Calculation Method Of Deformation Research Articles

Calculation of creep deformation of stiffness-degraded RC beams after strengthening with increased cross-section

The strengthening of existing reinforced concrete beams (RCBs) has mainly focused on short-term mechanical properties such as flexural resistance and shear resistance, while long-term deflection of RCBs has seldom been studied. In this study, six RCBs with different types and degrees of damage were designed and strengthened by the section enlargement method. Mid-span deflection and concrete strain were used to evaluate the influence of stiffness degradation due to fatigue or corrosion damage on the creep behavior of strengthened RCBs (SRCBs). The experiment results revealed that time-varying curves of creep deformation from fatigue or from corrosion-damaged SRCBs were consistent among the six specimens. Creep in a damaged SRCB was found to increase faster than that in an undamaged beam, and to reach over 90 % of final creep in about six months. Based on the mean curvature method and creep models, taking fatigue and corrosion damage as examples of stiffness degradation, a calculation method for creep deformation of SRCBs was established, and sensitivity analysis of stress levels, reinforcement height, consolidation time, and other parameters were carried out. The research results can provide a theoretical basis and guidance for evaluating creep deformation of stiffness-degraded RCBs after reinforcement with increased cross-section.

Deformation Calculation Method of Reinforcement Part Considering the Randomness of the Welded Joint Stiffness

Deformation Calculation Method of Reinforcement Part Considering the Randomness of the Welded Joint Stiffness

Deformation investigation of electromagnetic diaphragm pump rubber diaphragm.

A diaphragm pump is a type of volumetric pump that has excellent sealing performance. An electromagnetic diaphragm pump is a kind of widely adopted diaphragm pump that has a simple structure, low power loss, and high cost performance. However, the calculation method of deformation for the electromagnetic diaphragm pump rubber diaphragm is presently lacking. Herein, a calculating method of deformation for the electromagnetic diaphragm pump rubber diaphragm is proposed. By establishing and analyzing a deformation model of the electromagnetic diaphragm pump rubber diaphragm, a theoretical relationship between the deformation of the electromagnetic diaphragm pump rubber diaphragm, the size of the electromagnetic diaphragm pump rubber diaphragm and the pressure of fluid is determined. The experimental results indicate that the biggest difference between the tested axial deformation and the calculated axial deformation of the electromagnetic diaphragm pump rubber diaphragm is 0.04 mm and the calculation results show agreement with the experimental results.

Research on the Optimal Design of Retaining Piles of a Wide Metro Tunnel Foundation Pit Based on Deformation Control

Engineers pay more and more attention to the economic benefits of foundation pit engineering. At present, the optimal design of the foundation pit supporting structure mainly focuses on strength and functional design, and there is no mature theoretical design method for deformation control. In this paper, a method for calculating the overall deformation of a foundation pit supporting structure based on the principle of minimum potential energy is proposed. Based on this method, the optimal design of the foundation pit of Guangzhou Baiyun District Comprehensive Transportation Hub Metro Station is realized. The deformation calculation results and optimization design scheme are validated by finite element numerical simulation and field monitoring data. The results show that the proposed theoretical algorithm predicts the pile deformation curves better than the finite element method, suggesting the proposed theoretical method is reasonable and the optimization scheme of the retaining pile is feasible. In the optimized design, the deformation of the foundation pit retaining pile is controlled by its push-back effect. The proposed deformation calculation method can realize the overall deformation calculation of the foundation pit supporting structure.

The present strain rate of Quang Nam - Quang Ngai and the surrounding region

Studying the present strain rate is significant in determining the characteristics and origin of geological anomalies in the region. Tectonic strain occurs under the influence of various factors, especially tectonic forces, and only a few cases of deformation occur at speeds observable by humans. This research uses velocity data from GNSS measurements in Quang Nam - Quang Ngai and surrounding regions to assess present tectonic strain. The combination of methods used in this study includes calculating the ITRF Earth-fixed frame to minimize errors, the method of relative velocity calculation to compare the speed variations between station positions, and the deformation calculation method using the QOCA software developed by NASA's Jet Propulsion Laboratory (JPL). The calculated results show that the coastal areas of the study have relatively low strain rates with the principal strain rate <15 nano-strain/year, the magnitude of deformation is always less than 7.5 nano-strain/year, and the area is conducive to the development of dominant reverse faulting.

