Comparative Sensitivity of Structured Cam Clay Parameters in Predicting the Undrained Behaviour of Cement-Treated Soil

Comparative Sensitivity of Structured Cam Clay Parameters in Predicting the Undrained Behaviour of Cement-Treated Soil

(A parametric assessment of residual sandy clay from Isheri, Nigeria)

Alhassan Ahmed Igbeneghu (1) Stephen Abednego Osariyekemwen (2) Omenaimen Ikhide (3)

Department of Civil Engineering, Auchi Polytechnic, Edo State, Nigeria

Abstract – The Structured Cam Clay (SCC) model separates intrinsic soil behaviour from structure-dependent effects, making it suitable for interpreting cement-treated soils. This study provides a comparative parametric assessment of four SCC parametersdestructuring index b, additional void ratio at initial yielding e, intrinsic compression index *, and flow-rule parameter using five sample-specific parameter sets derived from an underlying study of cement-treated residual sandy clay from Isheri, Nigeria. The reported undrained simulations indicate that b mainly changes the deformation trajectory associated with structural degradation; e affects the magnitude of deviatoric and volumetric deformation; * governs intrinsic plastic compressibility; and modifies the plastic-flow/loading trajectory. Terminal deviatoric strength is comparatively insensitive to these four parameters in the reported responses and is more directly associated with the cementation-related cohesion parameter C and critical-state stress ratio M*. Because the five sample parameter sets vary simultaneously, these observations are treated as comparative parameter-response evidence rather than formal isolated sensitivity coefficients. The study also identifies conflicting source entries that require verification before quantitative sensitivity indices are reported. The resulting framework separates strength-controlling from deformation-controlling parameters and provides a controlled one-at-a-time and global-sensitivity protocol for subsequent SCC calibration and validation.

Keywords – Structured Cam Clay; cement-treated soil; destructuration; additional void ratio; compression index; flow rule; undrained behaviour; constitutive modelling; parametric analysis; Isheri clay.

1. INTRODUCTION

   Cement treatment modifies the mechanical response of fine- grained geomaterials through changes in bonding, fabric, stiffness, compressibility and strength. For constitutive modelling, these mechanisms should not be represented solely by an increase in apparent cohesion because cementation can also alter the deformation path and the rate at which initial structure is destroyed.

   The Structured Cam Clay (SCC) model provides a critical-state framework for distinguishing intrinsic soil-skeleton behaviour from structure-dependent behaviour. In the underlying study, intrinsic parameters include M*, e*ic, *, * and *, while b and e describe important aspects of structural behaviour. Here, * represents intrinsic plastic compression, * the elastic swelling response, b the destructuration-rate parameter, and e the additional void ratio associated with initial structure.

   For cement-treated soil, the strength contribution is represented through a cementation-related cohesion parameter C, with the peak-strength relationship written as q_peak = M*p + C. This distinction is important because C directly contributes to the strength envelope, whereas b, e, * and primarily affect the evolution of deformation, compressibility and plastic flow.

   Recent constitutive studies increasingly represent cementation and structure through evolving internal variables, while anisotropic critical-state formulations emphasize the separation of yield-surface evolution from plastic-flow behaviour. The present paper therefore focuses on a narrower methodological question: which SCC parameters are primarily associated with strength, and

   which primarily control the deformation path of cement-treated soil?

   1. Research Gap

      Existing SCC application to the Isheri materials provides sample-specific parameter values and simulated responses, but the comparison does not constitute a statistically controlled sensitivity experiment because several parameters change simultaneously between samples. The methodological gap is therefore the absence of a clearly separated interpretation of parameter effects and sample variability, together with a reproducible protocol for controlled sensitivity analysis.

   2. Objectives

      • Examine the reported effect of b, e, * and on the undrained SCC response.

      • Distinguish parameters primarily associated with strength from those associated with deformation and volume change.

      • Identify limitations in interpreting sample-to-sample parameter differences as isolated sensitivity effects.

      • Establish a controlled sensitivity-analysis protocol for subsequent SCC calibration and extension to cement-treated Isheri soil.

2. CONSTITUTIVE FRAMEWORK

   The SCC framework represents the total void ratio as the sum of intrinsic and structure-related components:

   e = e* + e

   where e* is the intrinsic or reconstituted response and e is the additional void-ratio contribution associated with soil structure. The destructuring parameter b controls the rate at which the structure-related component changes during loading.

   For cemented soil, the source formulation represents strength through the cementation-related cohesion parameter C:

   q_peak = M* p + C

   where q_peak is peak deviatoric stress, p is mean effective stress, M* is the intrinsic critical-state stress ratio, and C is the cementation-related strength contribution. The four parameters investigated here are therefore interpreted primarily through their reported influence on deformation and structural response rather than as direct strength increments.

