Coefficient Of Subgrade Reaction Research Articles

Numerical Simulation Study Considering Discontinuous Longitudinal Joints in Soft Soil under Symmetric Loading

In shield tunneling, the joint is one of the most vulnerable parts of the segmental lining. Opening of the joint reduces the overall stiffness of the ring, leading to structural damage and issues such as water leakage. Currently, the Winkler method is commonly used to calculate structural deformation, simplifying the interaction between segments and soil as radial and tangential Winkler springs. However, when introducing connection springs or reduction factors to simulate the joint stiffness of segments, the challenge lies in determining the reduction coefficient and the stiffness of the springs. Currently, the hyperstatic reflection method cannot simulate the discontinuity effect at the connection of the tunnel segments, while the state space method overlooks the nonlinear interaction between the tunnel and the soil. Therefore, this paper proposes a numerical simulation method considering the interaction between the tunnel and the soil, which is subjected to compression rather than tension, and the discontinuity of the joints between the segments. The model structure and external load are symmetrical, resulting in symmetrical calculation results. This method is based on the soft soil layers and shield tunnel structures of the Shanghai Metro, and the applicability of the model is verified through deformation calculations using three-dimensional laser scanning point clouds of sections from the Shanghai Metro Line 5. When the subgrade reaction coefficient is 5000 kN/m3, the model can effectively simulate the deformation of operational tunnels. By adjusting the bending stiffness of individual connection springs, we investigate the influence of bending stiffness reduction on the bending moment, radial displacement, and rotational displacement of the ring. The results indicate that a decrease in joint bending stiffness significantly affects the mechanical response of the ring, and the extent and degree of this influence are correlated with the joint position and the magnitude of joint bending stiffness.

Random Responses of Shield Tunnel to New Tunnel Undercrossing Considering Spatial Variability of Soil Elastic Modulus

This paper investigates the effect of spatial variability of soil elastic modulus on the longitudinal responses of the existing shield tunnel to the new tunnel undercrossing using a random two-stage analysis method (RTSAM). The Timoshenko–Winkler-based deterministic method considering longitudinal variation in the subgrade reaction coefficient and the random field of the soil elastic modulus discretized by the Karhunen–Loeve expansion method are combined to establish the RTSAM. Then, the proposed RTSAM is applied to carry out a random analysis based on an actual engineering case. Results show that the increases in the scale of fluctuation and the coefficient of variation of the soil elastic modulus lead to higher variabilities of tunnel responses. A decreasing pillar depth and mean value of the soil elastic modulus and an increasing skew angle strengthen the effect of the spatial variability of the soil elastic modulus on tunnel responses. The variabilities of tunnel responses under the random field of the soil elastic modulus are overestimated by the Euler–Bernoulli beam model. The results of this study provide references for the uncertainty analysis of the new tunneling-induced responses of the existing tunnel under the random field of soil properties.

Investigation on deformation behavior and bearing capacity of a segmental ring based on the horizontal convergence

AbstractIn this study, a refined numerical model, which contains the detailed geometric construction of the longitudinal joints, is established to investigate the bearing performance of the segmental ring based on the horizontal convergence. Firstly, the model is verified by comparing it with the reported results of a documented full‐scale model test. Then, according to the load‐structure method, this numerical model is employed to investigate the deformation behavior and bearing capacity of the segmental ring. Moreover, the effects of the coefficient of lateral pressure and subgrade reaction are extensively taken into consideration through comprehensive numerical analyses. According to the numerical results, a bilinear model is proposed to describe the relation between the convergent displacement and the stratum pressure, which could be used to preliminarily estimate the convergence after the completion of tunnel construction. Otherwise, the development of structural defects, such as the joint opening and the water leakage, has close association with the horizontal convergence. Therefore, a simple evaluation method for tunnel structure safety assessment is proposed using horizontal convergence deformation as an indicator to predict the tunnel service state. Since this indicator is easy to obtain during the tunnel operation, it is convenient for the engineers to assess the bearing capacity of the segmental ring and the service state of the tunnel structure quickly.

