Shakedown Concept Research Articles

Mechanical Response of Cement-Stabilized Pond Ash during Repeated Loading Based on Shakedown Concept

Mechanical Response of Cement-Stabilized Pond Ash during Repeated Loading Based on Shakedown Concept

Energy-based insight into characterization of shakedown behavior of fully weathered red mudstone

Weathered Red mudstone is widely distributed in Sichuan basin. The compacted weathered red mudstone has been used as subgrade fill materials of high-speed railway in southwestern of China. Dynamic responses of such materials under cyclic loading are critical to long-term stability of subgrade. Shakedown concept is widely employed in characterizing the permanent deformation behavior of soils. According to the evolution of axial strain (Werkmeister’s theory) or unit dissipated energy (Tao’s theory) with loading cycles, the behavior of unbound granular materials can be classified into three categories: plastic shakedown, plastic creep and incremental collapse. However, both theories are more suitable for the unbound granular materials with some limitations when used to separate the plastic creep and incremental collapse behavior. To overcome the limitations of the current theories, 26 cyclic triaxial tests were conducted on a saturated fully weathered red mudstone (SFWRM) to study the evolution of axial strain and unit dissipated energy during cyclic loading. A clear dependency of axial strain, axial strain rate on the unit dissipated energy level under various cyclic stress states were observed. A new criterion which is based on the responses of unit dissipated energy with cyclic stress ratio, was proposed to determine the limit between plastic creep and incremental collapse. Comparing with Werkmeister’s criterion and Tao’s criterion, the proposed criterion showed a better performance in identifying the incremental collapse behavior of the SFWRM.

МОЖЛИВОСТІ ПРОЄКТУВАННЯ НЕУКРІПЛЕНИХ ОСНОВ НЕЖОРСТКИХ ДОРОЖНІХ ОДЯГІВ ЗА РЕЗУЛЬТАТАМИ ВИВЧЕННЯ ДЕФОРМАЦІЙНОЇ ПОВЕДІНКИ ДИСПЕРСНИХ СУМІШЕЙ

Introduction. The introduction to the paper highlights the role of the modeling of deformation behavior of unbound granular mixtures (UGMs) under repeated mechanical loading as the base aspect of designing flexible road pavement with an unbound base layers due to the fact that UGMs have been recognized as the most vulnerable materials of the flexible road pavement under action of negative climatic (seasonal) or technogenic factors. Problem statement. The issues of the paper concern the problems related to unstable deformation behavior of UGMs in unbound base/subbase layers during flexible road pavement designing and maintenance. Purpose. The main goal of the paper is to perform an analytical review of the theoretical background to the construction and calculation of an unbound base layer of the flexible road pavement according to the results of the study of UGMs’ deformation behavior with their following categorization. The results of the analytical review are intended to be used during implementation of a national standard concerning the method of testing of unbound granular mixtures by the triaxial cyclic loading identical to the related European standard. Results. The “shakedown concept” was reviewed which allows the categorization and also the appropriate selection of granular mixture during road pavement design and construction. It was established, that the “shakedown concept” sets up three types of permanent behavior of UGMs which, only after being tested via the triaxial cyclic loading method, can be categorized considering the design input data as stable or unstable ones. Also, an analytical comparison of various possible approaches to the UGMs’ categorization within the “shakedown concept” was fulfilled. By the standardized approach, the limits of three categories shall be established at progressively increasing stresses taking into consideration the restrictions on accumulated axial permanent strains. The other approach may be potentially effective for UGM selection and is based on the value of the permanent axial strain rate per one loading cycle. Further, the aspects of an empirical designing of flexible road pavements were reviewed where the parameters of deformation behavior of UGM were adopted, via the Finite Elements Method, to calculate the distribution of stresses and to model rutting in an unbound base layer considering variable thickness of asphalt pavement and variable climatic factors as well.

Strength and permanent deformation properties of demolition wastes, glass, and plastics stabilized with foamed bitumen for pavement bases

