Approximate Analytical Solution for the Temperature Field in Welding

To determine the temperature fields associated with welding, significant efforts have been made to establish the relative merits of numerical approaches with variable material properties and the analytical approaches with constant material properties. Currently, analytical solutions are either based on the temperature field generated by a point source of heat or are developed for a finite domain derived approximately by using an infinite or semi-infinite heat kernel. Furthermore, the heat kernel applied in these solutions is derived from the Image method (for example, Nguyen’s book (Thermal Analysis of Welds, 2004)). The main problem with the heat kernels obtained from Image method is that they face the problem of singularity at and around the point where the heat source is located, and they do not satisfy the boundary condition accurately. That is why the Laplace transform method has been applied here instead of using the Image method to formulate a heat kernel that (1) converges rapidly, (2) avoids the problem of singularity, and (3) gives a good and robust approximation of the real analytic solution for the temperature field. The results obtained from the analytical solutions were compared with the results obtained from finite element method. The current work is believed to make a considerable contribution to the avoidance of previously mentioned problems by deriving a new approximate analytical solution for the temperature field on a three-dimensional finite body.     

能源桩三维螺旋线热源的瞬态传热模型

将螺旋埋管等效为三维螺旋线热源,考虑螺旋埋管能源桩的传热过程,运用格林函数和第一型曲线进行积分,推导给出了考虑时间、空间位置、埋管参数和岩土体热物理性质4参数的螺旋埋管能源桩的温度场解析解,建立高精度三维螺旋埋管能源桩的传热模型。并通过在数值模拟软件中建立螺旋埋管能源桩三维模型,依据边界条件,求解得出三维螺旋埋管能源桩温度场数值解。对比结果表明:所建立的能源桩三维螺旋线热源模型具有很高的解析精度。最后,基于解析模型讨论了螺旋埋管能源桩换热温度场的空间分布和时间效应。      

Nonlinear Analyses for Coupled Problem of Temperature and Seepage Fields in Cold Regions Retaining Walls

In this paper, a mathematical mechanical model and the governing differential equations of the coupled problem of temperature and seepage fields, with phase change, are derived from the theories of heat transfer and seepage. The finite-element formulation of this problem is then obtained using Galerkin’s method. Lastly, an illustrative example is provided. The example shows that the effect of seepage field on the temperature field of cold region retaining walls is large. The effect of this factor on cold region retaining walls should be taken into account in cold regions engineering design. Comparisons of the results of this approach with the measured data in the field have been made. The agreement is very good.     

Investigation of Settlement of a Jointed Concrete Pavement

A section of jointed concrete pavement on U.S. 75, which was built from 1982 to 1985, in the Paris District of the Texas Department of Transportation (TxDOT) experienced severe pumping and settlement, even though two types of treatment (full depth repair and polyurethane foam injection) were performed. An extensive field investigation was conducted using ground penetrating radar, falling weight deflectometer, dynamic cone penetrometer, and coring to identify the causes of the continued pumping and settlement problems, and develop an optimal repair strategy. The pavement evaluation included tie bar condition, load transfer efficiency (LTE) at transverse and longitudinal construction joints, and base support conditions. Some of the tie bars failed in shear due to corrosion, which resulted in substantially low LTEs (<40%) at longitudinal construction joints. Pumping and settlement problems were more pronounced where the tie bars failed; the resulting large deflections exacerbated the pumping and settlement problems. The results demonstrate the importance of adequate LTEs (>80%) provided by tie bars, base and subgrade support, in providing satisfactory JCP performance. Inadequate design or construction of any of these critical elements could lead to performance problems, potentially including severe settlement, which is quite difficult to repair. To repair this pavement section, the Paris District of TxDOT is planning to retrofit tie bars by the “slot stitching” method, along with filling the voids under the slab using grout, followed by thin overlay using latex modified concrete to correct the differential elevation problems at longitudinal construction joints. It is expected that this repair strategy will address the distress problems and extend the pavement life.     