Analytical solution for buried pipeline deformation induced by normal and reverse fault considering structural joint influence

AbstractPrevious studies take less account of analytical solution analysis for buried pipeline under the action of active fault. Furthermore, current theoretical studies of fault‐pipeline interactions generally treat the structure as continuous pipeline, with less attention given to the effect of joints. This paper provides an analytical method to estimate the deformation and internal force of jointed pipelines under normal and reverse fault. By introducing the simplified soil deformation model and error function, the soil greenfield deformation curves under the influence of normal and reverse fault are obtained. Considering the interaction between the pipeline structure and the disturbed soil, the two‐parameter Pasternak foundation model is adopted to analyze the forces on pipeline infinitesimal elements. Then, the mechanical response of the jointed pipeline structure due to the fault additional load is solved by finite difference method. The accuracy of the presented analytical solution is verified by comparisons with observed data of model test and 3D numerical simulation results. Finally, the parametric analyses are performed to estimate the influence for the characteristics of the foundation, fault and joint, including subgrade shear stiffness, subgrade reaction coefficient, fault dip, joint rotational stiffness, joint spacing, and intersection of fault and pipeline.

Field measurement and CPT-based settlement prediction of existing railway subgrade reinforced by battered helical piles with grouted shafts

In order to ensure the normal operation of the existing freight railway, it is difficult to adopt the common reinforcement measures (e.g., jet grouting or deep mixing) to meet the requirements. Reinforcement of existing railway subgrade by battered helical piles can meet the normal operation requirements of existing railways. However, there is no report on the research on the reinforcement of existing railway subgrade with battered helical piles. This paper reports on a field case study of railway subgrade improved by battered helical piles with grouted shafts (BHPGS) to mitigate the ongoing settlement due to temporary backfilling of subgrade without meeting the compaction requirement after heavy rain, which can be potentially harmful to the long-term operation of the railway. The measured coefficients of subgrade reaction (K30) of the 3 locations after BHPGS installation increased by 48 %∼166 % compared with the installation before. The long-term settlement of the railway subgrade reinforced with BHPGS was monitored by hydrostatic level and gradually stabilized after an adjustment period of about half a year, with the maximum settlement of 2.76 mm located at the center of the subgrade reinforcement section. In addition, a simplified method of calculating settlement based on CPT for the railway subgrade reinforced with BHPGS is proposed, with the calculated value of 2.99 mm in good agreement with the measured 2.76 mm.

Random analysis method for nonlinear interaction between shield tunnel and spatially variable soil

The spatial variability of soil properties is likely to have a remarkable influence on the longitudinal responses of shield tunnels. This paper proposes a one-dimensional random analysis method (RAM) for the interaction between the shield tunnel with circumferential joints and the spatially variable soil with nonlinear elastoplastic behaviors. A deterministic short beam-spring model with longitudinal variation in the initial subgrade reaction coefficient and the ultimate soil resistance is developed and solved by the finite difference method. The random field of the soil properties discretized by the Karhunen-Loeve expansion method is used to establish the RAM. A hypothetical example is further presented to demonstrate the applicability of the proposed method. The results imply that the soil nonlinearity may lead to a negative effect on the reliability control of the tunnel structure and should be considered to obtain more reasonable probabilistic evaluations of the tunnel deformations. The increasing joint rotational stiffness or shearing stiffness results in the lower variabilities of the maximum tunnel settlement, and reduces the probabilities of the maximum joint opening or joint dislocation exceeding the allowable value, respectively.

