Solution For Consolidation Research Articles

A Novel Analytical Solution for Slurry Consolidation Induced by a Vacuum-Assisted Prefabricated Horizontal Drain

A Novel Analytical Solution for Slurry Consolidation Induced by a Vacuum-Assisted Prefabricated Horizontal Drain

A general solution of consolidation for a double-layer foundation soil induced by pre-excavation dewatering with bottom reinforcement considering delayed responses of water table

Precisely predicting soil deformation at each construction stage of foundation pit engineering is crucial for enhancing construction safety standards. However, the mechanics of ground settlement, both inside and outside foundation pits caused by pre-dewatering in an unconfined aquifer, remain unclear. Hence, this study proposes a semi-analytical solution that considers factors, such as soil stratification, pit bottom reinforcement, and unsteady pumping-induced flow in the unconfined aquifer, using finite Fourier transform and boundary transformation techniques. It verifies the acceptability of the proposed solution by comparing experimental and numerical results from COMSOL Multiphysics. A detailed parametric analysis is conducted to discuss how pit reinforcement parameters, specific yield, and soil stratification influence the behaviors of drawdown and deformation. The results indicated that increasing the reinforcement thickness at the pit bottom and reducing the permeability of the reinforcement layer can effectively mitigate soil deformation and drawdown. In contrast, the compression modulus of the reinforcement layer affects only the ultimate value of deformation. In addition, a larger specific yield significantly delays the rate of drawdown and deformation but does not impact their final values. For double-layer foundation soils, the final value of deformation and drawdown is reduced when the lower layer has higher permeability, resulting in less time for settlement completion. This study provides a theoretical reference for the engineering design of foundation pit projects.

Axisymmetric consolidation behavior of multilayered unsaturated soils with transversely isotropic permeability

Time-dependent consolidation behavior of unsaturated soils is a vital problem in the geotechnical engineering. With the aid of the Fredlund consolidation theory, this work further assumes the total stress of soils skeleton freely change, and extends the Fredlund consolidation theory to a Biot-type theory, establishing the fully-coupled equation model of multilayered unsaturated poroelastic media with transversely isotropic permeability. To convert the partial differential governing equation into ordinary differential equations, the integration transform technology is applied. Subsequently, the precise integration method is used to acquire the time-dependent consolidation solution of multilayered unsaturated media with transversely isotropic permeability in the transformed domain, which is further solved in the actual domain by the inverse Hankel transform. A verification examples is provided to compare the present results with the existing work in the literature, showing a great coincidence and proving the feasibility of the present solution. Finally, numerous numerical examples are presented to investigate the evolution of excess pore pressure and settlement under quasi-static loads, revealing the consolidation behavior of unsaturated soils. The results demonstrates that the ramping time, stratification, permeability, depth and m1w have a significant effect on the consolidation behavior.

Analytical Solutions for Composite Foundations Reinforced by Partially Penetrated Stone Columns and Vertical Drains

ABSTRACTWhen stone columns or vertical drains are applied to improve soils, it is common to face situations where the soft soil layer is too thick to be penetrated completely. Although consolidation theories for soils with partially penetrated vertical drains or stone columns are comprehensive, consolidation theories for impenetrable composite foundations containing both two types of drainage bodies have been few reported in the existing literature. Equations governing the consolidation of the reinforced zone and unreinforced zone are established, respectively. Analytical solutions for consolidation of such composite foundations are obtained under permeable top with impermeable bottom (PTIB) and permeable top with permeable bottom (PTPB), respectively. The correctness of proposed solutions is verified by comparing them with existing solutions and finite element analyses. Then, extensive calculations are performed to analyze the consolidation behaviors at different penetration rates, including the total average consolidation degree defined by strain or stress and the distribution of the average excess pore water pressure (EPWP) along the depth. The results show that the total average consolidation rate increases as the penetration rate increases; for some composite foundations with a low penetration rate, the consolidation of the unreinforced zone cannot be ignored. Finally, according to the geological parameters provided by an actual project, the obtained solution is used to calculate the settlement, and the results obtained by the proposed solution are in reasonable agreement with the measured data.

Analytical Solutions for Consolidation of Soft Ground With Impervious Columns Considering Non‐Darcian Flow

ABSTRACTCohesive material columns have been extensively used in foundation improvement projects to enhance the bearing capacity of composite foundations and mitigate post‐construction settlement. However, the low permeability of cohesive material columns restricts the dissipation of pore water primarily through the top surface of the foundation, potentially resulting in longer drainage paths compared to foundations treated with granular material columns or vertical drains. Moreover, the impact of non‐Darcian flow within soils on consolidation behavior becomes increasingly pronounced as the drainage path increases. Consequently, a novel analytical model for the consolidation of impervious column‐assisted foundations is established, which can incorporate the seepage model accounting for the initial hydraulic gradient. The accuracy and reasonableness of the obtained solution are then validated by conducting a comparative analysis with existing models and through a detailed case study. Furthermore, a parametric analysis is conducted to delve into the influence of several crucial factors on the consolidation performance. The findings demonstrate that non‐Darcian flow has a greater influence on composite foundations compared to natural foundations. Additionally, the threshold value of the well‐diameter ratio decreases with the increase in the initial hydraulic gradient. Finally, the final seepage front remains at a shallower position when the column–soil modulus ratio becomes larger, and the influence of non‐Darcian flow on the consolidation rate becomes more pronounced.

