This study develops two three-dimensional fractional derivative viscoelastic models and introduces a novel L2-1 sigma difference formula for numerical implementation. In deriving the fractional derivative models, a spring-pot element, defined by Caputo fractional calculus, replaces the dashpot or spring in the classical Kelvin-Voigt model. Using the Laplace transform approach, the creep compliance and stress relaxation modulus of the fractional derivative model are derived. Additionally, the models are extended into a generalized three-dimensional form, and a novel L2-1 sigma difference algorithm is employed to discretize the constitutive equations. This method has been shown to provide superior computational efficiency and accuracy compared to the GL algorithm, with a convergence order of 3-alpha. Subsequently, one of the models was compiled and implemented through the UMAT interface of ABAQUS, facilitating both element-level and large-scale project simulations. The numerical predictions from the model were compared with the results of triaxial creep tests conducted on Hangzhou clay and Hong Kong marine clay. The results confirm a reasonable degree of agreement between the predicted and experimental results, validating the accuracy and feasibility of both the model and the L2-1 sigma difference algorithm. Furthermore, when applied to a practical case involving the long-term deformation of an artificial island construction project, the predictions from this model exhibit strong consistency with the measured data. This work provides valuable insights into understanding and predicting the time-dependent behavior of viscoelastic materials.

Engineering waste mud is commonly generated during construction activities. Improper disposal or indiscriminate piling of this waste may pose significant risks to environmental geology. An eco-friendly hydrophobic polymer can be used as an effective additive for soil reinforcement, and the modified soil has the potential to be reused as infrastructure materials. This study investigates the disintegration characteristics of hydrophobic polymer-modified mud soil under climate-induced conditions, such as flooding or rainfall. Soil slaking tests were conducted to investigate the effects of the polymer treatment on soil immersion disintegration resistance. Wetting-drying (WD) cycle tests were carried out to investigate the effects of the polymer treatment and the number of WD cycles on mechanical strength and microstructural evolution. The digital image correlation (DIC) technique was used to examine the effect of the polymer treatment on the deformation patterns of the specimens. The results indicated that: (1) The polymer significantly enhanced the soil's disintegration resistance to disintegration under complete immersion conditions. The disintegration ratio decreased from 92.9 % to 44.3 %, as the additive dosage increased from 0 % to 5 %. (2) The polymer-modified soil exhibited better resistance to strength deterioration under WD cycles, with a strength loss of 9.0 % for the modified soil (reinforced with 5 % hydrophobic polymer) compared to the untreated soil after 7 cycles. (3) Microstructural analysis demonstrated that the polymer reduced porosity and increased microstructural integrity by filling soil pores and cementing particles while mitigating WD damage. Papilla-like structures resembling the micro/nanostructures on the natural lotus leaf were observed, which are believed to enhance the water resistance of the soil. This research provides valuable insights into the use of hydrophobic polymer for improving waste mud and the potential reuse of modified mud in geological and geotechnical engineering.

Fractional calculus has proven to be highly effective in simulating the viscoelastic and memory-dependent behavior of materials. This paper presents a three-dimensional fractional derivative standard linear solid (FSLS) model and its numerical implementation. By introducing the Caputo fractional operator to define a new Koeller spring-pot element, a one-dimensional FSLS model is developed, which can degenerate into other fractional derivative models, including the fractional derivative Maxwell (FM) and fractional derivative Kelvin-Voigt (FKV) models. The three-dimensional constitutive relationships are derived using a tensor generation method, and high-precision difference equations are formulated using the L_1 time-discretization scheme. The model is implemented in ABAQUS using the UMAT interface and validated through creep and relaxation tests. The results indicate that: (1) The FSLS model based on the Caputo fractional operator is better suited for finite element computations because it avoids singularity issues, preventing computational difficulties; (2) The L_1 discretization formula, with improved accuracy of order 2- α , can be employed to develop three-dimensional fractional derivative models and facilitate their numerical implementation in engineering applications; (3) A comparison between model predictions with experimental data demonstrates that the proposed model effectively captures the time-dependent behavior of geotechnical materials. The proposed model and discretization method provide valuable support for understanding and simulating the time-dependent deformation of geomaterials.