An Iterative Calculation Method for Internal Forces and Deformation of Curved Tunnel Lining

The accurate prediction of lining forces and deformations is crucial for the design of arched tunnel lining. However, in traditional tunnel structural mechanics methods, the distribution shape of the surrounding rock elastic resistance (SRER), as well as the zero point and maximal point locations of SRER, are not clearly defined. In this paper, an iterative calculation method is proposed based on the gradual convergence of the unitized values of SRER and total displacement (TD) of the lining, and the one-to-one functional relationship between the two in the stability process of the surrounding rock and lining. In this method involves using the initial displacement caused by the pressure of the surrounding rock pressure is used to initiate the iterative process, and iterative calculation is carried out until the errors between the unitized value of SRER and the unitized value of TD of the lining structure meet the error requirements. This enables precise determination of the SRER and TD. In order to verify the effectiveness of the proposed method, a case study is conducted on the tunnel of Lianghe Expressway tunnel in Yunnan province, China. The results showed that when the semi-lining structure is divided into unit blocks and the average error of consistency is required to be less than 1e-3, it takes about 20 iterations are needed to meet the error requirement. Furthermore, the accuracy of the calculated results is verified through site-measuring experiments. This method provides an effective tool for failure analysis of arched tunnel lining structures.

In-situ Test and Calculation Method for Horizontal Deformation of Soil Induced by Multi-row Grouting

Multi-row grouting can be used to repeatedly mitigate the deformation of critical structures like tunnels. Nevertheless, no comprehensive investigation into the development patterns of soil deformation and excess pore water pressure, induced by multi-row grouting in soft soil, has been conducted to date. To address this gap, this study carried out a field test of multi-row grouting, systematically exploring the evolution and accumulation of soil horizontal displacement (SHD) and excess pore water pressure (EPWP) resulting from multi-row grouting. The findings demonstrated that the grouting process during multi-row grouting respectively exerted reaction and shielding effects on the subsequent grouting for the behavior of soil surrounding the grouting area. The reaction and shielding effects increased proportionally with the number of grouted rows. To predict the SHD induced by multi-row grouting, considering the reaction and shielding effects, this study provided a theoretical calculation method based on cavity expansion theory and the concept of upper and lower bounds, and proposed an optimal grouting scheme.

Calculation Method for Traffic Load-Induced Permanent Deformation in Soils under Flexible Pavements

Rutting is one of the most common types of distress in flexible pavement structures. There are two fundamental methods of designing pavement structures: conventional empirical methods and analytical approaches. Many analytical and empirical design procedures assume that rutting is mostly of asphalt origin and can be reduced by limiting the vertical deformation or stress at the top of the subgrade, but they do not quantify the rutting depth itself. Mechanistic–empirical models to predict the permanent deformations of unbound pavement layers have been well investigated and are rather common in North America; however, they are not widely utilized in the rest of the world. To date, there is no generally accepted, widely recognized, and documented procedure for calculating permanent deformations and thus for determining the rutting depth in flexible pavement courses originating from the unbound granular layers. This paper presents a layered calculation method with which the deformation of soil layers (base, subbase, and subgrade courses) under flexible pavements due to repeated traffic load can be determined. In the first step, the cyclic strain amplitude is calculated using a nonlinear material model that is based on particle size distribution parameters (d50 and CU) and dependent on the mean normal stress, relative density, and actual strain level. In the second step, the HCA (High Cycle Accumulation) model is used to calculate the residual settlement of each sublayer as a function of the number of cycles. It is shown that the developed model is suitable for describing different types of subgrades and pavement cross-sections. It is also demonstrated with finite element calculations that the developed model describes both the elastic and plastic strains sufficiently accurately. The developed model can predict the settlement and rutting of pavement structures with sufficient accuracy based on easily available particle size distribution parameters without the need for complex laboratory and finite element tests.

Research on regionalised digital image slope monitoring methods.

The digital image correlation method is a high precision and non-contact ground deformation monitoring method, which is widely used in surface deformation monitoring. However, according to its principle, different surface characteristics have great influence on the monitoring results. In this paper, a regional digital image slope monitoring method is established to meet the monitoring requirements of different areas of the same slope. Firstly, the features of different regions in the image are identified according to the optical region detection, and then the deformation calculation method is matched according to the features of different regions. Finally, according to the binocular vision principle, the three-dimensional displacement of the slope is obtained. Taking a highway slope in Qinhuangdao as an example, we realised all-weather and full-field deformation monitoring of slope, and verified the applicability and feasibility of regional digital image slope monitoring method. The applicability of digital image correlation method in slope monitoring is improved.