Bearing capacity of lunar soil ground under extraterrestrial environmental effects

Lunar environment features a low gravity field and ultra-high vacuum which shows significant effects on the bearing behavior of lunar soil ground for future lunar habitation. Therefore, the 2D Discrete Element Method was employed to simulate the plate load tests under different gravity fields in non-vacuum (i.e., excluding the van der Waals force) and high-vacuum (i.e., including the van der Waals force) environments, analyzing the bearing behavior and soil response under extraterrestrial environmental effects. The results show that a bilinear line bounded by 1g can be employed to describe the gravity effect on the gravity factors for ultimate bearing capacity and coefficient of subgrade reaction. The slopes are different in low and high-gravity fields, indicating that the high-gravity effect in a centrifuge cannot be directly applied to predict the bearing behavior of lunar soil ground in a low-gravity field. The affected area becomes deeper in depth and narrower in width with the decreasing gravity level in non-vacuum environment, while the affected area becomes deeper in depth and wider in width with the decreasing gravity level in high-vacuum environment. Such observations can provide advice for developing analytical models for the bearing capacity of lunar soil ground considering the extraterrestrial environmental effects.

Displacement-based seismic performance of RC bridge pier

To correctly manage the road infrastructure before and after an earthquake, it is necessary to estimate and even predict the seismic performance of the bridge. The quantification of the bridge's seismic performance response was present in terms of displacement and also based on previous research of reinforced concrete bridge pier models. The displacement did define from a force lateral-displacement response diagram corresponding to the capacity curve, calculated through a non-linear static pushover analysis of the reinforced concrete bridge pier model for each limit state, from intact state to collapse. Thus, six defined displacements correspond to the cracking displacement, the yielding displacement, the spalling displacement, the crushing displacement, the buckling displacement, and the fracturing displacement. The six defined limit states correspond to the cracking limit state, the yielding limit state, the spalling limit state, the crushing limit state, the buckling limit state, and the fracturing limit state. Also, parametric analysis did carry out to evaluate the influence, relative importance, and trend of the input parameters in response to the seismic performance of the reinforced concrete bridge pier model. Eleven input parameters did analyze as the concrete compressive strength, the yield stress of reinforcing steel, the concrete cover thickness, the pier aspect ratio, the configuration of the transverse reinforcement, the spacing of the transverse reinforcing steel, the transversal diameter of the transverse reinforcing steel, the longitudinal reinforcement ratio, the transversal diameter of the longitudinal reinforcing steel, the axial load ratio, and coefficient of subgrade reaction.

KUMLU ZEMİN ÜZERİNDEKİ RADYE TEMELLERİN WİNKLER VE PSÜDO-EŞLENİK YÖNTEMLERİ İLE ANALİZİ

The settlements occurred in building foundations depend on many soil parameters. Thus, these parameters make the solution both difficult and complex during the calculating process. Therefore, finite element programs use the subgrade reaction coefficient to facilitate the foundation solution. Two different methods, which are Winkler method and Pseudo coupled method, are used in the basic solutions with the coefficient of subgrade reaction. While the Winkler method can be solved with a single field, the pseudo method can be solved with 2 or more fields. In this study, a 10 story building with a 36 m x 36 m square foundation was separately designed on four different sand soils. Two of these soils are classified as C and the others are classified as D according to Eurocode 8. The foundation of this building built on four different soils was divided into six different areas (one region, two regions, three regions, five regions, seven regions, 10 regions). Consequently, 24 analyzes were performed by using the ETABS program. According to the results obtained from these analyzes, while it is appropriate to use the Winkler method in weak sand soils for rigid foundation acceptance, it is more appropriate to use the Pseudo-coupled method in dense sand soils. Pseudo-coupled method should be used in flexible foundation solutions built on weak sand soils. The Winkler method should be used for flexible foundations built on dense sand soils. In the Pseudo-coupled method, the highest settlements were obtained in the two-region solutions. An optimum number of fields was found to be 7 for Pseudo-coupled method.

