Effective Friction Angle Research Articles

Study on the Characteristics of Effective Internal Friction Angles of Silty Clay from the Yellow River Delta and the Inverse Method of CPTu Testing

This study focuses on the silty clay of the Yellow River Delta, conducting laboratory experiments to explore the strength characteristics of typical silty clay in the Yellow River Delta. The study utilizes CPTu calibration chamber tests to systematically reveal the features of cone tip resistance (qt), side friction resistance (fs), and pore water pressure (u2) of the silty clay. This research provides a theoretical basis for Delta investigation in the Yellow River region. The study compares the applicability of existing CPTu inversion methods and highlights the NTH method’s advantages in evaluating silty clay’s effective internal friction angle. Supported by indoor calibration chamber tests, the study confirms the reliability of the NTH method in estimating the effective internal friction angle under normally consolidated conditions while also identifying its limitations. These research findings offer data support for the in situ rapid and accurate estimation of design parameters, like the internal friction angle and undrained shear strength of the silty clay in the Yellow River Delta. Moreover, they provide insights for obtaining other crucial in situ data.

Bearing capacity and failure mechanism of strip footings lying on slopes subjected to various rainfall patterns and intensities

Footing on slope is a prevalent construction encountered in geotechnical engineering, and its safety is receiving increased attention. A natural rainfall event will inevitably have adverse influences on the stability and bearing capacity of strip footings lying on slopes; however, the conventional practice to simulate the rainfall is realized by varying the soil moisture content and the actual rainfall characteristics cannot be fully reflected. As a result, the finite element (FE) software ABAQUS is employed in this study to model the temporally varying rainfall, and the bearing capacity, as well as failure mode of the strip footing placed at the top of slopes, is estimated accordingly. A series of FE analyses are carried out to quantify the influences of rainfall pattern, rainfall intensity, soil strength properties (i.e., effective cohesion c′ and effective friction angle φ′) and several geometric parameters associated with the location of embedded footing with B in width, such as the edge distance ratio L/B and the embedded depth ratio D/B. Results show that the bearing capacity will be decreased and the failure mode evidently changes under rainfall condition. Moreover, it is noted that the rainfall pattern produces less substantial impact on the bearing capacity and failure mode, compared with the rainfall intensity.

Investigating the strength and durability properties of alkali activated red mud for tailings pond embankment material

This article investigates the applicability of alkali-activated red mud (RM) as a geo-material for the construction of tailings pond (TP) embankments. A series of unconfined compressive strength (UCS) and direct shear tests (DST) are carried out to examine the mechanical performance of RM activated with sodium hydroxide (NaOH). While doing so, the influence of NaOH concentrations, curing conditions and curing period are also investigated. Furthermore, durability tests are performed to examine the weathering resistance of stabilized RM specimens against extreme environmental conditions. Finally, the effectiveness of alkali activated RM (as an embankment material) is demonstrated with the help of numerical analysis performed on a model TP. Based on the experimental results, the compressive strength of bare RM is improved from 0.34 MPa to 5.6 MPa, 0.57 MPa to 10.55 MPa and 0.97 MPa to 29.34 MPa under controlled ambient curing (CAC, 25±2 °C), open air curing (OAC, 25±7 °C) and dry curing (DC, 60 °C) conditions respectively. On the other hand, effective friction angle and cohesion of bare RM is found to increase from 16.76° to 52.85° and 6.58 kPa to 391.11 kPa respectively, after alkali activation. Furthermore, alkali activated RM specimens exhibit a significantly high weathering resistance than bare RM against 12 cycles of alternate wetting and drying. The numerical analysis reveals a notable increase in the factor of safety values when alkali activated RM is utilized for the construction of TP, indicating its potential as an embankment material.

Determination of Mechanical Properties of Soils Based on CPTU Data

Abstract The study aimed to interpret the results of cone penetration tests with pore pressure measurement (CPTU). Tests were performed on a section of the designed road about 200 m long. The subsoil under consideration was characterized by organic soils deposited to a depth of approximately 8 m. Due to the problematic soil and water conditions, improvement with geosynthetic encased columns (GEC) was performed. According to the Recommendations for Design and Analysis of Earth Structures using Geosynthetic Reinforcements – EBGEO, the constrained modulus Eoed and effective friction angle φ’ of soil below the GEC column base should be higher than 5 MPa (Eoed > 5 MPa) and 30° (φ’ > 30°), respectively. In this study, the Eoed and φ’ parameters were determined based on CPTU tests conducted in 12 locations. Analysis of the CPTU data showed that the constrained modulus and effective friction angle of the soil deposited below the GEC column base did not meet EBGEO requirements in most locations. It was also concluded that the minimum value of the constrained modulus required by EBGEO is too low compared with the requested value of the effective friction angle.