Foamed bitumen (FB) stabilization is an in-place soil improvement technique that has become popular in recent times. Nevertheless, a lack of understanding exists about the strength and deformation responses of FB stabilized recycled demolition wastes in pavements. This paper aims to introduce the application of FB stabilized recycled demolition waste blends with glass and plastic in the pavement base layer. A suite of laboratory tests was undertaken to evaluate the indirect tensile strength, unconfined compressive strength, California bearing ratio, and permanent deformation behavior of FB stabilized blends. Recycled concrete aggregate (RCA) was blended with recycled glass (RG), recycled plastic (RP), and reclaimed asphalt pavement (RAP) in various percentages and the performance of the FB stabilized blends were characterized through extensive experimental testing. A multi-stage repeated load triaxial (RLT) testing procedure was adopted to evaluate the permanent deformation behavior of the unbound and FB stabilized blends under various stress levels. The ITS, UCS, and CBR values exhibited decreasing trends with increasing the RAP, RG, and RP contents. The permanent deformation of the blends was found to be reduced as a result of FB stabilization, most notably for the blends with higher percentages of RAP, RG, and RP. The permanent deformation responses of the blends were ranked using the shakedown concept that indicated the FB stabilized demolition wastes exhibited relatively stable responses under cyclic loads. The deformation response of the blends with 50%RAP and 7%RP changed from incremental collapse to plastic creep as a result of FB stabilization. The results indicated that the FB stabilization of recycled aggregates is a suitable practice for developing more sustainable roads with enhanced ductility and resistance to rutting.

Characterizing the permanent deformation Response-Behavior of subgrade material under cyclic loading based on the shakedown theory

Coarse-grained soil is widely used as a filling material in the railway subgrade to provide foundational support to the long-term effects of dynamic (cyclic) train loads transmitted by the track structure. Despite this wide usage, there is limited literature on its permanent deformation behavior characterization under different magnitudes of dynamic stress. The GDS (Geotechnical Digital System) dynamic triaxial tests were presented in this paper to characterize and quantify the dynamic response-behavior of coarse-grained railway subgrade soils when subjected to dynamic loading. Based on the shakedown concept, the patterns of accumulated axial plastic strains for the coarse-grained soil under different magnitudes of dynamic stress were classified into three categories, namely plastic shakedown, plastic creep, and incremental collapse. As a result, the critical dynamic stresses for plastic shakedown and plastic creep state could easily be determined. The experimental test results indicated that whilst the critical dynamic stress of the coarse-grained soil increased with an increase in the effective confining pressure, it correspondingly decreased as the loading frequency increased from 1.0 to 3.6 Hz, respectively. From the regression fitting-analysis of the experimental test results, an empirical model is proposed in this paper, which denotes the critical dynamic stress of coarse-grained subgrade soils as a function of the effective confining pressure. As a contribution to the literature and potential engineering applications, the proposed models may provide theoretical significance for the subgrade state evaluation and settlement control.

Evaluation of permanent deformation and resilient modulus of pavement base with different gradations and percentages of clay plasticiser

Characteristics of unbound granular pavement materials vary among transportation and road association around the world based on function, environmental conditions, and materials availability. Plasticity index (PI) is one of the most important characteristics of unbound granular pavement courses both in the construction stage and throughout its service life. It indicates the range of moisture contents over which the fines in the pavement material behave plastically. This study investigates the effect of a refined clay plasticiser called Claypro (CP) on the elastic and plastic behaviour of unbound granular base materials at different gradations. This paper aims to find the optimum clay content (CP) that achieves an acceptable PI and maintains high elastic performance and high plastic strain resistance under traffic loading. Elastic and plastic responses of 18 mixtures at three different gradations, representing two types of crushed rock materials namely; Hornfels and Basalt, were evaluated at three different CP contents. Repeated load triaxial (RLT) test was carried out with a high number of cycles to estimate the resilient modulus (MR) and the permanent deformation of these mixtures. The shakedown concept was also applied to assess the deformation behaviour of the tested engineered mixtures under multi-stage RLT test. Results showed that 1% Claypro (CP) content is considered the optimum for all gradations of both aggregate types considered herein.

Recycled Glass Blends with Recycled Concrete Aggregates in Sustainable Railway Geotechnics

This research investigates the static and cyclic characteristics of recycled glass (RG) as a supplementary material with recycled concrete aggregate (RCA) in the rail track capping layer. RG was blended by-weight with RCA in 10% increments up to 50% RG content. A performance-based laboratory testing scheme was designed according to the field loading conditions of capping layers in rail tracks. Basic geotechnical properties of RG + RCA blends were evaluated through their particle size distribution, compaction properties, and California bearing ratio. Effect of flooding was assessed with one-dimensional static and cyclic compression tests. Multistage triaxial compression tests were performed to determine the effect of RG content on shear strength parameters. A new repeated loading triaxial testing protocol was introduced for railway capping layer materials to assess the stiffness of RG blends to cyclic loading. Long term performance of samples also was evaluated through multistage cyclic permanent deformation tests. The shakedown concept was used to assess the permanent deformation results of RG + RCA samples. Results indicated that RG can be used effectively as a supplementary geomaterial in construction of rail track substructure.