Deformation State Analysis and Design Method of Bottom-Confined Gravity Retaining Walls

The deformation failure modes of gravity retaining walls include overturning, toppling, deep sliding, and eccentric failure. The complex eccentric failure mode, which involves the multi-stage deformation of retaining walls, suffers from a lack of mechanical models and design theories. Based on the basic theory of reinforced concrete construction, this study established a deformation calculation model of bottom-confined reinforced concrete gravity retaining walls (RC-GRWs), which are composed of tensile, compressive, and rigid zones. Then, this study defined RC-GRWs’ normal-operation, cracking, yield, and ultimate limit states, as well as the displacement of RC-GRWs in these states, according to the concrete cracking and steel reinforcement yield conditions. Accordingly, this study proposed a design method and process to determine the deformation of bottom-confined RC-GRWs. A project case shows that the calculation method for RC-GRW deformation proposed in this study can effectively assess the deformation state of in-service retaining walls and that optimized cracked retaining walls can meet the deformation-based design requirements.

Calculation method for internal force and deformation of the prestressed I-beam on the elastic foundation

The elastic foundation beam theory has been widely used in civil engineering, including railway, tunnel, and building foundations. With the development of fabricated structures, more elastic foundation beams need to be prestressed. In order to explore the frame foundation beam with the fabricated anchor-cable in the slope reinforcement project, in this article, prestress is applied to both ends of the beam. Then, according to the calculation method of internal force and deformation of the beam under concentrated force and the equivalent load theory of the prestressed structure, three new methods: the finite difference method (FDM) of the Euler–Bernoulli beam on the Winkler foundation, FDM of the Euler–Bernoulli beam on the Pasternak foundation, and theoretical analytical solution of the Timoshenko beam on the Winkler foundation, are deduced to calculate internal force and deformation under prestress force and concentrated force, respectively. Typical calculation parameters are selected for design and verification via the three new methods and GEO5, respectively. The results show that the calculated values of the three new methods are basically consistent with those calculated using GEO5 software, which verifies the feasibility of the three new methods.

A temporal correlation micro-visco-elastohydrodynamic lubrication model and its applications on internal combustion engine

The time lag of bearing deformation caused by viscoelasticity cannot be ignored under time-varying load. This paper proposes a new temporal correlation micro visco-elastohydrodynamic lubrication (T-MVEHD) model. It corrects the calculation method of deformation for dynamically loaded bearings based on the finite element method and viscoelastic constitutive equation and improves the efficiency by uncoupling the stiffness and Reynolds equations. Further, it is applied to the lubrication analysis of internal combustion engine bearing. The simulation results show that the discernment of the new model to the impact is increased by 29.6% than the micro elastohydrodynamic lubrication model. It has better continuity and compatibility when the lubrication state changes and captures the asperity contact of connecting rod bearing 12° in advance.

Study for Longitudinal Deformation of Shield Tunnel in Side of Foundation Pit Based on Virtual Image Technique

A prediction model of enclosure structure deformation caused by the excavation of foundation pit is established. Based on the virtual image technique, the soil deformation caused by sidewall deformation is calculated. Meanwhile, the deformation model considering rotating and staggering of shield tunnel is used to establish a calculation method of longitudinal deformation of adjacent shield tunnel. The result suggests that: (a) The horizontal displacement of adjacent shield tunnel is normally distributed. (b) With increasing retaining structure deformation, it is obvious that deformation value and range of adjacent shield tunnel also increase. (c) As the distance between the adjacent shield tunnel and the enclosure structure increases, the horizontal displacement of the side shield tunnel decreases nonlinearly. (d) The shield tunnel with shallow buried depth is greatly affect by the excavation of adjacent foundation pit. As the depth of the tunnel increases, the impact gradually decreases.