Shear strength of stockpiled coking coal – Insights from stability analysis of two instrumented stockpiles

ACARP Report C4057 (Eckersley, 2000) describes flowslides and other stability issues in stockpiles of coking (metallurgical) coal at Australian coal operations and export terminals, and summarizes 1973 to 2000 research at James Cook University (JCU). Eckersley (2022) partly updated that work with SEEP/W transient seepage modelling of a 12m high coal stockpile constructed at Hay Point in late 1991. Eckersley (2023) summarized available laboratory strength data for saturated and unsaturated coking coal to assist in selection and critical assessment of parameters for slope stability analyses of coal stockpiles. The current paper explores application of this data to stability analyses of two instrumented experimental stockpiles constructed at Hay Point, one of which collapsed suddenly and completely by flowsliding after extensive wetting. The stability analysis results tentatively confirm that the parameters and approach proposed are reasonable where stockpiles are subject to potential liquefaction-induced collapse. Significant questions raised by Eckersley (2023) regarding how the coking coal strength data should be applied are considered in the context of the stability analyses. The analyses tentatively confirm that effective strength parameters for saturated coal derived from peak deviator stress in isotropically consolidated, undrained (CIU), strain controlled triaxial tests are reasonable. For loose saturated coal these are at low strains and substantially less than critical state values. However, for unsaturated coal forming the bulk of a stockpile, unsaturated strength and apparent cohesion should be assessed from the effective friction angle at critical state and not the value mobilized at low strains. Use of total stress parameters derived from testing unsaturated coal may over-estimate factor of safety.

Analytical Solution for Bearing Capacity of Reinforced Strip Footings on Unsaturated Soils under Steady Flow

The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils in real engineering. In this paper, a new formula for the bearing capacity of reinforced strip footings on unsaturated soils is presented. Two sliding failure mechanisms are constructed based on the position of the reinforcement layer relative to the sliding surface. The distribution of apparent cohesion in the depth direction is calculated by considering the effect of matrix suction. By additionally considering the work conducted by the reinforcement and the contribution of the apparent cohesion, the bearing capacity formula is obtained using the upper bound theorem of limit analysis. The bearing capacity solution is obtained by adopting the sequential quadratic programming (SQP) algorithm. Comparing the results under two failure mechanisms, the optimal bearing capacity and the optimal embedment depth of reinforcement are obtained. The results of this paper are consistent with those of the existing literature. Finally, the effects of reinforcement embedment depth, effective internal friction angle, uniform load, and unsaturated soil parameters on the optimal bearing capacity are investigated through parametric analysis. This paper provides useful recommendations for the engineering application of reinforced strip footings on unsaturated soils.

How climate-induced wetting–drying cycles contribute to gully erosion: A case study from southern China

Collapsing gully erosion developed upon granite residual soil is the most devastating form of soil erosion in southern China. However, despite extensive investigations of the controlling factors of gully erosion, including granite regolith properties (pedon scale), slope geometry and hydraulic conditions (watershed scale), and local climate (regional scale), little is known about the interrelationships among these three-level factors and how these contribute to the initiation of gully erosion. This study presents how the wetting–drying cycles induced by the subtropical climate in southern China alter the properties of granite residual soil, with particular focus on the soil disintegration behavior. The test results indicate a finer texture (clay content increasing by 218%), lower shear strength (effective cohesion and internal frictional angle decreasing 55% and 30%, respectively), and five-times higher permeability for soil subjected to eight wetting–drying cycles. In addition, the wetting–drying cycle triggers more-apparent disintegration behavior, with the disintegration rate improving by 7 times. Such alterations are found to be caused by microstructural alterations including deaggregation and crack initiation, as revealed via scanning electron microscopy and mercury intrusion porosimetry. The implications of the variations of the multilevel soil properties for the development of gully erosion are discussed, with the degraded soil properties lowering the resistance to erosion and the high permeability facilitating soil–water interactions. This study improves the understanding of gully erosion and provides effective technical suggestions.