The Effect of Foundation Shape on Subgrade Reaction Coefficient

This paper numerically examines the effect of foundation shape on the subgrade reaction coefficient. The distribution of the subgrade reaction coefficient on the foundation area and the values of this coefficient in different regions are studied. A method is also introduced to determine the subgrade reaction coefficient of unusually shaped foundations sometimes encountered in practice. It has been shown that it is possible to divide the foundation area into several regions, and the subgrade reaction coefficient of each part is a multiplier of the central point reaction coefficient. The reaction coefficient of a trapezoidal foundation is equal to the reaction coefficient of a rectangular foundation with a similar area, and the length of the rectangle is the same as the height of the trapezoid. Also, the settlements of two foundations are equal. An L-shaped foundation’s reaction coefficient is a product of multiplying the reaction coefficient of a rectangular foundation to a ratio of the rectangular area by an L-shaped area if the settlements of the two foundations are equal. Besides, the reaction coefficient of a ring-shaped foundation is a product of multiplying the reaction coefficient of a circular foundation with the same outside diameter by the ratio of the circular area to the ring area if the settlements of both foundations are the same.

梁ばねモデルによる杭の水平抵抗解析に用いる水平地盤反力

In this study, evaluation methods of subgrade reaction for horizontal resistance analysis of piles using the beam-spring model were studied by simulation analysis of horizontal loading test results of pile. As a result, the analysis for pile head horizontal load obtained results on the safe side when the method of the guideline was used for an evaluation of subgrade reaction. On the other hand, the analysis using an evaluation method of coefficient of subgrade reaction proposed by the authors and an evaluation method of plastic subgrade reaction proposed by Kishida-Nakai produced results that generally corresponded to the measured values.

Seismic Response of a Liquefiable Site-Underground Structure System

To study the dynamic response of a saturated sand-underground structure system subjected to earthquakes, a series of shaking table tests with a geometric scale ratio of 1/30 were conducted. Based on the experimental acceleration records of testing soil deposits, the relationship between dynamic shear stress and horizontal soil displacement was analyzed by the 1D shear beam inverse calculation method. Meanwhile, the development law of the equivalent dynamic horizontal subgrade reaction coefficient and the dynamic strain of the sidewall in the underground structure has also been discussed. The testing results indicate that the dynamic shear stress of the soil deposit under the bottom plate of the underground structure is larger than that of the soils surrounding the sidewall and above the roof plate; in addition, the soil displacement tends to decrease with the buried depth. The dynamic shear stress–displacement hysteretic loop of the soil deposits tends to be plump as the input amplitude increases. The spectral characteristics of ground motions obviously influence both the dynamic shear stress–displacement hysteretic curve and the excess pore water pressure ratio of saturated sand soil, especially under medium and strong excitations. The equivalent dynamic horizontal subgrade reaction coefficient decreases with the increase of soil depth, and the difference between the coefficient above and underneath the underground structure model can reach 7.589 MN/m3. On the contrary, the equivalent dynamic horizontal subgrade reaction coefficient decreases with the increase of the input amplitude of ground motions, and the maximum reduction ratios of the coefficient are 74.4%, 66.7%, and 47.3%, corresponding to the El-Centro, Kobe, and Wolong ground motions, respectively. The soil liquefaction has a certain effect on the equivalent dynamic horizontal subgrade reaction coefficient. In general, the dynamic strain at the top of the sidewall in the underground structure is higher than that at the bottom of the sidewall, which illustrates that the deformation of underground structures is in good agreement with the seismic deformation mode of soil deposits.

Inverse Analysis of Subgrade Reaction Coefficient of Subway Based on Computer Neural Network

Inverse Analysis of Subgrade Reaction Coefficient of Subway Based on Computer Neural Network

AN ATTEMPT TO UNIFY EVALUATION OF GROUND DEFORMATION MODULUS USED FOR COEFFICIENT OF HORIZONTAL SUBGRADE REACTION EVALUATION OF PILES

In this paper, deformation modulus in an evaluation method of coefficient of subgrade reaction were evaluated. As a result, the variation of deformation modulus obtained from the pressuremeter tests can be suppressed its variation by considering the strain dependency of the ground rigidity. Furthermore, the relationships between the deformation modulus obtained from the pressuremeter test and the PS logging can be approximated proportionally, and the relationships between the deformation modulus and the SPT N-value are approximated by a power approximation formula with an intercept, which enable to unify evaluation of the deformation modulus.