Study on size effect of jointed rock mass and influencing factors of the REV size based on the SRM method

Based on the Yaojiayu tunnel of Binlai Expressway, the size effect of jointed rock mass and influencing factors of the representative elementary volume (REV) were studied. The point cloud image of jointed rock mass near the tunnel face was collected by 3D laser scanning technology. Through the Geology Plane software independently developed by Shandong University, the structural plane data were processed and obtained. According to the structural plane data, the discrete fracture network (DFN) was established. Based on the laboratory test results of rock samples in the tunnel site, the particles were embedded into DFN to construct the synthetic rock mass (SRM). The size effect and REV of the jointed rock mass were studied based on the uniaxial compressive strength (UCS) and Young's modulus obtained by uniaxial compression test simulations. It is concluded that the REV size of the jointed rock mass is 7 m × 7 m × 14 m, which provides the criterion and calculation parameters for simulating tunnel excavation in jointed rock mass by the continuous deformation calculation method. In order to study the influence of joint geometric parameters (trace length, spacing, and dip angle) on REV size, different multi-scale SRM models were established by changing the parameters of structural planes. It is observed that within a certain size range, the REV size is negatively correlated with the joint trace length and dip angle, while positively correlated with the joint spacing. And the size of REV is gradually stable with the increase of geometric parameters of joints. Based on the influence law of joint geometry parameters on REV, the REV size range of different engineering can be estimated approximately.

Research on Interface Slip of Composite Reinforced Steel Truss-Concrete Test Beam and Its Calculation and Analysis Method

In this study, a model of test beam in negative moment area is designed, and the slip characteristics of test beam under overlimit static load and variable amplitude cyclic load are studied, respectively. By constructing the relationship between shear stiffness and slip parameters of the test beam, the deformation calculation method of the test beam under different fatigue cycles is derived, and the accuracy of the calculation model is verified by experiments. The results show that the maximum slip value (0.038 mm) of static load after 10,000 times of limited fatigue load is increased by 58.3% compared with that before overlimit fatigue load is applied (0.024 mm). When the fatigue cycle is 0-2 million times, the total slip is between 0.019 and 0.026 mm and the residual slip percentage is between 4.17 and 8.33%. The maximum residual values are 0.022 mm, 0.027 mm, and 0.028 mm after 1.5 times, 2 times, and 3 times of overload and variable amplitude fatigue loads, respectively, and the slip values have no obvious fluctuation, all of which show good working performance. The average value of the ratio between the deformation value and the measured value of composite beams is 0.89, and the standard deviation is 4.86%. When the fatigue loading times are more than 2.8 million, the ratio between the calculated value and the measured value is less than 0.85, so the adaptability of the calculation model has certain limitations. On the whole, the calculation model proposed in this study fully considers the factors such as the stiffness and fatigue loading times of composite beams, and the error between the calculated results and the measured results is within 5%, with high accuracy, which can be used as a reference for the actual design.

Models and design procedure for cross-laminated bamboo rocking walls

To conduct a comprehensive parametric and limit state study of Cross-Laminated Bamboo (CLB) rocking walls, this study established a finite element model (FEM) and a modified analytical model (MAM) for rocking walls based on tests. The initial prestress, cross-sectional area of the posttensioned rebars, aspect ratio of the CLB wall, and friction force of conventional friction dampers (CFDs) were studied. Parametric analysis showed that the lateral capacity of the rocking wall increased with the initial prestress and cross-sectional area of the posttensioned rebars, while the cross-sectional area of the rebars also led to an increase in the stiffness. A CLB wall with a high aspect ratio has good ductility and low stiffness. The increase in CFD friction force was an effective method to enhance the energy dissipation capacity of the rocking wall. The MAM was proposed based on the limit states and considered the action of the CFDs in the initial stage while modifying the calculation method of shear deformation of the CLB wall. The MAM was verified by the test and FEM results. Design procedure was then developed to ensure the lateral capacity and stiffness of the rocking wall at the collapse prevention (CP) hazard level.

Simplified Calculation Method for Overlying Pipeline Deformation Induced by Tunnel Construction in Soil Based on the Energy Principle

The deformation of the overlay pipeline caused by the excavation of the soil tunnel in the case of small spacing cannot be ignored. Based on the experience of previous engineering, this paper assumes that the settlement of the overlying pipeline caused by tunnel excavation satisfies the basic morphology of Gaussian distribution. On this basis, the soil displacement is converted into load acting on the pipeline, and the energy variation principle is introduced, and the energy variation equation of the pipe‐soil system is established, which is iteratively solved based on the principle of minimum potential energy, so as to obtain the calculation method of overlay pipeline vertical deformation caused by soil tunnel excavation, which is more simple and practical than the previous method. The calculation results were compared with the existing tests and engineering examples to verify the correctness of the proposed formula. Finally, the influence of pipeline material, formation loss rate, and intersection angle between the tunnel and pipeline on pipeline vertical deformation was analyzed. The comparative analysis shows that the pipeline deformation decreases with the increase of tunnel angle and pipeline elastic modulus, but increases with the increase of formation loss rate.