A two-dimensional consolidation model for unsaturated–saturated soils under plane strain conditions is developed based on Fredlund’s and Terzaghi’s consolidation theories for unsaturated and saturated soils, respectively. Furthermore, an interfacial flow contact model is proposed based on the Hagen-Poiseuille law to describe the laminar flow induced by low-velocity pore water movement at the layer interface. Semi-analytical solutions for pore water pressure, pore air pressure, and settlement were derived using Laplace transforms, their inverses, and Fourier sine series expansion. The effects of the flow contact transfer coefficient (Rw) and flow partition coefficient (ηw) on pore water pressure, pore air pressure, and settlement are discussed based on these solutions. Results show that the interfacial flow contact resistance effect impedes the discharge of pore water, thereby generating a relative pore pressure gradient at the interface. Simultaneously, it slows the settlement rate of unsaturated–saturated soil systems. As the flow contact transfer coefficient increases or the flow partition coefficient decreases, the relative pore pressure gradient at the interface becomes more pronounced, resulting in a slower settlement rate.

In response to the growing ecological issues caused by engineering waste mud and the lack of effective solutions. This study first examines the physical properties and the microstructure of raw waste mud. Subsequently, environmentally friendly and sustainable lignocellulosic fibers from industrial waste were incorporated to improve the waste mud soil, with an addition ratio ranging from 0 % to 4 %. The effects of fiber content on the strength reinforcement and stress-strain behavior of the reinforced soil specimens were evaluated through a series of direct shear tests and unconfined compressive strength (UCS) tests. The environmental properties were assessed through pH tests, and microstructure changes were analyzed using scanning electron microscopy (SEM). Finally, the reinforcement mechanism was revealed by combining mechanical performance and microstructural evolution. The results indicate that the addition of lignocellulosic fibers effectively enhances the mechanical strength and deformation resistance of the reinforced specimens compared to natural mud. The UCS of untreated mud soil is 144 kPa, while the UCS of the treated soil, with an optimal fiber content of 3.0 %, increases to 304 kPa after 7 days of curing. The pH test results indicated that regardless of the fiber content, the pH remained approximately 8.8, suggesting that the incorporation of lignocellulosic fibers has minimal impact on the acidity or alkalinity of the specimens. The reinforcement mechanism of lignocellulosic fibers in mud primarily involves microparticle filling effects that compact pore spaces and bridging effects that connect soil particles. This study offers valuable insights into the use of fibers as additives for waste mud treatment and their potential for reuse in geotechnical engineering.

Open-ended pipe piles (OEPPs) are widely used in offshore foundations, yet accurately predicting their driving responses remains challenging due to soil plug complexities. Existing pile driving analysis models inadequately characterize the effects of soil plug, potentially leading to driving problems such as hammer refusal, pile running, and structural damage. This paper proposes an effective soil plug (ESP) model for OEPP driving analysis. The ESP model considers the effective range of soil plug, which exerts internal resistance that increases exponentially with depth while the beyond of effective range contributes only mass inertia. It also accounts for the relative slippage at the pile-soil plug interface. A differential iterative method is developed to solve the ESP model. Subsequently, investigations including the model validation and parameter analysis are conducted. Model validations against existing models and field measurements confirms the reliability of the ESP model. Parameters sensitivity analysis reveals the importance of soil plug length and distribution type of internal resistance on the pile dynamic responses. In addition, if soil plug slippage occurs, the displacement peak of soil plug increases with depth rather than one-dimensional wave attenuation. Furthermore, contrary to previous assumptions of continuous slippage, the soil plug experiences a discontinuous “jump-sliding” mode under long-duration impact loading. These findings provide theoretical basis for OEPP driving simulation and interpretations of high-strain dynamic test.

Engineering waste mud, primarily produced during the construction of bored piles and slurry shield tunneling, represents a challenging type of construction waste to treat. Additionally, the disposal of industrial by-products also presents significant challenges. In this study, a sustainable solution is proposed by utilizing industrial by-product lignocellulosic fibers as reinforcement materials in geotechnical engineering, complemented by an eco-friendly hydrophobic polymer to treat the waste mud. The impact of additive content on mechanical properties was assessed through unconfined compressive strength (UCS) tests. The reinforcement mechanism was elucidated through microstructural observation tests, including scanning electron microscopy (SEM), X-ray diffraction (XRD), and mercury intrusion porosimetry (MIP). The results show that composite soil additive effectively improves the UCS of the engineering waste mud. The strength of the reinforced mud samples increases with the additive content and curing age, and the optimum dosages were found to be 4