Surface Loading of a Multilayered Viscoelastic Pavement: Semianalytical Solution

In this paper a new method is proposed to analyze the mechanical response of a linear viscoelastic pavement. The material parameters of the asphalt concrete are characterized by the relaxation modulus and creep compliance, which are further represented by the Prony series. By virtue of the Laplace transform and the correspondence principle, the solution in the Laplace domain is first derived. The interconversion between the relaxation modulus and creep compliance is then applied to treat the complicated inverse Laplace transform. The displacement, strain, and stress fields are represented concisely in terms of the convolution integral in the time domain, which is subsequently solved analytically. Therefore, responses of the viscoelastic pavement are finally expressed analytically in the time domain and numerically in space domain, called a semianalytical approach. Since both the relaxation modulus and creep compliance are used simultaneously, instead of only one parameter in the conventional methods, the present method is also called a dual-parameter method. The present formulation is verified at both the short- and long-term time limits analytically and at the other finite time numerically, as compared to the conventional numerical methods. We clearly show that the present dual-parameter and semianalytical method can predict accurately the time-dependent responses of the viscoelastic pavement, especially at the long-term time. The present formulation could also be employed to validate the widely used collocation method.     

Global Optimization of Pavement Structural Parameters during Back-Calculation Using Hybrid Shuffled Complex Evolution Algorithm

In this paper, the use of a hybrid evolutionary optimization algorithm is proposed for global optimization of pavement structural parameters through inverse modeling. Shuffled complex evolution (SCE) is a population-based stochastic optimization technique combining the competitive complex evolution with the controlled random search, the implicit clustering, and the complex shuffling. Back-calculation of pavement layer moduli is an ill-posed inverse engineering problem, which involves searching for the optimal combination of pavement layer stiffness solutions in an unsmooth, multimodal, complex search space. SCE is especially considered a robust and efficient approach for global optimization of multimodal functions. A desirable characteristic of the SCE algorithm is that it uses information about the nature of the response surface, extracted using the deterministic Simplex geometric shape, to direct the search into regions with higher posterior probability. The hybrid back-calculation system described in this paper combines the robustness of the SCE in global optimization with the computational efficiency of neural networks and advanced pavement system characterization offered by employing finite-element models. This is the first time the SCE approach is applied to real-time nondestructive evaluation of pavement systems required in the routine maintenance and rehabilitation activities for sustainable transportation infrastructure.     

Dynamic Response Solution in Transient State of Viscoelastic Road under Moving Load and Its Application

In order to study the dynamic response of an asphalt road, a dynamic model of the road under a moving load is proposed, in which the viscoelastic characteristics of the base and pavement are all considered, the pavement is regarded as an infinite beam on a Kelvin viscoelastic base. By using Green’s functions, Laplace transforms, and Fourier transforms, the analytical solution in transient is deduced. As the viscosity of the pavement is included in the model, the analytical solution can be used to investigate more of the factors that affect the dynamic response, such as vehicle speed, temperature, and road material properties. Using this analytical solution, some numerical calculations are given to illustrate the effects of vehicles’ speeds and different damping on the deflection with the displacement.     

稳态胞晶生长控制方程的解析解及其传输行为

建立了稳态胞晶生长温度场数学模型。通过在复数域内应用分离变量法对控制方程进行求解,得到了问题的解析解。讨论了在某些特定情形下的能量传输特性。     

Validation of 3DFE Analysis of Rigid Pavement Dynamic Response to Moving Traffic and Nonlinear Temperature Gradient Effects

The response of dowel jointed concrete pavements to the combined effect of nonlinear thermal gradient and moving axle load is examined using three-dimensional finite-element (3DFE) modeling. The 3DFE-computed response to moving axle load was field validated versus measured concrete slab response to a fully loaded moving dump truck. The 3DFE-predicted slab curling due to nonlinear thermal gradient through the slab thickness was validated versus: (1) corner-dowel bar bending as measured using instrumented dowel embedded in an instrumented rigid pavement section in West Virginia; and (2) Westergaard’s closed-form solution. The effects of slab thickness, slab length, axle loading position, and axle type on slab stresses are examined. It is shown that while a negative temperature gradient reduces the intensity of traffic-induced stresses, positive temperature gradient increases it several fold. Formulas are developed for the computation of the peak principal stresses due to the combined effect of tandem axle load and nonlinear thermal gradient.     

