Elastic Foundation Beam Theory Research Articles

Study on Damage of Shallow Foundation Building caused by Surface Curvature Deformation in Coal Mining Area

Coal mining can lead to various forms of surface deformation, the damage caused by curvature deformation is the most extensive, which has become the key to restricting the development and utilization of coal resources under villages. Therefore, it is very important to master the deformation and destruction mechanism of buildings under surface curvature deformation for the rational exploitation of coal resources under villages. In this paper, the deformation and damage of buildings caused by curvature deformation are studied with theoretical analysis and numerical simulation, aiming at the shallow foundation building in rural China, and the following objectives are achieved: 1) Based on the theory of elastic foundation beam, the longitudinal and transverse walls are considered as a whole and analyzed, and a mathematical model of the cooperative deformation in building walls under surface curvature deformation is established. 2) The failure mechanism of masonry buildings is analyzed, including the distribution of internal stress and the form of wall cracks. 3) The influence of various factors on the internal stress changes of buildings is discussed. 4) The results of numerical simulation of wall stress distribution are similar to theoretical analysis, and the influence of doors and windows on the additional stress distribution is analyzed emphatically. This study can provide important guidance for the optimization of coal mining design under villages and the protection of village buildings.

Optimization Analysis of Deformation of Underlying Tunnel in Dewatering and Excavation of Phreatic Aquifer

This paper theoretically analyzed the deformation law of the underlying tunnel caused by dewatering and excavation of deep foundation pit in the phreatic aquifer area, which is based on the Mindlin solution and the double-sided elastic foundation beam theory, and used the finite difference method and the fluid-solid coupling principle to conduct three-dimensional numerical simulation of dewatering and excavation of deep foundation pit with fluid-solid coupling by using FLAC3D5.00. This research shows that the layered and segmented excavation method from the middle to the end by dewatering the skip layer has a better effect on optimizing the deformation of the underlying tunnel through the simulation of three excavation methods and two dewatering schemes crossing each other, which is about 2.5% less than the layer-by-layer dewatering scheme. In addition, the deformation law of the simulated value is the same as the theoretical value, and the simulated value is slightly larger than the theoretical value. Underlying tunnel only just exists vertical deformation at the direct center of the foundation pit, and the maximum deformation is about 3.054 mm under the dewatering well of the jumping layer and W3. With the dewatering of jumping layer and the third excavation mode (W3), underlying tunnel only just exists lateral displacement at the position where is the retaining structure, and the maximum displacement is 1.606 mm.

Study on the enhancement coefficient of the local compressive strength improvement of masonry under a cantilever beam

Locally compressed masonry under a cantilever beam is restrained by the surrounding masonry, resulting in improved local compressive strength. The code for design of masonry structures stipulates that the enhancement coefficients of the local compressive strength of masonry(γ) with single- and T-wall supporting cantilever beams are 1.25 and 1.5, respectively; however, these two values, which stem from the material performance test of masonr’s local compressive strength, are not testified from the local compression of masonry under cantilever beam. Further, the γ of L-shaped wall supporting cantilever beam is not presented in the Code. This study theoretically deduced the effective length of the masonry’s compressive stress distribution based on the elastic foundation beam theory, obtaining the theoretical results in good agreement with the test values. The theoretical, test, and code values of the effective length of the masonry’s compressive stress distribution were adopted for calculating γ with single- and T-wall supporting cantilever beams, revealing the code value of γ was relatively small. Herein, the enhancement coefficient of the local compressive strength of masonry has been investigated using an L-shaped wall supporting cantilever beam; according to the calculation results, an enhancement coefficient of 1.4 is recommended for safety reasons.

Influence of Different Propulsion Speeds on the Characteristics of Mine Pressure in the Fully Mechanized Caving Face During Rotary Stage

Owing to the influence of advancing speed, the movement characteristics of roof are special, and there exists a risk of pressure frame and roof fall. To understand the influence of the advancing speed on the strata pressure distribution of the fully mechanized top-coal caving roadway during the transition period, this study takes the 301 fully mechanized top-coal caving face of Changchun Xing coal mine as the engineering background. The influence of the advancing speed on the distribution of the abutment pressure is analyzed on the basis of the elastic foundation beam theory, and the characteristics of strata pressure display are verified by both numerical simulation and field measurement. The results show that when the advancing speed of the working face increases, the value of the bearing pressure at the azimuth position in front of the working face also increases. Within a certain range, the peak value of the bearing pressure at the front of the working face is proportional to the advancing speed, and the position of the peak value of the supporting pressure in advance is closer to the working face. The conclusions obtained can provide technical support for stop and end surrounding rock control measures in similar working faces.