Thermal and mechanical properties of demolition wastes in geothermal pavements by experimental and machine learning techniques

Despite the growing interest in using construction and demolition (C&D) waste materials in geotechnical engineering projects, there is limited knowledge of their thermo-mechanical properties, which is essential for the design of energy geostructures, such as geothermal pavements. The pavement unbound layers can be integrated with heat exchangers to form a novel pavement concept, namely geothermal pavements. This study focuses on recycled concrete aggregate (RCA), crushed brick (CB), waste rock (WR), and reclaimed asphalt pavement (RAP), and aims to investigate the thermal conductivity of these C&D materials as well as their response to combined dynamic loads and temperature. Thermal conductivity was measured using a prototype divided bar equipment. Temperature-controlled repeated loading triaxial (RLT) tests were undertaken to evaluate the effect of temperature on deformation properties of the C&D materials. RLT tests were conducted at 5 °C, 20 °C, 35 °C, and 50 °C. Deformation behavior of the C&D materials at different temperatures was characterized using the shakedown concept. Thermal conductivity measurements indicated that CB and RCA had higher thermal conductivity compared to WR and RAP. RLT results showed that RCA exhibited plastic shakedown (Range A) behavior in all temperatures, while CB and WR demonstrated plastic creep (Range B) behavior. RAP exhibited plastic creep behavior at 20 °C and 5 °C, and incremental collapse (Range C) behavior at 35 °C and 50 °C. An artificial neural network (ANN) model was developed considering the physical properties and test variables as input parameters. Sensitivity analysis was then performed on the proposed ANN model. Results of the ANN modeling provided new insight into the deformation behavior of C&D materials at different temperatures and agreed with the experimental results.

A constitutive model for the accumulated strain of unsaturated soil under high‐cycle traffic loading

AbstractThe road base is normally situated above the water table and thus in unsaturated state. Experimental results show that the accumulated strains of the unsaturated road base aggregate under high‐cycle traffic loads are significantly influenced by the matric suction. To predict the accumulated strain of unsaturated road base aggregate under high‐cycle traffic loads, a constitutive model was developed based on the Barcelona Basic Model (BBM) and the shakedown concept. In this model, the shakedown and plastic creep boundaries of the aggregate under cyclic loads were supposed to exist and to have the same shape as the “static” yield surface in BBM. The strain accumulation rates were described as an exponential function of the distance between the peak cyclic stress point and the conjugated point at the current cyclic yield surface. An explicit calculation methodology was adopted to avoid large calculation errors and to improve the calculation efficiency of the model. Comparison between model predictions and testing results proved the accuracy of the proposed model, which can be used as a basic model to predict the long‐term deformation of unsaturated road base aggregate under high‐cycle traffic loads.

Characterization of permanent deformation of fine-grained subgrade soil under intermittent loading

Understanding the permanent deformation characteristics of subgrade soils under traffic loads can provide a basis for subgrade design and evaluation. During repeated load triaxial (RLT) tests, accurate simulation of traffic loads is critical. RLT tests on silt under continuous loading and intermittent loading (cycles of continuous loading and intermittent stage) were performed using an RLT apparatus. The effects of the intermittent stage on the development of axial strain, pore water pressure and accumulated plastic strain were analyzed, and the dynamic behaviors of accumulated plastic strain under intermittent loading were also studied. The results show that the existence of the intermittent stage plays an active role in dissipating pore water pressure and improving the ability of the specimen to resist permanent deformation. Based on shakedown concept, an expression of critical stress and a prediction model for the accumulated plastic strain of silt under intermittent loading were proposed. The research results provide reference values for understanding the permanent deformation characteristics of silt.

Effect of compaction water content and stress ratio on permanent deformation of a subgrade lateritic soil

Permanent deformation is a potential distress that affects the functional characteristics of pavement. Subgrade soil might contribute to different levels of permanent deformation depending on traffic intensity. This paper assesses the stress ratio effects as well as compaction water content variation on permanent deformation of subgrade soil, presents some contributions to understanding the Shakedown concept in fine-grained soils and evaluates models for estimating soil plastic strain. Repeated load triaxial (RLT) tests were performed on lateritic sandy soil in order to obtain: permanent deformation and Shakedown parameters. Findings indicated a prevalence of stress ratio in permanent deformation for a specified compaction water content range (wopt ± 1.5%). However, analysis of plastic strain rates showed that permanent deformation might be more influenced by compaction water content than by stress ratio, mainly in cases where compaction water content range is wider. Furthermore, stabilization, i.e. Shakedown first phase occurrence, was achieved under all test conditions, in spite of low deformation levels. Lastly, the model adjusted in function of stress ratio and compaction water content closely represented the complexity of soil plastic strain accumulation.