Analytical solution for radial consolidation of combined electroosmosis-vacuum-surcharge preloading considering free strain and cyclic loading

In this study, electro-osmotic consolidation considering smear effect and free strain under cyclic loading was investigated. The analytical solution of radial consolidation of electroosmosis-vacuum-surcharge combined preloading is derived by using the Bessel function and eigenfunction methods. Subsequently, the effectiveness of the proposed method is validated through comparison with existing numerical solutions. Based on the derived solutions, the influence of the smear effect, applied voltage, vacuum pressure, and cyclic loading on soil consolidation characteristics was analyzed. The results showed that the smearing effect slows the rate of consolidation, but the final average consolidation and negative excess pore water pressure are enhanced. Compared with only cyclic loading, the combined effect of electroosmosis, vacuum, and surcharge preloading enables the soil to achieve higher strength and consolidation. When the effect of electroosmosis alone on reinforcing low-permeability soils is not significant, the combination of electroosmosis with vacuum preloading helps enhance the soil reinforcement effect.

An Analytical Solution for Nonlinear Consolidation of Composite Foundations Improved by Impermeable Columns and Vertical Drains with Time-Dependent Well Resistance

An Analytical Solution for Nonlinear Consolidation of Composite Foundations Improved by Impermeable Columns and Vertical Drains with Time-Dependent Well Resistance

Semianalytic Solution for Two-Dimensional Consolidation of Interbedded Soil

Semianalytic Solution for Two-Dimensional Consolidation of Interbedded Soil

Large strain consolidation of soft soils with partially penetrating PVDs: Analytical solutions incorporating variable well resistance

The large-strain geometric assumptions and nonlinear compressibility and permeability have significant effects on the consolidation of soft soils with high compressibility. However, analytical solutions for large-strain nonlinear consolidation of soft soils with partially penetrating PVDs have been rarely reported in the literature. A double logarithmic model is adopted to describe the nonlinear compressibility and permeability of soft soils with high compressibility, and a large-strain consolidation model for soft soils with partially penetrating PVDs under the condition that the excess pore water pressure at the interface between the improved and unimproved layers is equal is established based on Gibson’s large-strain consolidation theory. The analytical solution for the large-strain nonlinear consolidation model for soft soils with partially penetrating PVDs is obtained. The reliability of the analytical solution obtained in this study is verified by comparing it with the existing solutions under different conditions, and the maximum deviation between the two methods does not exceed 5 %. On this basis, consolidation behaviors of soft soils with partially penetrating PVDs under different conditions were analyzed by extensive calculations. Finally, the proposed analytical solution for the large strain consolidation model is applied to the settlement calculation of the Bachiem Highway Project, which further demonstrates the applicability of the consolidation model.

Analytical Solution for Radial Consolidation of Combined Electroosmotic, Vacuum, and Surcharge Preloading Considering Smear Effects

Analytical Solution for Radial Consolidation of Combined Electroosmotic, Vacuum, and Surcharge Preloading Considering Smear Effects

Comparison Regarding the Carbon Footprint of Various Sustainable Seismic Consolidation Solutions for Romanian Orthodox Churches

In Romania, there are numerous Orthodox churches, many of which are historical monuments of great cultural value that have suffered multiple degradations over time due to various natural or man-made reasons. In a context that is currently increasingly focused on environmental protection, we aim to analyse the carbon footprint of several different consolidation proposals to an Orthodox church with structural deteriorations (and more) and the equivalent impact if a similar building were erected with new materials. The research is proposed to be a stepping stone for determining the sustainability of interventions for orthodox churches, as the existing literature is scarce when it comes to the emissions of these churches and there is no norm to prevent unsustainable interventions. The Orthodox Church “Sfintii Voievozi”, the subject of the analysis, is in the city of Tg. Jiu, Gorj County. The construction was documented to be between 1748 and 1764 and is a historical monument listed in the LMI GJ-II-m-A-09189 registry. The architectural solutions for the church and the structural elements that comprise the load-bearing system are presented. A detailed investigation was conducted to determine structural and non-structural degradations, specifying the main causes that have produced them. With regard to consolidation solutions, two options are presented and compared in this paper: Alternative I—minimal intervention and Alternative II—maximal intervention, both of which are reversible. The carbon footprint calculation was carried out for both options, determining the associated material consumption, and compared to the carbon footprint for the case of a new construction. In conclusion, the consolidation methods with a minimal degree of intervention is recommended as the “most environmentally friendly”, considering carbon emissions when comparing the options.