Dynamic Response of Double Elastic Cantilever Beam Attributed to Variable Uniformly Distributed Load

Based on the double-layer elastic foundation beam theory, the rails and the wall plates of the electromagnetic launching device are modeled as a double-layer elastic cantilever foundation beam. After establishing the kinetic differential equation and setting the boundary condition of the cantilever beam, the displacement solution of double-layer elastic cantilever foundation beam under no load condition is obtained. Applying the Heaviside Function, the deflection equation of the upper and lower beam, the expression of the bending moment, and the stress are obtained. In the case of given motion parameters and structural parameters, the analytical solutions of the rail and the wall plate are calculated. The ANSYS numerical analysis is carried out under the same condition and the results of both solutions are in good agreement. The results can provide theoretical basis for the design of strength and stiffness of the electromagnetic launch device.

Calculation model for bar-wrapping during prestressing of an embedded bar-wrapped cylinder concrete pressure pipe

A new type of water conveyance pipe called bar-wrapped cylinder concrete pressure pipe is introduced. Prestress mechanism of this pipe is described. A planar deformation calculation model nested with each other is built to calculate the core deformation under the prestress of single ring. From two-dimensional to three-dimensional, based on the elastic foundation beam theory, a calculation model for bar-wrapping during prestressing is proposed and used in an embedded bar-wrapped cylinder concrete pressure pipe with an inner diameter of 1400 mm. A field experiment was designed to validate the model. Finally, the calculation results with the model were well supported by experimental ones.

Calculating Jacking Forces for Circular Pipes with Welding Flange Slabs from a Combined Theory and Case Study

Recently, the Steel Tube Slab (STS) curtain method has been successfully used in the construction of ultra-shallow metro stations in modern urban areas. By using the STS curtain method, the external surfaces of pipes are welded with flange slabs, and then the pipes are jacked into soils. However, the nature and extent of the influence of flange slabs on the calculation of jacking force is unclear. This paper presents the first combined theoretical and case study to calculate the increase of jacking forces for circular steel pipes with welded flange slabs during the entire jacking process. The increase of jacking forces was assumed to balance the friction at the soil-pipeline interface. Theoretical formulae were firstly developed to calculate earth pressure based on pressure arch theory and elastic foundation beam theory. A case study was then performed to verify the theoretical results with the field data from Olympic Metro Station on the Shenyang Metro Line 9 in China. Subsequently, factors influencing the calculation of jacking force were analyzed and discussed. Results show that the theoretical formulae produced good results with minor errors. The implications of these findings regarding the prediction of jacking force and selection of hydraulic jack are discussed.

Analytical analyses of the effect of filled karst cavern on tunnel lining structure under complex geological conditions

In this study, based on the elastic foundation beam theory, a local elastic foundation model has been developed. Using the model, the mechanical characteristics of the effect of tunnel-filled karst on the lining structure has been investigated. Incorporating the characteristic of the karst area, the formulas for the displacement, bending moment, and shear force of an equivalent beam have been derived. By applying the formulas to a beam under different working conditions, such as different cavern sizes and different compression modulus ratios of the filling media, analyses of the mechanical states have been carried out. The results show that if the compression modulus ratio of different filling media is close to unity, the effect of the cave on the lining structure is very small. On the other hand, if the ratio is much less than unity, the effect is more significant. The effect on the stability of the lining structure is greater for the larger caves, and smaller for the smaller caves. For the tunnel bottom equivalent beam, its bending point is at the point where the cave is in contact with the surrounding rock. Further, the maximum shear force is at the contact surface. For a beam that is closer to the karst, the displacement is larger. Under this situation, the beam section is in an adverse force state and prone to cracks. The results from this study can be used as a significant guide for the design, maintenance and construction of a tunnel which has a cavern at the base of the tunnel.