   A. Physical Interpretation of the Parameters

   Parameter	Physical role in SCC	Primary response expected
   b	Rate of destructuration	Stressstrain trajectory and structural degradation
   e	Magnitude of initial structural void-ratio contribution	Deviatoric and volumetric deformation
   *	Intrinsic plastic-compression slope	Plastic compressibility and deformation
   	Structure-related flow-rule modifier	Plastic-strain direction and loading trajectory
   C	Cementation-related strength contribution	Peak/undrained strength
   M*	Critical-state stress ratio	Critical-state strength relationship

   TABLE I. PHYSICAL INTERPRETATION OF THE SCC PARAMETERS

3. MATERIALS AND METHODS

   1. Study Material

      Five soil samples (S1S5) obtained from the Isheri area of Ogun State, Nigeria, form the basis of the analysis. The underlying thesis reports disturbed and undisturbed sampling and physical/classification testing. The present paper uses the sample- level parameter sets reported in that work and does not introduce additional laboratory values.

   2. Sample-Specific Parameter Sets

      Sample	b	e	*	*
      S1	0.5	0.288	0.16	0.45	0
      S2	0.6	0.408	0.22	0.43	1
      S3	0.6	0.377	0.23	0.28	2
      S4	5.0	0.309	0.30	0.28	4
      S5	1.0	0.390	0.16*	0.39	5

      TABLE II. SAMPLE-SPECIFIC SCC PARAMETER SETS USED IN THE COMPARATIVE ASSESSMENT

      * The source material contains a conflicting * value for S5 in another table. The value shown here is the one used in the present interpretation and must be verified against the original thesis calculation before submission.

   3. Undrained Simulation Procedure

      The source simulations evaluate deviatoric stress q against

      deviatoric strain d and volumetric strain v against d for the

      reported parameter sets. The analysis begins from the stress state specified in the underlying parametric study and follows the corresponding undrained loading path. The present manuscript retains the source simulation values for comparative interpretation rather than presenting new numerical simulations.

   4. Definition of Sensitivity

      Because S1S5 do not vary one SCC parameter while all other parameters remain fixed, the present results are not reported as formal sensitivity coefficients. They are interpreted as comparative parameter-response observations. For a response R and parameter P, a normalized local sensitivity coefficient may be expressed as:

      S_P = (R/R) / (P/P)

      where R may represent peak q, deviatoric strain, volumetric strain or stiffness. Such a coefficient requires controlled perturbation of P around a common baseline.

   5. Recommended Controlled Sensitivity Design

   Stage	Procedure	Purpose
   Baseline	Select one physically calibrated SCC parameter set	Reference response
   Local OAT	Vary one parameter while all others remain fixed	Isolate individual influence
   Range check	Use physically justified lower and upper bounds	Avoid nonphysical sensitivity
   Interaction study	Use factorial or Latin-hypercube sampling	Quantify parameter interaction
   Global analysis	Compute normalized/variance-based indices	Identify dominant parameters
   Validation	Compare sensitive parameters with independent tests	Establish physical identifiability

   TABLE III. RECOMMENDED CONTROLLED SENSITIVITY-ANALYSIS PROTOCOL

4. RESULTS AND PARAMETRIC INTERPRETATION

   1. Destructuring Index b

      The reported b values range from 0.5 to 5.0. The simulations indicate that b mainly modifies the deformation trajectory associated with structural degradation rather than producing a direct systematic change in terminal deviatoric strength. Sample S4, with b = 5.0, exhibits a substantially different trajectory from samples with lower b. Because S4 also has different e, *, * and values, however, this observation cannot be treated as an isolated b effect.

   2. Additional Void Ratio e

      The reported e values range from 0.288 to 0.408. Larger e values are associated in the source simulations with greater deviatoric and volumetric deformation. The parameter therefore represents the magnitude of the initial structural contribution and is particularly important when the modelling objective is deformation or settlement rather than peak strength alone.

   3. Intrinsic Compression Index *

      The reported * values used in the parametric interpretation range from 0.16 to 0.30. Increasing * is associated with greater plastic and volumetric deformation, while terminal deviatoric stress is comparatively insensitive in the reported responses. This

      is consistent with * being an intrinsic plastic-compressibility parameter rather than a direct critical-state strength parameter.

   4. Flow-Rule Parameter

      The reported values range from 0 to 5. The source simulations indicate that mainly modifies the loading trajectory and stiffness/flow response, with limited change in terminal strength and terminal volumetric strain. Its calibration should therefore be tied to stressstrain and volumetric response rather than peak strength alone.