Analytical Solution for Nonlinear Consolidation Considering Time-Dependent Well Resistance and Lateral Deformation under Vacuum Preloading

Analytical Solution for Nonlinear Consolidation Considering Time-Dependent Well Resistance and Lateral Deformation under Vacuum Preloading

Semi-analytical solution for one-dimensional coupling consolidation of original soil and electro-osmotic layer using horizontal electrodes

The application of horizontal electro-kinetic geosynthetics for electro-osmotic consolidation is becoming increasingly widespread. Such horizontal electrodes are typically arranged at intervals, allowing pore water in original soil to pass through the intervals and penetrate into the electro-osmotic layer. In this study, a one-dimensional semi-analytical solution for a double-layered electro-osmotic system incorporating the original soil was presented and verified. The effects of the soil properties on the consolidation process were investigated. Results revealed that original soil can achieve a significant consolidation effect, even better than electro-osmotic dredged soil. A smaller permeability coefficient of original soil significantly prolongs the consolidation time, while a thicker original soil can improve the average consolidation effect of the two layers. The proposed model provides new electrode arrangement ideas and theoretical support for horizontal electro-kinetic geosynthetics for electro-osmotic reinforcement.

Identification and Mitigation of Subsidence in Karstic Areas with Sustainable Geotechnical Structures: A Case Study in Gallur (Spain)

In various areas of the Ebro valley in Spain, including the region discussed here, the risk of sinkholes is becoming particularly severe, particularly impacting urban areas and roadways where land subsidence from karstic processes is common. However, knowledge of the area, its geological–geotechnical configuration, and the carrying out of specific research studies are allowing solutions to be tested in an attempt to resolve these situations. A case in point is the examination of settlement issues along a stretch of the access road leading to the city of Gallur from the east (known as Camino Real) in the Zaragoza province, Spain. Numerous surface manifestations of recent subsidence and/or collapse activities have been observed, manifesting as craters and ground undercuts, some several meters in diameter. The prevalence of highly karstifiable materials in the area, evident from the existence of subsidence pockets and collapse dolines, poses significant safety concerns, particularly for traffic and town access, prompting the closure of Camino Real for several years. Local and provincial authorities have embarked on studies to try to recognise this type of situation. Reports aimed at defining karstification processes, conducting geomechanical analyses of subsidence and cavity collapses, and proposing technical measures to mitigate risks have been prepared. Finally, a consolidation solution was proposed based on injections at column-depth of mortar with special characteristics, combined with the replacement and reinforcement of the most superficial soil by means of high-tensile-strength geotextile meshes.

Analytical model for geotextile-enhanced horizontal drain vacuum consolidation of slurries

Horizontal drains are gradually introduced to the vacuum preloading method to improve dredged slurries by adding geotextiles to alleviate the blockage in the consolidation process. This study considers the consolidation of slurries enhanced by the vacuum preloading method with geotextile combined horizontal drains based on a double-layered consolidation model. The model approximates geotextile as a special soil layer possessing an equivalent consolidation factor. An analytical solution of the layered consolidation model is obtained using the Laplace transform and the finite Fourier transform method. The effectiveness of the solution is verified by comparing it with the one-dimensional double-layered consolidation solution and the one-dimensional consolidation with a partially permeable boundary. Through comparison with laboratory experiments, the model shows good fitness with the test results in the literature. The influences of related parameters, including the drain arrangement densities, soil parameters, and geotextile parameters, are discussed on average consolidation degree and pore water pressure. The influence mechanism is explained regarding drainage path and vacuum pressure transfer. Findings demonstrate that geotextile facilitates vacuum transfer and promotes soil consolidation, especially when the smaller density of drains’ deposition and lower soil permeability are applied.

Preparation and research on cationic modified vermiculite with strong adsorption capacity for mineralizing bacteria

To address the challenge of low binding strength and inefficient adsorption between mineralized bacteria carrier and microorganisms., this study aims to develop a novel immobilized carrier (Vermiculite/AP-DE) by modifying the surface of carrier with cationic modified material 3-aminopropyltriethoxysilane (APTES), and diethylenetriamine (DETA). The negatively charged Sporosarcina pasteurii (S.p) can be tightly adsorbed onto the carrier's surface through the Coulomb force, thereby improving the efficiency of microbial induced calcite precipitation (MICP). The FT-IR results and Zeta points analysis show that —NH2 group was successfully introduced, and the carrier has a positive charge in the solution when pH < 9.74. Scanning electron microscope (SEM) images and Thermal gravimetric analyzer (TGA) results show that Vermiculite/AP-DE can tightly adsorb a large amount of microorganisms, and the calcite formation reached 30.5 % after MICP treatment, which is three times higher than traditional grouting materials. Sand reinforcement tests demonstrated that Vermiculite/AP-DE& S.p, as grouting material, exhibits a repair effectiveness on large-pore sand that surpasses traditional methods by more than threefold. This study provides a novel solution for MICP consolidation of coarse sand.