A Study on Dual-Load-Zone Model of Overlying Strata and Evolution Law of Mining Stress

The changeable structure and movement law of overlying strata are the main contributor to the change of mining stress. Starting from the relevant theory of key stratum and particularly based on the theory of mine ground pressure and strata control, this research proposed a new solution to mining stress problem by establishing a dual-load-zone stratum structural model. Elastic foundation beam theory was used to solve the stress of overlying strata of the two load zones with superposition method, which revised the traditional calculation method of mining stress. The abnormal increase of lead abutment pressure in the mining area was explained effectively, through which the evolution law of mining stress in the case of hard rock was obtained. The results indicate that mining stress experiences a drastic change within the range of 50m ahead of the coal wall due to the collapse of main roof; under the influence of main key stratum and inferior key strata, the influence range of lead abutment pressure is extended up to approximately 120m in the working face; this remarkable increase can be attributed to the excessive length of sagging zone. Results from both the dual-load-zone model experiment and field measurement demonstrate high consistency. The model can predict the influence range of abutment pressure effectively and thus guide the safety production of mining.

Method to Calculate Working Surface Abutment Pressure Based on Key Strata Theory

Overburden key strata (KS) have a significant influence on abutment pressure distribution. However, current calculation methods for working surface abutment pressure do not consider the influence of the overburden KS. This study uses KS theory to analyze the overburden load transferred to coal‐rock masses on both sides of the stope through fractured blocks in different layers of the KS in the fissure zone and KS in different layers of the curve subsidence zone. Using Winkler’s elastic foundation beam theory, we consider the fissure zone KS on the coal mass side and the curve subsidence zone KS as many elastic foundation beams interact with each other. A method to calculate the abutment pressure of the coal mass and the goaf was then established, considering the influence of the overburden KS. The abutment pressure distribution of working surface 207 after mining was then calculated using our method, based on mining conditions present in the Tingnan coal mine. The calculated results were verified using measurements from borehole stress meters and microseismic monitoring systems, as well as numerical simulations. In addition, the calculation results were used to determine a reasonable position for the stopping line and remaining width of the roadway’s protection coal pillar in working surface 207. The results of this study can be used to calculate the abutment pressure distribution of the working surface under a variety of overburden KS conditions. The results can also provide guidance for forecasting and preventing mine dynamic hazards, controlling the surrounding rock in mining roadways, determining reasonable widths for protection coal pillars, and designing the layout of mining roadways.

A brief analysis of behaviour possibility of a jointed rock mass near to longwall excavation face simulation using Distinct Elements Method (DEM) in the context of the Beam on Elastic Foundation (BEF) theory

Rock masses are discontinuous medium. Using the program based on the Distinct Element Method (DEM) UDEC (Universal Distinct Element Code) a 2D model of the rock mass near the longwall face was built. The UDEC code, due to its properties, is particularly suitable for modelling discontinuous and jointed rock masses. The coal bed lying at a depth of 700m had a thickness of 3m and was mined by longwall system with caving. The total face advance was 415m. The model had dimensions of 1500×500m (w×h). A vertical stress of σz=7.2MPa was applied to the upper edge of the model. The mechanized support protected the roof for a length of 4m at a distance of 2m from the face of the longwall. During simulation, among others, vertical displacements of roof and vertical stresses were closely examined. There were observed phenomena of bending, cracking, loosening and falling of roof blocks of rock. The results of numerical simulations were compared with the results of analytical solutions. The calculations were based on the solutions of the elastic foundation beam theory and the stress wave theory. Comparable shapes of arch pressure σzmax and the range of its impact were obtained.

Field Measurement and Mechanical Analysis of Height of the Water Flowing Fracture Zone in Short-Wall Block Backfill Mining beneath the Aquifer: A Case Study in China

Short-wall block filling mining (SBBM) technology has become an effective way to recover coal resources beneath the aquifer, which are unsuitable, or cannot be used by long-wall mining, such as corner coal pillars, industrial square pillars, and irregular coal blocks as well as the coal beneath buildings, railways, and water bodies. The SBBM method can not only enhance the recovery ratio but also provide a solution for the environment problems associated with gangues on the surface. However, whether the height of water flowing fractures will reach to the aquifer to cause water loss during SBBM has always been a key problem. Therefore, based on the theory of elastic foundation beam and SBBM characteristics, a mechanical model for calculating the height of a water flowing fracture zone in the overlying strata of SBBM was established, and this model calculated that the height of the water flowing fracture zone was 27.0 m in the experimental working face, and the height of the water flowing fracture zone was measured as 26.8 m according to washing fluid loss in the hole, core damage analysis, and drilling TV imaging detection. The comparison results demonstrated that the calculated value almost fit well with the field-measured data, validating the accuracy of the proposed mechanical model, while the predicted value (48.7 m) in the Regulations of coal mining under building, railways and water-bodies deviates greatly from the measured results. This reveals that the prediction formula in Regulations is not effective in predicting the height of the water flowing fracture zone in SBBM. The present research results are of great significance to further enhancing the recovery ratio of coal resources and improving the water-preserved mining theory.