Mechanical behaviour of densely compacted expansive soils during wetting and drying cycles: an analytical model based on shakedown concept

To improve the modelling of mechanical behaviour on densely compacted expansive soils during wetting and drying cycles, this article presents a straightforward one-dimensional model to simulate the deformation change of densely compacted expansive soils with suction cycles. The proposed method based on shakedown concept is first extended by the combined hardening plasticity, including the isotropic and kinematic hardening. To validate this model, two controlled suction oedometer tests in different laboratories are used to calibrate elasticity and plasticity parameters. Comparison of model estimations with the experimental results demonstrates that the proposed model is capable of predicting the mechanical behaviour of densely compacted expansive soils subjected to wetting and drying cycles.

Mesh-free shakedown analysis of cohesive-frictional pavement under moving traffic loads: deterministic and probabilistic frameworks

A mesh-free limit analysis approach has been modified and extended to comprise the problem of shakedown analysis of pavements. In this novel study, both deterministic and probabilistic frameworks are presented. Deterministic modelling is undertaken by the combination of Melan’s shakedown theorem, Shepard’s mesh-free technique and linear programming. A probabilistic framework is also introduced to incorporate soil’s shear strength inherent heterogeneity into the mesh-free shakedown analysis. In this context, the covariance matrix decomposition technique is used to generate the random fields of cohesion and friction angle. Thereafter, analyses have been conducted by employing Monte Carlo simulations which invoke mesh-free shakedown analysis several times. At the end of the paper, as an application of stochastic modelling, the probability of failure has been presented as a function of safety factor to quantify the geotechnical risks of pavement’s design from shakedown concept viewpoint.

Effect of Cyclic Stress Level and Overconsolidation Ratio on Permanent Deformation Behaviour of Clayey Subsoil

This paper presents the results of a series of one-way cyclic triaxial tests carried out to investigate the role of cyclic stress level and overconsolidation ratio (OCR) on the permanent deformation behaviour of saturated clayey subsoil during long-term cyclic loading. Based on the test results and shakedown concept, two cyclic threshold deviator stress ratios can be defined: the plastic shakedown limit cyclic deviator stress ratio CSRpt (0.46) and the plastic creep shakedown limit cyclic deviator stress ratio CSRpc (0.75). It was found that, below CSRpt, the soil experiences slight deformation and gradually achieves a long-term steady state response. Within the range of CSRpt<CSR<CSRpc, the plastic strain will accumulates substantially and becomes unstable. Once the CSRpc is exceeded significant deformation and failure may occur. In the practical engineering, CSRpt can be used for preliminary design of pavement foundation. In addition, based on the test results, a simplified permanent axial strain model that explicitly considers the effects of CSR and OCR is developed.

Accumulated permanent strain and critical dynamic stress of frozen silty clay under cyclic loading

A series of dynamic triaxial experiments have been conducted to study the dynamic properties of the frozen soil from the subgrade along the Qinghai-Tibet Railway. Under long term cyclic loading, the effects of initial stress state and stress level on cumulative permanent strain and critical dynamic stress were studied in the paper. The results indicate that the influence of dynamic amplitude on the curve of cumulative permanent strain versus cyclic loading number is significant. Besides, based on the shakedown concept, curves of cumulative permanent strain versus cyclic loading number under different initial mean stress and deviatoric stress can be separated to three possible categories of plastic shakedown, plastic creep and incremental collapse. In addition, the critical dynamic stress of frozen soil under specific condition is obtained, and the analysis on critical dynamic stress at different stress state is presented. Therefore, this study could provide an innovative approach for permanent deformation behavior analysis. Furthermore, it is important for practical design and evaluation on stability of frozen soil in the subgrade.

Finite element modelling of the mechanical behaviour of unsaturated expansive soils subjected to wetting and drying cycles with shakedown concept

A simplified model based on the shakedown theory (Zarka method) has been developed in this study for unsaturated expansive soils subjected to wetting and drying cycles. This method determines directly the stabilised limit state. The parameters of the proposed shakedown-based model are calibrated by the suction-controlled odometer tests obtained for an expansive soil compacted at loose and dense initial states, and then validated for the same soil compacted at intermediate initial state by comparing the model predictions with the experimental results. Finally, the finite element equations for the proposed shakedown model are developed and these equations are implemented in the finite element code CAST3M to carry out the full-scale calculations. The performed simulation is on a 2D geometry, made up of the expansive soil at the intermediate state subjected to successive extremely dry and wet seasons for the different applied vertical loads. The results show the swelling plastic deformations for the lower vertical stresses and the shrinkage deformations for the higher vertical stresses. Only inelastic heaving displacement can be observed in the geometry after considering the residual field.