   5. Comparative Response

      Paramet er	Dominant reported effect	Effect on terminal q	Calibration implication
      b	Structural degradation/deformation path	Limited	Tests sensitive to destructuration
      e	Magnitude of structural deformation	Limited	Compression/volume- change response
      *	Intrinsic plastic compressibility	Limited	Intrinsic/reconstituted compression
      	Plastic-flow/deformation trajectory	Limited	Stressstrain and volumetric response
      C	Cementation-related strength	Direct	Strength response

      TABLE IV. SUMMARY OF REPORTED PARAMETER EFFECTS AND CALIBRATION IMPLICATIONS

      The principal constitutive observation is a separation between strength control and deformation control. The source results associate cementation-related cohesion C with strength, whereas b, e, * and predominantly modify the deformation response. This separation can reduce parameter compensation during inverse calibration.

5. DATA QUALITY AND REPRODUCIBILITY

   Three source-data issues require explicit resolution before submission. First, one source table reports a volumetric strain of 428.0% for S2 at p = 0.06 kN/m², whereas the corresponding structural-parameter table reports a substantially different value. Second, the source contains conflicting * entries for S3. Third, * for S5 is reported differently in separate tables. These entries should be checked against the original thesis calculations, laboratory records and numerical output.

   The anomalous S2 value is not used to support a constitutive conclusion in this revised manuscript. To preserve reproducibility, the final submission should contain one verified parameter table, identify the exact simulation input associated with each response curve, and archive the numerical data used to generate the final figures.

6. DISCUSSION

   1. Strength versus Deformation Control

      The reported responses suggest that SCC calibration should not attempt to determine all parameters from peak-strength data. Cementation-related C and M* are associated primarily with strength, whereas b, e, * and govern aspects of the deformation path. Consequently, a calibration strategy based only on matching peak q may produce nn-unique combinations of structural and compressibility parameters.

   2. Parameter Identifiability

      The sample-to-sample comparison demonstrates why parameter identifiability is essential. The wide range in b, for example, cannot be attributed solely to destructuration because other material parameters also differ between samples. The same principle applies to e, * and . Controlled numerical perturbation around a common calibrated baseline is therefore required to establish partial parameter effects.

   3. Implications for Subsequent Anisotropic SCC Development

   The present results provide a parameter hierarchy for the broader SCC development programme. Intrinsic compressibility should be constrained independently of structure; cementation should be calibrated from strength and bonding response; destructuration should be constrained from tests capable of resolving structural degradation; and the flow rule should be constrained using volumetric and directional strain response. Once these components are independently constrained, fabric anisotropy and stress-induced rotation can be introduced without allowing anisotropy parameters to compensate for poorly identified structural parameters.

7. LIMITATIONS

   • The available results are based on five sample-specific parameter sets rather than a statistically independent global sensitivity design.

   • The present manuscript does not claim new experimental

     measurements or a new numerical constitutive implementation.

   • The anomalous and conflicting source entries identified in Section V require verification before quantitative sensitivity indices are reported.

   • The available simulations are principally undrained and therefore do not independently constrain all aspects of compressibility and flow-rule behaviour.

   • Formal sensitivity indices and parameter-interaction measures require additional controlled simulations.

8. CONCLUSIONS

   • The reported SCC simulations indicate that the destructuring index b primarily affects the rate and trajectory of structural degradation and deformation.

   • The additional void ratio e has a pronounced influence on the magnitude of simulated deviatoric and volumetric deformation.

   • The intrinsic compression index * strongly affects plastic compressibility and deformation while showing limited influence on terminal deviatoric strength in the reported simulations.

   • The flow-rule parameter primarily affects the

     deformation/loading trajectory rather than terminal strength.

   • The four investigated parameters should not be treated as interchangeable strength parameters; cementation-related C is more directly associated with the cementation-induced strength contribution.

   • Because the five source samples vary in several parameters simultaneously, the results should be regarded as comparative parametric evidence rather than formal isolated sensitivity coefficients.

   • A controlled one-at-a-time and/or global sensitivity analysis, supported by verified input data and independent experimental validation, is required for a definitive quantitative sensitivity study.

9. DATA AVAILABILITY

   The numerical values analysed in this manuscript are derived from the author’s thesis dataset. The complete verified laboratory dataset, constitutive-model input files and simulation output used to generate the final figures should be retained and, where permitted, deposited in an appropriate repository in accordance with journal requirements.

10. DECLARATIONS

1. Funding

   No specific funding was received for this work.

2. Conflict of Interest

   The author declares no conflict of interest.

3. Ethics Approval

   Not applicable.

4. Author Contribution

Alhassan A. I. Conception, and interpretation of parameter dataset, performed the comparative parametric analysis, and prepared the manuscript.

Stephen A. O. laboratory testing and data compilation

Omenaimen Ikhide: Data Compilation and paper administration

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