A Method for Calculating the Velocity of Corner-to-Corner Rear-End Collisions of Vehicles Based on Collision Deformation Analysis

To improve the efficiency of solving vehicle collision velocity and provide sufficient evidence for the identification of accident responsibility, we proposed a method combining the momentum equation and finite element simulation. We built a finite element simulation model of a vehicle where multiple collision simulation experiments were carried out, and studied the calculation method of collision deformation. After fitting and analyzing the simulated deformation data of an accident vehicle under different velocities through collision simulation experiments, a relationship model between collision velocity and deformation was established, and a method to solve the collision velocity was proposed by combing the existing two-dimensional collision momentum equation of the vehicle. For actual collision cases, the proposed velocity solution method and the simulation software were used for reconstruction analyses, respectively, and the results of the instantaneous contact velocity of vehicle collision were compared. It was found that the velocity calculation results obtained using the two methods above were in good agreement; the shape and depth of the simulated deformation were consistent with the actual deformation of the vehicle.

A Review of the Methods Calculating the Horizontal Displacement for Modular Reinforced Soil Retaining Walls

Most of the damage to reinforced retaining walls is caused by excessive deformation; however, there is no calculation method for deformation under static and dynamic loads in the design codes of reinforced soil retaining walls. In this paper, by collecting the measured displacement data from four actual projects, four indoor prototype tests and two indoor model tests under a total of 10 static load conditions, and comparing the calculation results with seven theoretical methods, the results show that the FHWA method is more applicable to the permanent displacement prediction of indoor prototype tests and that the CTI method is more applicable to the permanent displacement prediction of actual projects and indoor model tests. Two yield acceleration calculation methods and four permanent displacement calculation formulas were selected to calculate the displacement response of two reinforced soil test models under seismic loads and compared with the measured values, and the results showed that the Ausilio yield acceleration solution method was better. When the input peak acceleration ranges from 0.1 to 0.6 g, the Richards and Elms upper limit method is used, and when the input peak acceleration is 0.6–1.0 g, the Newmark upper limit method can predict the permanent displacement of the retaining wall more accurately.

Mechanical problems for the long-term stability of rocks surrounding deep level underground tunnels

Based on the research of Academician Tan Tjong-Kie on the long-term stability mechanics of underground tunnel and considering Academician Sadovsky’s structural hierarchy theories on complex geological rock masses, the inherent statistical mechanical properties of inhomogeneous structure and closed stress in deep rock masses were investigated. Two mechanical problems were mainly studied, i.e. characteristics of inherent non-uniform deformation and closed stress of rock masses, and long-term stability of deep tunnels. The quantitative mathematical characterization of inherent non-uniform deformation and closed stress of rock masses were given using the method of statistical mechanics. Based on the law of mass conservation, a general calculation method of long-term stability and deformation of rock masses surrounding deep level tunnels was proposed. The Maxwell model was used to calculate the threshold of splitting. A post-peak failure model of rock was established to estimate the in-situ stress at which rock undergoes post-peak failure. With the help of the theory of the hirerachical structure of rock masses, the maximum value of rock displacement due to splitting dilatation was obtained. A dimensionless energy factor was introduced to define the extent of zonal disintegration of surrounding rock masses. It was concluded that the splitting and dilatancy deformation is the main part of the deformation of surrounding rocks. The reasons why unloading splitting failure is more likely to take place in rock masses surrounding deep level tunnels were explained. The split evolution pattern of rock masses surrounding deep level tunnels and the calculation method of dilatancy displacement were obtained. The calculation results of the range of loosening zone, the location of the rupture zone in rock masses surrounding deep level tunnels, and the displacement of the sidewall were compared with the existing monitoring data in the underground powerhouse of the Jinping Ⅰ Hydropower Station, and the agreement is good.