During the process of treating soft soil foundations with prefabricated drainage drains (PVD), "soil columns" form around the PVD, and a "weak zone" forms outside the range of the "soil columns." The difference in properties between the two forms a distinct interface, leading to a gradual decrease in drainage efficiency and obstruction of vertical drainage channels, which in turn causes cracks and lateral displacement in the soil during consolidation. The interfaces between adjacent soil layers are incomplete contact, and the water within the interstices impedes the transfer of heat, manifesting a thermal resistance effect. To address this phenomenon, a synchronous measurement system for the thermal gradient and the heat flux density between the soil interfaces has been developed. Applying Fourier's law of heat conduction, the thermal resistance coefficient has been determined. Based on the theory of thermo-hydro-mechanical coupling, a multi-zone axisymmetric model for saturated soils that considers thermal resistance effect has been proposed. Semi-analytical solutions were derived and validated through comparison with the custom FEM model and field experiments. The thermal consolidation characteristics of the multi-zone soils under various thermal contact models have also been discussed, with a comprehensive analysis of the influence of different parameters. Outcomes show that: the generalized incomplete thermal contact model provides a better description of the thermal resistance phenomenon between multi-zone soils interfaces; ignoring the thermal resistance effect leads to an overestimation of the deformation during the thermal consolidation, and, the thermal resistance effect decreases the influence of the thermo-osmosis effect on the consolidation characteristics.

Waste slurry, a major by-product of urban construction, is produced in rapidly increasing volumes each year. Dehydrated waste slurry has potential as a roadbed material; however, its performance in freeze–thaw environments, which can induce frost heave and thaw settlement, and the mechanism of the influence of freeze–thaw cycles on its macro and micro properties are still unclear and need thorough investigation. This study explores the macroscopic and microscopic properties of waste slurry subjected to freeze–thaw cycles. We conducted unconfined compressive strength (UCS) and triaxial unconsolidated undrained (UU) shear tests, focusing on fissure compaction, elastic deformation, plastic yielding, and strain hardening stages. The results reveal a decrease in strength and elastic modulus with increasing freeze–thaw cycles, as well as in the damage degree generated by freeze–thaw cycles. To uncover the underlying microscopic mechanisms, we performed Scanning Electron Microscopy (SEM), X-ray diffraction (XRD), and mercury intrusion porosimetry (MIP) analyses. These tests highlighted the evolution of pores and microcracks during freeze–thaw cycles. These results have important reference values for the reutilization of waste slurry discharged from large-diameter bored piles for roadbed backfill materials that need to be repaired quickly in seasonally frozen areas.

The dynamic pile-soil interaction significantly affects the accuracy of pile vibration response analysis. However, currently, there is no well-established method for simulating pile toe soil under high-strain dynamic loading (HSDL), which presents a major challenge for pile driving analysis. This paper proposes a fictitious soil pile model to simulate reactions and stress wave propagation in the base soil under HSDL. The pile toe soil was regarded as a fictitious soil pile extending downward to the bedrock at a certain cone angle, considering the non-linear soil stiffness, radiation damping, and hysteretic damping. The solution of the soil responses was given by differential iterative method combined with MTLAB programming. The model's accuracy was validated against a three-dimensional (3D) finite element model and the Smith model. Sensitivity analysis was performed on parameters such as discreteness, time interval, cone angle, and non-linear stiffness. The model shows advantages in simulating stress wave propagation in pile toe soil under HSDL, with attenuation rates decreasing with depth and wave speeds stabilizing after an initial decrease. The soil elastic modulus, pile diameter, cone angle, and impact loads influence the attenuation rate, while only the elastic modulus significantly affects wave speed. The results could be helpful for the simulation of the pile toe soil under HSDL and the study of the attenuation of stress waves in the soil.

In this paper, the one-dimensional rheological consolidation characteristics of multilayered saturated soil foundations under time-dependent loading and heating are investigated by considering the semi-permeability and the interface thermal resistance. By introducing the fractional derivative model and the thermos-elastic theory, a thermo-mechanical coupling model is established to describe the rheological properties of saturated soils. Semi-analytical solutions for strain, temperature increment, pore water pressure and settlement were derived through the Laplace transform and its inverse. The accuracy of the solutions proposed in this paper has been verified by comparing with existing solutions. The effects of different thermal contact models of the interface on the rheological properties of saturated soils under semi-permeable boundary are discussed, and the effects of fractional derivative order, constitutive material parameters, and thermal conductivity of soil on the thermal consolidation process are investigated. The results show that: neglecting the thermal resistance effect can result in an overestimates of the impact of rheological properties on the thermal consolidation process of saturated soils under semi-permeable boundaries; As the thermal resistance coefficient increases, the influence of soil thermal conductivity on settlement decreases.