Mechanism of rock burst caused by fracture of key strata during irregular working face mining and its prevention methods

To study the occurrence mechanism of rock burst during mining the irregular working face, the study took irregular panel 7447 near fault tectonic as an engineering background. The spatial fracture characteristic of overlying strata was analyzed by Winkler elastic foundation beam theory. Furthermore, the influence law of panel width to suspended width and limit breaking span of key strata were also analyzed by thin plate theory. Through micro-seismic monitoring, theoretical analysis, numerical simulation and working resistance of support of field measurement, this study investigated the fracture characteristic of overlying strata and mechanism of rock burst in irregular working face. The results show that the fracture characteristic of overlying strata shows a spatial trapezoid structure, with the main roof being as an undersurface. The fracture form changes from vertical “O-X” type to transverse “O-X” type with the increase of trapezoidal height. From the narrow mining face to the wide mining face, the suspended width of key strata is greater than its limit breaking width, and a strong dynamic load is produced by the fracture of key strata. The numerical simulation and micro-seismic monitoring results show that the initial fracture position of key strata is close to tailgate 7447. Also there is a high static load caused by fault tectonic. The dynamic and static combined load induce rock burst. Accordingly, a cooperative control technology was proposed, which can weaken dynamic load by hard roof directional hydraulic fracture and enhance surrounding rock by supporting system.

Analytical cutting model for a single fiber to investigate the occurrences of the surface damages in milling of CFRP

The edge milling process of carbon fiber-reinforced plastics (CFRPs) is often accompanied by delamination and burrs on slot edges of the top layer. These damages impact on processing quality, processing efficiency, strength, and fatigue life of the materials, etc. To investigate the occurrence of these damages, the analytical cutting model for a single fiber of the top layer is established based on the Winkler elastic foundation beam theory. The critical fiber cutting angles and the corresponding engagement angles with different initial fiber orientations are predicted. Then, the milling experiments with the initial fiber orientations θ0 = 90° are carried out. The results show that the occurrences of the burrs and delamination can be correctly predicted. The suitable initial fiber orientations are chosen in the range from 30 to 60° for the smoother slot edges. There are two burr occurrence zones (BOZs) when θ0 = 90°. The delamination-inhibited zone (DIZ) is usually in the burr occurrence zone (BOZ).

Dynamic response of anchored sheet pile wall under ground motion: Analytical model with experimental validation

Anchored stabilizing pile is a typical earthquake-resistant structure in reinforced slope with advantages of safety, reliability and low cost. It demonstrated excellent seismic performance during the 2008 Great Wenchuan earthquake. However, due to the complexity of the structural system, the coupling relationship between soil, pile, and anchor cable is not well understood at present. This paper developed an analytical model in modeling the dynamic responses of the pile, anchor cable and soil slope system based on Winkler elastic foundation beam theory. The seismic design of the anchored sheet pile wall can then be carried out. An experimental shake-table test was conducted to validate the proposed analytical model. Through the test, the displacements of the pile, axial force of the anchor cable, and earth pressure along the pile derived from the analytical model were validated by the test results. It shows that the proposed analytical model is suitable for the practical application and can provide theoretical basis for dynamic response analysis and seismic design of anchored sheet pile wall.

Analysis of Development Pattern of a Water-Flowing Fissure Zone in Shortwall Block Mining

In order to effectively recover the residual coal resources, such as coal pillars and irregular coal blocks induced by large-scale extensive mining, in this study, we proposed a shortwall block mining (SBM) technology and examined the development pattern of the water-flowing fissure zone (WFZ) in the overlying strata during the SBM process. By analyzing the overlying rocks’ movement rules in SBM, the main controlling factors affecting the development of the height of the water-flowing fissure zone (HWFZ) determined are as follows: mining height, block length, and the width of the protective coal pillar among the blocks. Moreover, based on the elastic foundation beam theory, the mechanical model for the calculation of HWFZ in SBM was established. Based on the first strength theory, the calculation formula of the development HWFZ was derived. Using this model, the calculated HWFZ after SBM was 50.3 m, whereas the measured heights of the leakage of drilling washing fluid were 47.98 and 50.06 m, respectively. The calculated values almost fit well with the field-measured data, verifying the reliability of the proposed mechanical model. The results of this study can provide a significant reference for enhancing the recovery ratio of coal resources and optimizing water protection mining theory.

