
Soil model (for stacked mineral) are compared with those of the Mohr-Coulomb model, which is typically
used for both stacked mineral and soft fine soils. Table 5 also shows the failure surfaces obtained by the

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3D-SSRM in the residual soil area and part of the heap leach pad, using a mesh composed of 132 820 ten-
noded tetrahedral elements.
Conclusions
A low variation in the position and shape of the failure surfaces was observed across the four cases analyzed,
which contrasts with the findings reported by some authors for this type of analysis. However, the HS–
MCC case exhibits the largest failure volume. On the other hand, the four safety factors consistently fall
within a narrow and well-defined range (between 1.32 and 1.36), once again, the HS–MCC case is
confirmed as the most critical scenario, given that it produces the lowest safety factor.
These results suggest that the HS and MCC constitutive models are the most critical and should
therefore be prioritized when evaluating the stability of slopes in heap leach pads with complex geometries
and soft foundations similar to those examined in this study..
References
ASTM. (2011). Standard test method for consolidated undrained triaxial compression test for cohesive soils (ASTM
D4767-11). ASTM International.
ASTM. (2014). Standard test method for compressive strength and elastic moduli of intact rock core specimens
under varying states of stress and temperatures (ASTM D7012-14e1). ASTM International.
ASTM. (2020). Standard test method for consolidated drained triaxial compression test for soils (ASTM D7181-20).
ASTM International.
Brinkgreve, R. B. J., Kumarswamy, S., & Swolfs, W. M. (2019). PLAXIS 3D 2019 reference manual.
Chakraborty, D., & Goswami, R. K. (2018). Three-dimensional slope stability analysis using strength reduction
technique. Geotechnical and Geological Engineering, 36(6), 3647–3659.
Duncan, J. M. (2018). State of the art: Limit equilibrium and finite-element analysis of slopes. Journal of
Geotechnical Engineering, 122(7), 577–596.
Griffiths, D. V., & Lane, P. A. (1999). Slope stability analysis by finite elements. Géotechnique, 49(3), 387–403.
Li, H., & Shao, L. (2011). Three-dimensional finite element equilibrium method for slope stability analysis based on
the unique sliding direction. ASCE, Geotechnical Special Publication No 216.
Itasca Consulting Group, Inc. (2021). FLAC3D – Fast Lagrangian analysis of continua in 3 dimensions: User’s
guide (Version 7.0). Itasca Consulting Group, Inc.
Kang, B., Jiang, Y., & Wang, Y. (2022). Effects of slope shape on 3D slope stability analysis using strength
reduction method. Engineering Geology, 297, 106513.

10. TAILINGS AND MINE WASTE 2025 ● BANFF, CANADA
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Roscoe, K. H., & Burland, J. B. (1968). On the generalized stress-strain behavior of ‘wet’ clay. In J. Heyman & F.
A. Leckie (Eds.), Engineering plasticity (pp. 535–609). Cambridge University Press.
Schanz, T., Vermeer, P. A., & Bonnier, P. G. (1999). The hardening soil model: Formulation and verification. In
Proceedings of the Plaxis Symposium (pp. 1–16).
Sun, C., Chai, J., Xu, Z., & Qin Y. (2017). 3D Stability charts for convex and concave slopes in plan view with
homogeneous soil based on the strength-reduction method. International Journal of Geomechanics, 17(5).
Tschuchnigg, F., Medicus, G., & Schneider-Muntau, B. (2019). Slope stability analysis-Barodesy vs linear elastic –
perfectly plastic models. 7th International Symposium on Deformation Characteristics of Geomaterials:
Proceedings of the international symposium, Glasgow, 26 June 2019..
Tapia, J., Rojas, L., Minaya, J., & Huarcaya, A. (2025). Validation of failure surfaces of a heap leach pad in the
Peruvian Andes using LEM and SSR method. Rocscience International Conference 2025.
Wood, D. M. (1990). Soil behaviour and critical state soil mechanics. Cambridge University Press.
Wines, M. (2016). Geomechanics for mine engineers (2nd ed.). Australasian Institute of Mining and Metallurgy
(AusIMM).
Zhang, K., Li, W., & Shi, J. (2011). FEM Stability Analysis on Soil Slope with Different Constitutive Models.
GeoHunan International Conference II: Emerging Technologies for Design, Construction, Rehabilitation, and
Inspection of Transportation Infrastructure: Proceedings of the international symposium, China, 9-11 June
2011.