Double-Cell Prefabricated Utility Tunnel Composed of Groove-Shaped Elements: An Extended Study of Stiffness Reduction Method

Based on the semi-rigid characteristics of a double-cell prefabricated utility tunnel composed of groove-shaped elements (PUTCGE), this paper proposes an extended study of a stiffness reduction method for PUTCGEs by introducing the stiffness reduction and bending moment adjustment coefficients of the sidewalls. The effects of the joint stiffness ratio, the aspect ratio of width to height, the coefficient of subgrade reaction, and the embedment depth of the utility tunnel on the stiffness reduction and bending moment adjustment coefficients were investigated, and calculation formulas were established. The results showed that the stiffness reduction coefficient increased with the increase in the joint stiffness ratio, while the bending moment adjustment coefficient decreased with the increase in the joint stiffness ratio. The stiffness reduction coefficient increased with the decrease in the aspect ratio of width to height, while the effect of the aspect ratio of width to height on the bending moment adjustment coefficient was found to be very small. It was also found that neither the coefficient of subgrade reaction nor the embedment depth had a significant effect on the stiffness reduction and bending moment adjustment coefficients. The stiffness reduction method for the PUTCGE was validated through comparison with a full-scale physical model test. The proposed method can provide a reference for designing PUTCGEs for underground construction.

Centrifuge model tests on large-diameter monopiles in dense sand subjected to two-way lateral cyclic loading in short-term

To evaluate the lateral resistance of rigid monopiles for wind turbines in dense sand under lateral cyclic loading, centrifuge model tests are performed, focusing on the base resistance and degradation of the soil resistance under two-way lateral cyclic loading in the short-term. The slenderness ratio (embedded pile length to diameter) is varied from 3.75 to 8 and the loading frequency is in the range of 0.002 to 0.4 Hz in the prototype scale. Under cyclic loading with a maximum horizontal displacement of 5% of the pile diameter, the build-up of excess pore water pressure is observed, but the maximum value of the average excess pore water pressure ratio is around 50% in the steady-state for dense sand whose relative density is 80%. A simple analytical model for the rigid piles, considering the base resistance, is derived and then used to quantify the significance of the resistance at the pile base and the degradation of the soil resistance under cyclic loading. When the slenderness ratio is less than 5, a significant contribution of the moment resistance at the base is confirmed. The estimation of the degradation of the horizontal subgrade reaction coefficient using the simple analytical model suggests that, through cyclic shear tests for the determination of the deformation properties of the soil in a laboratory, it is possible to estimate the degradation of the soil stiffness and the parameters for the reduced sway-rocking type of foundation model.

Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil

Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton’s principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green’s function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%.

Порівняння методів розрахунку плитних фундаментів з урахуванням результатів інженерно-геологічних вишукувань та геодезичних спостережень за процесом просідання