Use of an Infrared Joint Heater to Improve Longitudinal Joint Performance in Hot Mix Asphalt Pavements

Longitudinal joint cracking is one of the most prevalent forms of distress in asphalt concrete pavements. The joint area does not achieve the same density as the mat due to an unconfined edge on the initial pass and a cold joint during the second pass. The lower density allows water to penetrate and the material cracks, usually within one?year of construction. There are many techniques for constructing longitudinal joints, one being to preheat the joint prior to paving the second lane. This paper describes a field study conducted in New Hampshire using an infrared joint heater. Thermocouples were embedded in the pavement to determine the extent of heat penetration from the infrared heaters. Cores were taken along the joint and in the travel lanes for both the control and test sections. Density and strength measurements were taken on the cores. Permeability measurements along the control and test joints were performed. A cracking survey performed one?year after construction showed that the section of pavement where the infrared heater was used had significantly less cracking than the control section.     

Assessment of Retrofit Dowel Benefits in Cracked Portland Cement Concrete Pavements

A parametric study was conducted using the finite-element rigid pavement program ISLAB2000. For cracks that utilize aggregate interlock as the sole means of load transfer, the integrity of the cracks was initially modeled using the aggregate interlock factor. A subsequent analysis was then performed on the same cracks for the case where both dowel bars and aggregate interlock were available for load transfer purposes. The latter scenario represents the case where dowel bar retrofitting (DBR) has been performed on the cracks. In both cases, the deflection load transfer efficiency and critical slab tensile stresses were computed in order to examine the immediate theoretical benefits of the dowel bars. The validity of these theoretical benefits was tested using data from falling-weight deflectometer testing on DBR sites in both Michigan and Washington. It was found that installation of dowel bars did not increase the load transfer efficiency for cracks that had levels greater than 89–95%, depending on pavement parameters. When temperature gradients were not considered, little change in tensile stress due to a load at the crack was exhibited when DBR was performed on cracks that had load transfer efficiency levels less than 70–80%.     

Utilizing Advanced Characterization Tools to Prevent Reflective Cracking

To prevent premature failures of rehabilitated concrete pavements, transportation authorities need tools to characterize the prerehab pavement condition of its load carrying capacity, and to determine the resistance of the overlay material to underlying crack/joint movements. Two quantitative methods, the rolling dynamic deflectometer (RDD) and overlay tester (OT), along with field performance data were employed in rehabilitation studies involving reflective cracks. The RDD is able to continuously assess vertical differential movements at joints/cracks that represent the potential for reflective cracks on existing pavements. The OT has the ability to determine the resistance of the overlay material to underlying crack/joint movements. The RDD W1?W3 deflections were used to determine areas that have a high potential for reflective cracking due to poor load transfer across joints and cracks. This paper documents results from the RDD and OT on the following five rehabilitation projects: (1) SH225; (2) US96; (3) SH12; (4) SH342; and (5) IH35W. Based on the available test results from these five projects, it was observed that the W1?W3 threshold values of 5.5 mils (0.140 mm) for exposed concrete pavement and 6.5 mils (0.165 mm) for composite pavement with existing hot mix asphalt overlay and an OT threshold value of 700 cycles correlated well with the field performance. Ignoring either of these critical factors may lead to premature reflective cracking.     

Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams

This paper presents frequency domain solution algorithms of the one-dimensional transient heat transfer equation that describes temperature variations in arch dam cross sections. Algorithms are developed to compute the temperature T(x,t), spatial distribution, and time evolution for the “direct” problem, where the temperature variations are specified at the upstream and downstream faces, and for the “inverse” problem, where temperatures have been measured at thermometers located inside instrumented dam sections. The resulting nonlinear temperature field is decomposed in an effective average temperature, Tm(t), and a linear temperature difference, Tg(x,t), from which the dam thermal displacement response can be deducted. The proposed frequency domain solution procedures are able to reproduce an arbitrary transient heat response by appending trailing temperatures at the end of thermal signals, thus transforming a periodic heat transfer problem in a transient one. The frequency domain solution procedures are used to develop the HTT (hydrostatic, temperature, time) statistical model to interpret concrete dam-recorded pendulum displacements. In the HTT model, the thermal loads are arbitrary and can contain temperature drift or unusual temperature conditions. The explicit use of Tm(t) and Tg(x,t) in the HTT dam displacement model allows extrapolation for temperature conditions that have never been experienced by the dam before (within the assumption of elastic behavior). The HTT model is applied to the 131-m-high Schlegeis arch dam, and the results are compared with the HST (hydrostatic, seasonal, time) displacement model that is widely used in practice.     

Time-Dependent Response of an Axially Loaded Elastic Bar in a Multilayered Poroelastic Medium

This paper considers load transfer from an axially loaded long elastic bar into a multilayered poroelastic half-space. The problem is analyzed by decomposing the bar-half-space system into an extended half-space governed by Biot’s theory of poroelasticity and a one-dimensional fictitious bar. The interaction problem is formulated in the Laplace transform domain. Vertical displacement of the bar is approximated by an exponential series with a set of arbitrary functions. The arbitrary functions are determined by using a variational method. The vertical displacement influence function of a multilayered half-space subjected to a buried uniform vertical patch load is required in the variational formulation. The required influence function is obtained by employing a previously developed exact stiffness matrix method. Time domain solutions are computed by using a numerical Laplace inversion scheme. Selected numerical results are presented to portray the influence of the bar length–radius ratio, layer configuration, poroelastic material parameters, and loading time history on the time dependent response of a bar.     

NJTxtr—A Computer Program Based on LASER to Monitor Asphalt Segregation

Abstract: This paper describes the research funded by the New Jersey Department of Transportation to develop an automated technology to monitor segregation during construction of hot-mix asphalt concrete pavements. A Laser-based system was used to measure surface texture and to detect segregation. Two segregated test sections and a control test section were tested to evaluate the applicability of Laser texture method to detect and quantify segregation. Laser texture data were gathered from all three sections. Ratios of texture in segregated areas to that in nonsegregated areas were set as the basis for detection of different levels of segregation. By combining the level of segregation and extent of segregation, an AREA index was developed to determine the acceptability of a pavement section. Based on AREA index, pay adjustment factors were proposed to reduce the payment to account for loss of pavement life due to segregation. Further remedial actions were proposed to correct segregated pavement sections with acceptable AREA index. Based on the above concepts, Windows-based computer program NJTxtr was developed to detect and quantify segregation. This computer program uses the Laser-equipment-collected pavement texture data and determines whether the pavement section is acceptable or unacceptable based on the level of segregation within a pavement section, and provides bonus or penalties to the contractor. The paper describes a novel technology using laser and associated software for construction quality control of asphalt concrete pavements. The proposed methodology was applied to detect segregation in an interstate highway section in New Jersey, and this section was repaved based on visual observation and recommendation from this study.     