Effect of Wall Stiffness on Excavation-Induced Horizontal Deformations in Stiff-Hard Clays

Excavation-induced ground movements are affected by the stiffness of the support system as well as the soil properties. Displacement estimations of deep excavations are generally made using the finite element method (FEM). However, the accuracy and reliability of the results obtained from the finite element calculations will change significantly in proportion with the quality of the parameters employed in the program, thus, the use of probabilistic analysis that considers soil variability’s impact has become a popular approach in recent studies. Based on these considerations, this study aims to investigate the influence of wall bending stiffness on excavation-induced lateral displacements for deep excavations in stiff to hard clays, and provide a practical methodology to be used in preliminary design. For this purpose, finite element analyses were carried out using various practically achievable support system stiffness values and soil parameters. Considering the inherent variability of the soil, effective stress friction angle and effective cohesion of the soil were randomly generated by Monte Carlo simulations to be used in the finite element analyses. The performance of the analyses was evaluated using results from 22 case histories from deep excavations in stiff-hard clays. The results indicate that, lateral movement in excavations in stiff-hard clays is minimally affected by the stiffness of the wall. Soil variability was found to have a significant impact on the outcome of Monte Carlo simulations, resulting in a wide range of normalized maximum lateral deformations for a given wall stiffness. A new stiffness factor has been proposed that incorporates the horizontal spacing of the support elements, which is capable of covering a wider range of excavation support system types, thus enhancing the accuracy of the analyses.

Research on effective pit fencing solutions for the construction of a two-level parking lot of a multi-story building

A study on the effective placement of the piles in the retaining wall of the pit was carried out. A comparison of internal forces and horizontal displacements of the retaining wall piles was drawn among three variants of their placements in the wall. The influence on the calculation results of the detailing of the soil excavation process during modeling using the Plaxis 2D was examined. Based on the research on the stress-strain state (STS) of the retaining wall piles using the spatial setting of the problem, a comparison to the problem with the flat setting was drawn. Additionally, an analysis of the bending moments and horizontal displacements in the retaining wall piles with a spatial setting of the problem was made.
 Based on the obtained results, information on the effectiveness of different variants of the pile placement in the retaining wall of the pit, as well as the convergence of the calculation results with different detailing of the excavation process modeling is presented. Also, a comparison of the values of internal forces, horizontal displacements, and the elevation of the pit bottom between flat and spatial problem settings was made. The distribution of forces between piles of the retaining wall using a spatial problem setting is presented.
 The finite element model consists of the soil base and retaining wall structure. Modeling of the base was executed using the Hardening soil model, in which the following soil characteristics are used during the calculation: γ – the specific weight of the soil in its natural state; γsat – the specific weight of the soil in the water-saturated state; c – cohesion; φ – the effective stress friction angle; ψ – dilatancy angle; E50 – stiffness for primary loading; Eoed – oedometer loading stiffness; Eur – stiffness for un-/reloading. The calculation was made using the Plaxis program complex.
 Today, the effective and the most rational way of retaining wall design during the construction of buildings and structures with underground parts is significant. A successful choice of the construction of the excavation fencing not only ensures the reliability of the construction but also allows using building materials in the most efficient way. In addition, the choice of the method of the problem definition and its detailing are important factors when approaching the modeling process of similar problems, as they affect the accuracy of the obtained results, the degree of labor-intensiveness, and the time spent on the calculation.

Comprehensive powder flow characterization with reduced testing

Powder flow is a critical attribute of pharmaceutical blends to ensure tablet weight uniformity and production of tablets with consistent and reproducible properties. This study aims at characterizing different powder blends with a number of different rheologic techniques, in order to understand how particles’ attributes and interaction between components within the formulation generate different responses when analysed by different rheological tests. Furthermore, this study intends on reducing the number of tests in early development phases, by selecting the ones that provide the best information about the flowability attributes of the pharmaceutical blends. This work considered two cohesive powders - spray-dried hydroxypropyl cellulose (SD HPMC) and micronized indomethacin (IND) – formulated with other four commonly used excipients [(lactose monohydrated (LAC), microcrystalline cellulose (MCC), magnesium stearate (MgSt) and colloidal silica (CS)]. The experimental results showed that powder flowability may be affected by materials particles’ size, bulk density, morphology, and interactions with lubricant. In detail, parameters, such as angle of repose (AoR), compressibility percentage (CPS), and flow function coefficient (ffc) have shown to be highly affected by the particle size of the materials present in the blends. On the other hand, the Specific Energy (SE) and the effective angle of internal friction (φe) showed to be more related with particle morphology and materials interaction with the lubricant. Since both ffc and φe parameters are generated from the yield locus test, data suggest that a number of different powder flow features may be understood only by applying this test, avoiding redundant powder flow characterization, as well as extensive time and material spent in early development formulation stages.