Computational assessment regarding structural rehabilitation of a reinforced concrete decanter tank

The article describes the analysis of an industrial structure (reinforced concrete decanter tank for the drinking water’s storage in the Iasi – Romania area) in order to justify the proposals for structural rehabilitation to ensure structural stability. In this regard, a computational model was created in Graitec Advanced Design, using the physico-mechanical characteristics of the materials (concrete, reinforcement) from the initial design. Subsequently, using the data obtained from the technical assessment report and the non-destructive tests carried out on the structural elements, it was found a depreciation of the concrete grade (C25/30 → C16/20), at the current stage. At this stage (the structure’s service state) a modelling of the degraded structure was achieved by comparing the results obtained by Graitec Advanced Design and Axis VM, in order to realise an extended structural analysis between initial and current state. A solution for the rehabilitation of degraded elements using polymeric composite materials reinforced with carbon fibers was proposed, which was validated by the Sika CarboDur Composite systems (software program for the design of consolidation solutions).

Semi-analytical solution for one-dimensional consolidation of multi-layered soil considering non-Darcian flow and multi-stage loading under continuous drainage boundary

Taking non-Darcian flow and multi-stage loading into consideration, a semi-analytical solution for one-dimensional consolidation of multi-layered soil under continuous drainage boundary based on a linearization method was derived in this paper. The correctness of the proposed solution was verified by comparing with the existing solutions and finite element method results. Accordingly, the influence of soil properties, load parameters, interface parameter and flow parameters on the consolidation characteristics of multi-layered soil was further analyzed. The results showed that the permeability coefficient and flow exponent of the first layer of soil has the most significant influence on the consolidation of multi-layered soil, while the volume compression coefficient of the bottom layer of soil has the greatest influence on the consolidation of multi-layered soil. Continuous drainage boundary, non-Darcian flow and multi-stage loading can all prolong the consolidation process of layered soil. However, the influence of continuous drainage boundary on soil consolidation is reduced when considering non-Darcian flow or multi-stage loading.

Analytical solution for consolidation of unsaturated composite foundation improved by permeable and impermeable columns considering depth‐dependent initial stress

AbstractThe combination of permeable and impermeable columns is commonly employed to enhance the stability of natural ground and expedite the consolidation process while effectively reducing foundation settlement. This study presents a comprehensive investigation of the consolidation characteristics of unsaturated composite foundations (USCF) using various methods. Firstly, a mathematical model is developed under the assumption of equal strain, considering depth‐dependent initial stress. To obtain more generalized analytical solutions for excess pore pressures and foundation settlement, separation of variables, Laplace transformation, and inversion Laplace transformation are employed. Secondly, the accuracy of the proposed analytical solutions is validated by comparing them with two specific cases reported in the existing literature, achieved by reducing the compression modulus of columns. Lastly, a series of parameters are investigated to examine the consolidation characteristics of USCF considering depth‐dependent initial stress. The results demonstrate that the final settlement of the foundation will be overestimated while the variation of vertical stress along the depth is neglected. Furthermore, adjusting the values of area replacement ratios proves to be more effective and straightforward than modifying the compression modulus of columns in the reinforcement treatment of USCF.

Rheological consolidation analysis of saturated clay ground under cyclic loading based on the fractional order Kelvin model

AbstractBased on Biot porous medium theory, considering the coupled reaction of soil skeleton rheology and pore pressure dissipation, the present work investigates the dynamic consolidation characteristics of saturated clay ground under cyclic loading. First, the rheological behavior of the soil skeleton was described by the fractional order Kelvin model. The dynamic consolidation governing equations for the saturated clay were established theoretically in a three‐dimensional axisymmetric coordinate system. Second, the transform domain analytical solution of the dynamic consolidation of saturated clay was obtained using the Hankel–Laplace coupled transform method, and the solution in the time–space domain was further obtained through numerical inversion. Finally, the rheological consolidation behavior of saturated clay under cyclic loading and the influences of parameters were analyzed. The results show that the rheology of the soil skeleton had an inhibitory effect on pore water permeability; compared with elastic skeleton soil, the rheological clay had a slower settlement rate in the primary consolidation stage, a faster rate in the secondary consolidation stage, and greater long‐term settlement. In addition, under cyclic loading, the pore pressure response in saturated clay lags behind the effective stress, and a larger viscous order is associated with faster development of cumulative settlement.