Layered unsaturated soils exhibit complex mechanical and physical properties. Owing to the roughness between unsaturated soil interfaces and the presence of irregularly distributed micro-pores, this study explores the laminar flow of pore water and counter-cyclonic flow of pore air through these channels at low velocities. In response to the complex consolidation behavior of unsaturated soils influenced by the flow and air contact resistance, an improved model is developed. The model incorporates the flow contact transfer coefficient (R-omega), flow partition coefficient (eta(omega)), air contact transfer coefficient (R-a) and air partition coefficient (eta(a)). Semi-analytical solutions for pore water pressure, pore air pressure and settlement in layered unsaturated soils are derived by employing the Laplace transform and its inverse transform. The rationality of the model is validated through comparative analysis with existing solutions. Analysis of the improved model yields critical insights: the presence of flow and air contact resistance leads to the development of relative pore pressure and air pressure gradients at interfaces, which diminishes the influence of the permeability coefficients of the water phase (k(omega)) and air phase (k(a)) on the consolidation process. Moreover, neglecting the flow and air contact resistance effects may lead to an overestimation of settlement.

An anisotropic egg-shaped bounding surface plasticity model (AESBS model) is proposed to describe cyclic and monotonic behaviors of saturated clays. The model is based on an innovative egg-shaped bounding surface, which not only eliminates the singularity present in most plasticity models and facilitates numerical calculation but also can be degenerated into various configurations. Moreover, to improve its representation when considering the initial consolidated state, an anisotropic tensor is incorporated into the bounding surface. Furthermore, a novel generalized isotropic hardening rule that combines isotropic and kinematic hardening is applied. It regards reversal stress points as homological mapping centers, hence leading to discrete and movable mapping centers. Notably, the elastic zone concept is employed to produce a more realistic performance of nonlinearity during cyclic loading. These modifications formulate the novel model that can be utilized to enhance the ability in predicting the behavior of saturated clays. To improve the convergence of the model, an implicit integration scheme is used to solved the constitutive relationship through some nonlinear algebraic equations. The comparison of simulation results and published experimental data from one-way undrained cyclic and monotonic triaxial tests for saturated clays demonstrates the efficiency of this model under different consolidated conditions.

Laminar flow phenomena may occur when pore water flows at low velocities across the interfaces of soils with different properties, thus causing flow contact resistance. To explore the impacts of interfacial flow contact resistance and rheological characteristics on the thermal consolidation process of layered saturated viscoelastic soil foundation featuring semi-permeable boundaries. This paper established a new thermal consolidation model by introducing a fractional order derivative model, Hagen-Poiseuille law and time-dependent loadings. The semi-analytical solutions for the proposed thermal consolidation model are derived through the Laplace transform and its inverse transform. The reliability and correctness of the solutions are verified with the experimental data in literatures. The influence of constitutive parameters, flow contact resistance model parameters on thermal consolidation process and the interfacial flow contact resistance on foundation settlement, is further explored. The results indicate that the impact of the constitutive parameters and permeability coefficient on the thermal consolidation of viscoelastic saturated soil is related to the flow contact resistance. The enhanced flow contact resistance effect leads to a significant increase in pore water pressure and displacement during the consolidation process.

Prefabricated vertical drains combined with heating is a new approach to improving the mechanical properties of soft clay foundations. Rising temperatures cause the formation of concentric and radially aligned soil regions with distinct heterogeneous characteristics. This results in incomplete contact between adjacent soil layers, with the water in the interstices impeding heat transfer and manifesting as a thermal resistance effect. Based on the theory of thermo-hydro-mechanical coupling, a two-dimensional dual-zone axisymmetric marine soft soil model improved by a prefabricated vertical thermo-drain has been established. A generalized incomplete thermal contact model has been proposed to describe the thermal resistance effect at the interface of concentric soil regions. The effectiveness of the numerical solution presented in this paper is verified by comparison with semi-analytical solutions and model experiments. The thermal consolidation characteristics of concentric regions of soil at various depths under different thermal contact models were discussed by comprehensively analyzing the effects of different parameters under various thermal contact models. The outcomes indicate that the generalized incomplete thermal contact model provides a more accurate description of the radial thermal consolidation characteristics of concentric regions of soil. The influence of the thermal conductivity coefficient on the consolidation characteristics of the concentric regions soil is related to the thermal resistance effect.