Deformation analysis of underwater shield tunnelling based on HSS model parameter obtained by the Bayesian approach

Deformation analysis and control of underwater large-diameter shield tunnels is a prerequisite for safe tunnel construction. Reasonable selection of constitutive model and its parameters is the key to accurately predicting the deformation induced by underwater shield tunnelling. In this paper, the finite element analysis of cavity expansion during the piezocone penetration test (CPTU) based on the hardening soil model with small strain stiffness (HSS) model was carried out, and the correlation model of the normalized cone tip resistance Q with the reference secant modulus E50ref and the effective internal friction angle φ’ was established and verified using mini CPTU chamber test. Then, a Bayesian probability characterization approach for E50ref of silty clay based on CPTU was proposed. Furthermore, the deformation analysis of Jinan Yellow River tunnel crossing the south embankment was carried out to verify the reliability of the proposed approach. The good agreement between the field measurement and numerical simulation confirms that the parameters obtained by the Bayesian approach are reliable. Finally, a sensitivity analysis was performed to study the law of riverbed settlement induced by underwater large-diameter shield tunnelling. The results show that the increasing support pressure could effectively reduce the riverbed settlement, but there is an upper limit. The optimal support pressure of established model is between 0.45 MPa and 0.5 MPa. The uphill section causes greater riverbed settlement than the downhill section. Under the same condition, increasing buried depth and water level will lead to a more significant settlement.

Investigating the compressibility and flowability of cocoa powders: A solution for chocolate industry

AbstractThe flowability and compressibility properties were determined for two types of cocoa powders, which are used commercially in chocolate industries; alkalized and natural cocoa powders. Physical and flow properties have a very significant role in the flow behavior, which relates to the handling, transportation, and storage of bulk powders. Throughout the research, it was observed that the properties of both cocoa powders are similar. The objectives of this work are to compare the compressibility and flowability between alkalized and natural cocoa powders and to design the minimum opening size of hopper for mass flow based on their flow properties. Jenike's mathematical methodology is applied during the research for the design of conical hoppers for mass flow. Besides, powder flow analysis using powder flow analyzer is one of the testing methodologies in this research. In addition, direct shear box tests were performed with three different normal stresses. The alkalized cocoa powder needs 1.366 m in diameter for the opening of the hopper, while the natural cocoa powder needs 1.531 m. From the results of the study conducted, it was concluded that both cocoa powders are very cohesive and have poor flow properties. This research reveals that the physical and flow properties of two main types of cocoa powder contributed a lot to the process of hopper design, enhance process understanding, and also applicable for analyzing the powder behavior at any stage in industry.Practical applicationsCocoa powder is the essential ingredient of chocolate manufacturing and other food industry having a chocolate‐like flavor including beverages, biscuits, desserts, and so forth. In chocolate industry, the flow behavior of cocoa powders can affect manufacturing efficiency, which directly affects the production capacity and product quality in terms of its weight and content uniformity. In this study, the critical design parameters such as hopper angle and size of opening were determined to improve the flowability of cocoa powders when passes through hopper. The findings of the present study make it possible for an accurate estimation of a correct intersection with the hopper flow factor line and effective angle of internal friction (δ), extrapolating the powder flow function ff curve to obtain hopper opening size for each cocoa powder for better flowability.

Experimental study on soil-water characteristics and strength characteristics of complete-intense weathering mudstone in seasonal frozen area.