ANALYSIS ON EFFECT OF PLATE SPACING ON SHEAR STIFFNESS OF PERFOBOND CONNECTORS

In order to discuss the reasonable plate spacing of perfobond connector, the influence of plate spacing on the shear stiffness of perfobond connector is analyzed through the push-out model test and based on the theory of elastic foundation beam. The calculation formula for perfobond shear stiffness is proposed, which accounts for the influence of plate spacing. Research results indicate that the plate spacing has little effect on shear capacity and peak slip of perfobond connector but changes the shear stiffness. Shear stiffness approximately linearly increases as the plate spacing increases, gradually approaching the single plate shear stiffness. The main influence factor for the shear stiffness of perfobond connector is the spacing-diameter ratio, which is suggested to be no less than 3.3 when multi perfobonds are arranged in parallel.

RETRACTED: Micro-macro-mechanical model and material removal mechanism of machining carbon fiber reinforced polymer

Abstract The present paper studies the material removal mechanism of machining carbon fiber reinforced polymer (CFRP) by a micro-mechanical model, and proposes prediction models of cutting forces from the microscale to the macroscale. At the microscale, the micro-mechanical model for cutting a fiber in orthogonal cutting CFRP is established via the elastic foundation beam theory with explicit description of the carbon fiber and the matrix. The deflection and failure of the fiber constrained by the surrounding composite are analyzed under the cutting effects by the tool edge. In addition, the fiber failure under the pressing of the flank face is analyzed based on the undulating fiber theory. Analytical expressions are established at the microscale for evaluating the force for cutting a single fiber and the compression force for a single fiber from the flank face. At the macroscale, the chip length is determined by analyzing the characteristics of the cutting force signals of orthogonal cutting experiments. The characteristic chip length is used for establishing the trans-scale prediction model of cutting forces from the microscale to the macroscale. The total cutting and thrust forces at the macroscale during the formation of a chip are predicted based on the micro-mechanical results and the characteristic chip length, which agree well with the experimental results for orthogonal cutting of CFRP. Furthermore, the fiber failure modes and the debonding between the fiber and the matrix under different supporting conditions are discussed by the micro-mechanical model, by which subsurface damages are recognized.

A general analytical model based on elastic foundation beam theory for adhesively bonded DCB joints either with flexible or rigid adhesives

A new general analytical model based on elastic foundation beam theory is proposed for adhesively bonded double cantilever beam (DCB) specimens. The new model accounts for any stress state (from plane stress to plane strain) in the adhesive and therefore, the model is able to predict the mechanical response of a DCB specimens whatever the adhesive type (from rigid to flexible), the stress state, and the width/thickness relationship of the specimen are. The model is validated with DCB tests for flexible Silkron-H100 and stiff Araldite-2021 adhesives. A comparison with other models from the literature demonstrates that more accurate predictions in terms of stress distribution in the middle plane of the adhesive layer, adherend deflections and load predictions are obtained. The model is especially suitable when flexible adhesives and/or thick adhesives are used. In addition, a new method to accurately obtain Poisson’s ratio for flexible adhesives is proposed.

The Dynamic Responses of the of the Submerged Floating Tunnel under Seismic effect

Based on the theory of elastic foundation beam, dynamic equations of submerged floating tunnel(SFT) tube under seismic force are presented. For investigating the influence of P wave, tunnel length and stiffness of anchorage system on SFT tube, the nonlinear dynamic analysis method is applied. By regarding SFT as an elastic-plastic vibrating system and inputting seismic acceleration records, numerical simulation results are obtained. The research results indicate that with the increase of the spring stiffness, the response of the tube decreases under the effect of the observed seismic force and the peak value appearance time of mid-span displacement response put off gradually. Besides, the effect of tunnel length on the displacement response is limited when the spring stiffness value is fixed. As the key to SFT design, the scope of stiffness design parameters are given in this paper. The research would provide a reference for seismic design and further study of SFT.