Purpose The purpose of this paper is to suggest an implicit integration method for updating the constitutive relationships in the newly proposed anisotropic egg-shaped elastoplastic (AESE) model and to apply it in ABAQUS. Design/methodology/approach The implicit integration algorithm based on the Newton–Raphson method and the closest point projection scheme containing an elastic predictor and plastic corrector are implemented in the AESE model. Then, the integration code for this model is incorporated into the commercial finite element software ABAQUS through the user material subroutine (UMAT) interface to simulate undrained monotonic triaxial tests for various saturated soft clays under different consolidation conditions. Findings The comparison between the simulated results from ABAQUS and the experimental results demonstrates the satisfactory performance of this implicit integration algorithm in terms of effectiveness and robustness and the ability of the proposed model to predict the characteristics of soft clay. Research limitations/implications The rotational hardening rule in the AESE model together with the implicit integration algorithm cannot be considered. Originality/value The singularity problem existing in most elastoplastic models is eliminated by the closed, smooth and flexible anisotropic egg-shaped yield surface form in the AESE model. In addition, this notion leads to an efficient implicit integration algorithm for updating the highly nonlinear constitutive equations for unsaturated soft clay.

This paper presents the experimental investigation carried out for evaluation of the rheological behaviours of Hangzhou soft clay, and proposes a three-dimensional elastic viscoplastic model to describe the rheological characteristics under triaxial condition. Firstly, the time-dependent behaviours of Hangzhou soft clay, such as creep and strain rate effects, were observed and discussed based on the analysis of rheological tests. Subsequently, a constitutive model was formulated under the framework of Perzyna’s overstress theory and incorporates other developments, including: 1) A smooth and continuous egg-shaped yield surface, whose shape can change from an ellipse to a teardrop shape, thus providing greater flexibility for better modelling; 2) An equivalent time concept, which enables the model to describe the time-dependent behaviours under different loading paths. By varying the shape parameter, the newly established model can be degenerated into modified Cam-clay (MCC) model or Yin-Graham elastic viscoplastic model. Finally, the model was solved numerically using the fourth-order convergent iterative method combined with the Runge-Kutta method. Comparison of simulation results and experimental data shows that the newly proposed model has an ability to predict creep characteristics and strain rate effects of soft clay.

The frequency of mudflow disasters induced by rainfall in the Loess Plateau is increasing with the occurrence of global warming. The initial water content is one of the basic properties of soil, which affects the initiation of loess mudflow. In this work, the field study of the debris flow gullies in Yan’an City, Shaanxi Province, China, was conducted, and the main factors that induce gully loess mudflow were summarized. Based on the investigation results, a flume model was designed to carry out flume tests with different initial soil water contents. The experimental results demonstrate the following. (1) Different initial soil water contents lead to different soil failure models. The damage of soil by water flow when the soil water content is in the range of 0−5% is mainly gully erosion; that within the range of 10−15% is mainly rill surface erosion; that within the range of 20−25% is mainly dam breach failure. (2) When the water content of loess is equal to or less than 5% or equal to or greater than 20%, soil can promote the formation of loess mudflow, and the destruction of soil is more likely to cause mudflow disasters. In contrast, when the water content is within 10−15%, loess mudflow is not easily produced. The research results of the initial water content provide not only theoretical support for the study of loess mudflow disasters, but also a reference for the prevention and control of loess mudflow disasters in the Loess Plateau.

The impact of shield tunnels on neighboring buildings during construction has received more attention, while the impact of tunnels on neighboring buildings during operation has been little studied. However, in order to guarantee the safety of the architectures, the influence on adjacent ancient architectures which are sensitive to vibration and displacement should not be neglected during tunnel operation period. In this paper, numerical simulation is used to study whether the vibration and displacement of the adjacent ancient pagoda, Hangzhou White Pagoda, meet the safety control standards during the operation of the shield tunnel. According to the Finite Element Method analysis, judgment on safety of White Pagoda was made. The results of numerical simulation showed that the tunnel operation had a low impact on the adjacent White Pagoda.

The amount of underground engineering increases steadily in large and medium-sized cities as unban construction develops rapidly. Then surrounding effect caused by tunneling is of great concern, especially the effect to important building and vibration-sensitive buildings. For tunneling engineering construction effect of Hangzhou Zijiang road to Hangzhou white pagoda, comprehensive numerical simulated analyses were conducted. Three dimensional Foundation-tunnel-pagoda FEM model has established. Effect caused by tunneling engineering construction to Hangzhou white pagoda was calculated with ABAQUS software. The simulation results showed that the calculated vibration value has gone beyond the limitation of standard regulation value without protective measures. It does not satisfy isolative vibration requirement under isolation trench of superficial layer (8.2 m). And it can satisfy the requirement under isolation trench of medium layer (17.45 m) and better satisfies the requirement under isolation trench of deep layer (32.7 m).