To study the soil-water characteristics and shear strength of unsaturated complete-intense weathering mudstone, the soil-water characteristic curve of complete-intense weathering mudstone and the matric suction of mudstone samples under natural state were measured. This measurement was through a soil-water characteristic test using a pressure plate instrument. Based on the results of soil-water characteristic test, an unsaturated (saturated) triaxial shear test was carried out. Under different temperatures and confining pressure conditions, the shear strength and deformation characteristics of complete-intense weathering mudstone under natural water content and saturation conditions were investigated. The results show that the percentage of silt and clay in unsaturated complete-intense weathering mudstone in natural state is relatively high, with the mudstone having less sand, and a weak permeability and exhibiting a significant capillary phenomenon. The complete-intense weathering mudstone with a natural moisture content of 19.15% has a matric suction of 210 kPa. When the temperature is constant, the shear stress of the sample increases with the increase of confining pressure. When the temperature decreases from 0 to -20°C, the influence of confining pressure on the rock samples gradually decreases. The rock sample has the property of strain hardening during shearing. Under the same matric suction, the total cohesion increases with the decrease of temperature. At a positive temperature, the effective internal friction angle increases with the decrease of temperature. At a negative temperature, the lower the temperature, the smaller the effective internal friction angle. The test of shear strength parameters of saturated complete-intense weathering mudstone is simple and conservative. In practical engineering, the basic properties of unsaturated complete-intense weathering mudstone can be predicted by testing the shear strength parameters of saturated complete-intense weathering mudstone. The results of the study are important for better understanding the nature of unsaturated complete-intense weathering mudstone and improving the safety of engineering construction in complete-intense weathering mudstone areas.

Stability Analysis of Box Tunnel Working Face under Non-Uniform Support Pressure

For rectangular section tunnel construction, soil bin pressure fluctuates under biaxial emergence conditions. Support pressure is difficult to uniformly distribute, and it can easily cause instability of the tunneling face. The Silo-wedge model is used to perform horizontal strip splitting of parts of the soil at risk for instability under unsupported conditions. In the ultimate equilibrium analysis, the strength discounting method is introduced, a new expression for the safety factor is derived by combining the horizontal strip splitting equilibrium equations, and the safety factor is solved numerically. When the opening range is greater than 0.75 and the effective internal friction angle of the soil is less than 25°, the safety coefficient is less than 1, and destabilization damage is likely to occur. The field application of a box tunnel project in Suzhou demonstrates that the research results have good engineering applicability to the issue.

Impact of mica on geotechnical behavior of weathered granitic soil using macro and micro investigations

The micaceous weathered granitic soil (WGS) is frequently encountered in civil engineering worldwide, unfortunately little information is available regarding how mica affects the physico-mechanical behaviors of WGS. This study prepares reconstituted WGS with different mica contents by removing natural mica in the WGS, and then mixes it with commercial mica powders. The geotechnical behavior as well as the microstructures of the mixtures are characterized. The addition of mica enables the physical indices of WGS to be specific combinations of coarser gradation and high permeability but high Atterberg limits. However, high mica content in WGS was found to be associated with undesirable mechanical properties, including increased compressibility, disintegration, and swelling potential, as well as poor compactability and low effective frictional angle. Microstructural analysis indicates that the influence of mica on the responses of mixtures originates from the intrinsic nature of mica as well as the particle packing being formed within WGS. Mica exists in the mixture as stacks of plates that form a spongy structure with high compressibility and swelling potential. Pores among the plates give the soil high water retention and high Atterberg limits. Large pores are also generated by soil particles with bridging packing, which enhances the permeability and water-soil interactions upon immersion. This study provides a micro-level understanding of how mica dominates the behavior of WGS and provides new insights into the effective stabilization and improvement of micaceous soils.

Statistical Analysis of the Effective Friction Angle of Sand Tailings from Germano Dam

Tailings dam accidents emphasize the importance of an adequate understanding of the strength parameters of tailings to improve the efficiency and effectiveness of the design, construction, and operation of such structures. Usually, the tailings strength is addressed in a deterministic manner. However, a statistical approach would better represent their behavior due to its inherent heterogeneity. The literature about tailings strength distribution is relatively rare or superficial, which impairs the probabilistic analyses which are essential for risk management. Therefore, this article focuses on the probability density function (PDF) of the effective friction angle (ϕ′) of iron ore tailings from the reservoir of Germano dam, Mariana, Brazil, based on data from publicly available CPTu tests. The influence of the relative density (Dr), and the presence of plastic layers amidst the sand tailings on the strength of the sand are also discussed herein. Several correlations were employed to estimate ϕ’ and Dr. According to the results, the presence of plastic layers influences the estimated properties, and the relative density has a log-normal distribution. The effective friction angle, on the other hand, presents a normal distribution.