Perturbation Solutions for Thermal Process of Honeycomb Regenerator

 A parameter perturbation for the unsteady state heat transfer characteristics of honeycomb regenerator is presented. It is limited to the cases where the storage matrix has a small wall thickness so that no temperature variation in the matrix perpendicular to the flow direction is considered. Starting from a two phase transient thermal model for the gas and storage matrix, an approximate solution for regenerator heat transfer process is derived using the multiple scale method for the limiting case where the longitudinal heat conduction of solid matrix is far less than the convective heat transfer between the gas and the solid. The regenerator temperature profiles are expressed as Taylor series of the coefficient of solid heat conduction item in the model. The analytical validity is shown by comparing the perturbation solution with the experiment and the numerical solution. The results show that it is possible for the perturbation to improve the effectiveness and economics of thermal research on regenerators.     

Factors Affecting Initial Roughness of Concrete Pavement

Past studies have shown that initial pavement roughness greatly affects future pavement roughness and roughness progression rate. Initial pavement roughness is also an important input to the roughness prediction model in mechanistic-empirical design guide. This study analyzed the design and construction factors affecting initial pavement roughness. Initial international roughness index of 90 concrete pavements constructed in Wisconsin from 2000 to 2004 were analyzed using multiple regression method. The factors considered in this study included concrete pavement slab thickness, project location, dowel bar placement, joint spacing, base type, and pavement length. The factors affecting initial pavement roughness were identified.     

矿热炉炉衬结构的温度场分析

为进一步研究矿热炉炉衬中温度场的分布情况,采用ANSYS仿真软件对真实简化的炉衬模型进行仿真分析。通过改变炉内温度和对流换热系数的数值,得到炉壁处的温度数据,与实测数据进行对比,验证模拟数据的合理性。结果表明,炉衬中不同耐火材料的温度分布存在差异;炉壁温度会随着炉内温度的增大而逐渐升高,随着对流换热系数的增大而降低;炉壁温度随对流换热系数的变化曲线斜率从0.13降到0.06,当曲线斜率逼近于0时,对流换热系数不再影响炉壁温度的变化,得到最优化的对流换热系数;模拟数据占实测数据的百分比在3%~8%范围内时,模拟数据能合理反映炉壁温度值。这为炉体保温结构设计和耐火材料的选用提供依据。     

Heat-transfer enhancement using weakly ionized, atmospheric pressure plasma in metallurgical applications

Experimental measurements and computational analysis of heat transfer in atmospheric pressure, midtemperature range (1200 to 1600 K) plasma flow over an aluminum cylinder have been carried out. A comparison of transient temperature measurements for the aluminum cylinder under convective unionized air flow and those with convective plasma flow shows significantly higher heat transfer from plasma flow compared to air flow under identical temperature and flow conditions. A heattransfer problem is computationally modeled by using available experimental measurements of temperature rise in the cylinder to determine the degree of ionization in the plasma flow. The continuity, momentum, and energy conservation equations, as well as conservation equations for electrons and ions, and the Poisson’s equation for self-consistent electric field are solved in the plasma by a finite volume method. The conjugated transient heat transfer in the cylinder and in the plasma is obtained by simultaneous solution of the transient energy conservation equations. It is shown that the enhancement of heat transfer in plasma flow is due to the energy deposited by charged species during recombination reaction at the solid surface. An important finding is that even a small degree of ionization (<1 pct) provides significant enhancement in heat transfer. This enhancement in heat transfer can lead to a productivity increase in metallurgical applications.     

Application of Graded Finite Elements for Asphalt Pavements

Asphalt paving layers, particularly the surface course, exhibit vertically graded material properties. This grading is caused primarily by temperature gradients and aging related stiffness gradients. Most conventional existing analysis models do not directly account for the continuous grading of properties in flexible pavement layers. As a result, conventional analysis methods may lead to inaccurate prediction of pavement responses and distress under traffic and environmental loading. In this paper, a theoretical formulation for the graded finite element method is provided followed by an implementation using the user material subroutine (UMAT) capability of the finite element software ABAQUS. Numerical examples using the UMAT are provided to illustrate the benefits of using graded elements in pavement analysis.