Dynamic simulation of a flexible pavement layers considering shakedown effects and soil-asphalt interaction

Abstract This research evaluates the effects of shakedown and soil asphalt interaction on the dynamic simulation of flexible layered pavement structure. In a newly developed assessment methodology the shakedown concept is implemented for the granular layer under asphalt concrete. Under this assessment granular material behaviour changes from plastic to elastic as a function of the number of loading cycles. Interactional forces are considered through contact elements placed between the base and the asphalt layer. A nonlinear stress dependent model in the elastic domain and the Mohr–Coulomb constitutive model in the plastic domain are utilised to simulate the behaviour of granular layers and the results of the simulation are validated with previously published literature. One static simulation and three different dynamic simulations under cyclic Haversine loading of a single tyre dual axle are then compared with each other. The first dynamic simulation assumes Mohr–Coulomb plasticity, the second simulation considers the shakedown effects and the third simulation calculates soil asphalt interactional forces.

Effects of Density and Moisture Variation on Dynamic Deformation Properties of Compacted Lateritic Soil

A series of repeated load triaxial tests were conducted in this study to investigate the influences of compaction density and postcompaction moisture variation on the dynamic elastic modulus (Ed) and plastic permanent strain (PPS) of compacted lateritic soil. Specimens were compacted at optimum moisture content (OMC) and three degrees of compaction (90%, 93%, and 96%). Then the specimens were dried or wetted to different moisture contents (OMC,OMC±3%,OMC±6%, andOMC+9%) prior to testing forEdand PPS. Results show that moisture content has greater influence on theEdand PSS than compaction degree, and the increase in moisture content leads to a decrease ofEdand an increase of PPS. Furthermore, an empirical relationship betweenEdand applied cyclic stress (σd) is developed that incorporates density and moisture variations. Three different evolution types of PPS with number of load cycles, plastic stable, plastic creep, and incremental collapse, are identified as the increase of moisture content. In addition, the critical dynamic stress (σdc) separating stable and unstable deformation is determined based on the shakedown concept. The envelope curves ofσdc-moisture of lateritic soil with different degrees of compaction are also determined to provide reference for the pavement design.

Permanent deformation behavior of unbound granular base materials with varying moisture and fines content

Specifications for unbound granular base materials vary among transportation agencies based on the availability of materials, climatic conditions, and function. Specifications aim to provide durable materials that meet design requirements and achieve the target design life with cost effective materials. This paper investigates the effect of the percentage fines (particles passing sieve No. 200) and moisture content on the plastic behavior of unbound granular materials. Plastic response of six gradations representing two types of material, 100% crushed limestone and gravel, was evaluated at two levels of moisture content. The shakedown concept was used to classify the deformation behavior of the materials. Results showed that limestone with an optimum fines content of 4.5% and gravel with an optimum fines content of 9% had better resistance to plastic deformation than other fines contents.

Determination of traffic-load-influenced depths in clayey subsoil based on the shakedown concept

The determination of the depth of traffic load influence is significant for pavement and embankment design on soft soil. In this study, a method based on strain-controlled criteria is presented to estimate the depths within which the behavior of a saturated clayey subsoil is affected by cyclic traffic loads. Based on the shakedown concept, the following depths of influence can be defined: (1) the threshold depth, beyond which the dynamic effect of the traffic loads is insignificant; (2) the plastic shakedown limit depth, within which the subsoil experiences noticeable and continuous deformation; and (3) the critical failure depth, within which the soil fails due to the accumulation of strain. This method for determining the depths of influence is advantageous because it is applicable to various soil types. The data required for this method consist of vertical stress responses along the soil profile and three cyclic stress limits of the soil. Based on the development of pore pressure and the dynamic strain behaviors during undrained cyclic triaxial tests, the following cyclic stress limits of the soft clay subsoil are determined: a threshold cyclic stress ratio CSRt of 0.03, a plastic shakedown limit stress ratio CSRp of 0.33 and a critical cyclic stress ratio CSRc of 0.44. These cyclic stress limits are used to determine the corresponding depths of influence, which are then used to implement ground improvements and strengthen the dynamic carrying capacity of the road structures.