Evaluating friction angles for clays: piezocone tests compared with Atterberg limits

A limit plasticity solution for evaluating the effective stress friction angle in clays from piezocone tests was assessed and compared with the popular notion of using laboratory Atterberg limits on remoulded specimens. The results showed that the in situ piezocone-based method provided a far more accurate and robust interpretation of the friction angle values of 155 separate clays than empirical correlations with plasticity index when compared with laboratory benchmark values obtained from triaxial compression tests. For illustration, the piezocone-based method was shown successfully to capture the effective stress parameter of four clays with friction angles of 20–37°: normally consolidated kaolin clay in chamber tests; natural soft clay deposit located at Bothkennar, UK; Troll offshore clay in the North Sea; and soft plastic lacustrine deposits in Bogota, Colombia.

Experimental investigation and modeling of the mechanical behaviour of Yanji swelling mudstone subjected to wetting-drying-freezing-thawing cycles

Rocks and soils in seasonally frozen regions are subjected to cyclic wetting–drying-freezing-thawing (WDFT) process. The influence mechanism of WDFT process on their mechanical behaviour is not fully understood and the existing constitutive models are not capable of capturing the strain-softening behaviour under WDFT cycles. In the present study, a series of consolidated drained triaxial compression and mercury intrusion porosimetry tests were performed on Yanji mudstone subjected to WDFT cycles. Results indicated that the WDFT cycles could induce a large amount of cracks and large pores between aggregates and compress the aggregates with a decrease of the intra-aggregate pores. After cyclic WDFT process, the specimens exhibited more significant strain-softening and dilative behaviour. The elastic modulus, peak and residual shear strengths of the mudstone decreased significantly with increasing WDFT cycles, especially in the case of low confining pressures. These decreases were more pronounced in the first four cycles and became negligible after 4 cycles. As the cyclic number increased, the cohesion of specimens decreased remarkably owing to the presence of cracks and the destruction of bonds between aggregates. By contrast, the effective friction angle, Poisson’s ratio and dilatancy angle increased with the WDFT cycles due to the more compact aggregates induced by the high suction during drying process. A nonlinear elastic constitutive model was developed for describing the strain-softening behaviour of Yanji mudstone subjected to WDFT cycles. The deviator stress-axial strain relationship predicted by the proposed model agreed well with the measured one, indicating the relevance of the predictive model.

Prediction Models of Newmark Sliding Displacement of Slopes Using Deep Neural Network and Mixed-effect Regression

For assessing the seismic stability of slopes, the Newmark sliding displacement is an essential consideration. This study develops a deep neural network (DNN) prediction model and a hybrid prediction model with ground-motion intensity measures for the Newmark slope sliding displacements. The models are developed using a large number of ground motions and critical accelerations (ac) samples generated under a wide range of slope conditions. The DNN and hybrid models we proposed are more efficient and sufficient than the conventional regression models. In comparison with conventional regression models (SR08), they significantly reduce the standard deviations. For the first time, within- and between-ac residuals are distinguished in the hybrid model using a mix-effects regression algorithm. Further, the hybrid model that includes the effective friction angle improves prediction performance greatly. As a final step, the proposed models are applied in probabilistic slope displacement hazard analysis (PSSDHA) to demonstrate their effectiveness in engineering applications.

Strength of partially frozen sand under triaxial compression

To investigate the effect of the pore matrix (i.e., ice and unfrozen water) on the strength of partially frozen sand, a series of triaxial compression tests with internal pore water pressure (PWP) measurements were performed. Both dense and loose saline sand samples were prepared by rapidly freezing the samples and then slowly warming the samples to, and subsequently shearing at the temperature of −3 °C. Test results indicate the temperature only affects the effective cohesion, not the effective friction angle of sand. The pore ice stress was estimated using Ladanyi and Morel’s 1990 postulate on the internal stresses within frozen soil; the stress (hydrostatic) change in pore ice was reflected by an equal change in PWP in the partially frozen loose sand. Based on Ladanyi and Morel’s 1990 concept of internal confinement in frozen sand, a Mohr–Coulomb model that uses effective failure and residual friction angles from unfrozen sand to estimate the strength of partially frozen sand is presented. The proposed model reflects how the pore matrix contributes to the strength of partially frozen sand. For loose sand, the peak strength is enhanced by the internal confinement and cohesion resulting from the pore water (suction) and pore ice, respectively. For dense sand, only pore ice affects the peak strength by incorporating the internal confinement and cohesion.