Increasing the height of buildings and structures in combination with the development of areas with unfavorable geotechnical conditions cause the use of foundations in the form of solid reinforced concrete slabs. In complex geotechnical conditions and under high loads, the soils can work beyond linear deformation. This necessitates the calculation of the system "building-foundation-soil" based on the assumptions of nonlinear soil mechanics. The issue of designing foundations for cylindrical structures of the agro-industrial complex, in particular granaries, is especially relevant. The task of this study is a comparative analysis of different methods for calculating the subsidence of slab foundations to select a rational model of deformation of the soil. The comparison of calculation methods is carried out on the example of the foundation under the granary with a volume of 8841 m3. The foundation is made in the form of a round reinforced concrete slab with a diameter of 20.4 m. The characteristics of the soil are established by the results of geotechnical surveys. The calculation according to the Winkler model (elastic base plate with one coefficient of subgrade reaction) was performed in the "Cross" module of the SCAD Office software package. With a total load on the foundation of 2741 tf, its average subsidence is 2.15 cm. The calculation according to the model of three-dimensional finite elements of cubic shape was performed in the environment of the SCAD Office software package. The average subsidence of the foundation is 2.4 cm. The calculation by the method of layer-by-layer summation according to the instructions of DBN B.2.1-10: 2018 gave the subsidence of the foundation slab equal to 13.7 cm. The actual average subsidence of the foundation during the observation period in different areas of the foundation was 1.1… 2.4 cm and averaged 1.75 cm. The comparison of the analyzed methods for determining the subsidence of the foundation indicates the closeness of the results of calculations on the model of the slab on an elastic basis and the model of three-dimensional finite elements to the actual value of subsidence and the greatly higher result of the calculation by layer summation. The use of the latter method leads to excessive reliability in the design of foundations.

GEOTECHNICAL PARAMETER ASSESSMENT AND BEARING CAPACITY ANALYSIS FOR THE FOUNDATION DESIGN

The main objective of this research is to determine the soil appropriateness for the construction of buildings, and it encompasses site investigation, a preliminary process for collecting geological, geotechnical, and other engineering information for safe and economical building design. Site investigation provides insight into unforeseen engineering problems; therefore, instability issues can be forestalled if done thoroughly. Residual soils from the research area comprise many clays, some of which can expand upon moisture increase. Therefore, a site investigation must be carried out to assess the site’s suitability for the proposed construction. The research includes nine boreholes and laboratory testing demonstrating the soil profile and bearing capacity within the settlement limit. The site’s soil is yellowish-brown, weathered, thickly bedded, loosely cemented, friable sandstone consisting of poorly graded sand (SP) and silt/sand (SP-SM) with clayey layers (ML-CL). Uniaxial compressive strength was recorded at 217 to 1238 kPa under natural and saturated conditions. Furthermore, the computed bearing capacity varies from 2.8 to 6.1 tsf using the Terzaghi approach, 7.1 to 8.0 tsf using Bowel’s method, and 4.7 to 5.4 tsf using the Meyerhof method. The coefficient of subgrade reaction for an isolated and raft foundation based on Bowels bearing capacity varies between 24.8 to 26.1 MN/m3 to 13.6 to 15.4 MN/m3, respectively. Based on the investigation and lab testing, a raft foundation would be appropriate for the structure. The proposed construction location didn’t find any significant geological defects; thus, it’s suitable for the construction of buildings. However, the paper’s recommendations must be implemented.

Estimating an empirical equation connecting subgrade reaction modulus with cone penetration test for sandy soils

In geotechnical engineering, the coefficient of subgrade reaction is regarded as one of the most important parameters used for describing the interaction of soil and structure as well as describing some soil characteristics, subgrade reaction coefficient can be calculated theoretically using many different formulas, laboratory via specific well-known tests, and in site through field plate loading test. On the other hand, the cone penetration test is one of the most frequently used field tests to investigate the soil. The lately carried out researches showed a good relation between the subgrade coefficient and the tip resistance collected from the CPT, but the results obtained from the proposed method are still doubtable. In this paper, fifteen plate load tests and thirty CPTs, already collected for private site investigation project, have been used for finding the best fit equation connecting the subgrade reaction coefficient Ks with the tip resistance qc. The finds of the established equation have been compared extensively with those of other well-known related equations. The results show the ability of the concluded equation to get Ks results in the acceptable range of sandy soils. However, the depth and shape effect on the suggested formula need further investigations since all the plate load tests in this project have been carried out on the soil surface with a 45 cm diameter circular plate.