Evaluating the in situ concrete compressive strength by means of cores cut from hardened concrete is acknowledged as the most ordinary method, however, it is very difficult to predict the compressive strength of concrete since it is affected by many factors such as different mix designs, methods of mixing, curing conditions, compaction, etc. In this paper, considering the experimental results, three different models of multiple linear regression model (MLR), artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS) are established, trained, and tested within the Matlab programming environment for predicting the 28 days compressive strength of concrete with 173 different mix designs. Finally, these three models are compared with each other and resulted in the fact that ANN and ANFIS models enables us to reliably evaluate the compressive strength of concrete with different mix designs, however, multiple linear regression model is not feasible enough in this area because of nonlinear relationship between the concrete mix parameters. Finally, the sensitivity analysis (SA) for two different sets of parameters on the concrete compressive strength prediction are carried out.
In recent few years, significant improvement has been made in developing largescale 3D printers to accommodate the need of industrial-scale 3D printing. It is of great feasibility to construct structural components and buildings by means of 3D concrete printing. The major issues of this innovative technique focus on the preparation and optimization of concrete materials which possess favourable printable properties as well as the measurement and evaluation methods of their workability. This paper firstly introduces three largescale 3D printing systems that have been successfully applied in construction industry. It then summarizes the commonly used raw materials in concrete manufacturing. Critical factors that should be particularly controlled in material preparation are specified. Easy-extrusive, easy-flowing, well-buildable, proper setting time and low shrinkage are significant for concrete mixture to meet the critical requirements of a freeform construction process. Thereafter, measuring methods that can be employed to assess the fresh and hardened properties of concrete at early stages are suggested. Finally, a few of evaluation methods are presented which may offer certain assistance for optimizing material preparation. The objective of this work is to review current design methodologies and experimental measurement and evaluation methods for 3D printable concrete materials and promote its responsible use with largescale 3D printing technology.
In the present work, carbon nano/microparticles obtained by controlled pyrolysis of peanut (PS) and hazelnut (HS) shells are presented. These materials were characterized by Raman spectroscopy and field emission-scanning electron microscopy (FE-SEM). When added to cement paste, up to 1 wt%, these materials led to an increase of the cement matrix flexural strength and of toughness. Moreover, with respect to plain cement, the total increase in electromagnetic radiation shielding effect when adding 0.5 wt% of PS or HS in cement composites is much higher in comparison to the ones reported in the literature for CNTs used in the same content.
The objectives of this study are to review and evaluate the developments and applications of pultruded fiber-reinforced polymer composites in civil and structural engineering and review advances in research and developments. Several case applications are reviewed. The paper presents a state-of-the-art review of fundamental research on the behavior of pultruded fiber reinforced polymer closed sections and highlights gaps in knowledge and areas of potential further research.
This paper presents a comprehensive review of modeling of alkali-silica reaction (ASR) in concrete. Such modeling is essential for investigating the chemical expansion mechanism and the subsequent influence on the mechanical aspects of the material. The concept of ASR and the mechanism of expansion are first outlined, and the state-of-the-art of modeling for ASR, the focus of the paper, is then presented in detail. The modeling includes theoretical approaches, meso- and macroscopic models for ASR analysis. The theoretical approaches dealt with the chemical reaction mechanism and were used for predicting pessimum size of aggregate. Mesoscopic models have attempted to explain the mechanism of mechanical deterioration of ASR-affected concrete at material scale. The macroscopic models, chemo-mechanical coupling models, have been generally developed by combining the chemical reaction kinetics with linear or nonlinear mechanical constitutive, and were applied to reproduce and predict the long-term behavior of structures suffering from ASR. Finally, a conclusion and discussion of the modeling are given.
Predicting the tunneling-induced maximum ground surface settlement is a complex problem since the settlement depends on plenty of intrinsic and extrinsic factors. This study investigates the efficiency and feasibility of six machine learning (ML) algorithms, namely, back-propagation neural network, wavelet neural network, general regression neural network (GRNN), extreme learning machine, support vector machine and random forest (RF), to predict tunneling-induced settlement. Field data sets including geological conditions, shield operational parameters, and tunnel geometry collected from four sections of tunnel with a total of 3.93 km are used to build models. Three indicators, mean absolute error, root mean absolute error, and coefficient of determination the (R2) are used to demonstrate the performance of each computational model. The results indicated that ML algorithms have great potential to predict tunneling-induced settlement, compared with the traditional multivariate linear regression method. GRNN and RF algorithms show the best performance among six ML algorithms, which accurately recognize the evolution of tunneling-induced settlement. The correlation between the input variables and settlement is also investigated by Pearson correlation coefficient.
Reinforced concretes (RC) have been widely used in constructions. In construction, one of the critical elements carrying a high percentage of the weight is columns which were not used to design to absorb large dynamic load like surface bursts. This study focuses on investigating blast load parameters to design of RC columns to withstand blast detonation. The numerical model is based on finite element analysis using LS-DYNA. Numerical results are validated against blast field tests available in the literature. Couples of simulations are performed with changing blast parameters to study effects of various scaled distances on the nonlinear behavior of RC columns. According to simulation results, the scaled distance has a substantial influence on the blast response of RC columns. With lower scaled distance, higher peak pressure and larger pressure impulse are applied on the RC column. Eventually, keeping the scaled distance unchanged, increasing the charge weight or shorter standoff distance cause more damage to the RC column. Intensive studies are carried out to investigate the effects of scaled distance and charge weight on the damage degree and residual axial load carrying capacity of RC columns with various column width, longitudinal reinforcement ratio and concrete strength. Results of this research will be used to assessment the effect of an explosion on the dynamic behavior of RC columns.
In the framework of finite element meshes, a novel continuous/discontinuous deformation analysis (CDDA) method is proposed in this paper for modeling of crack problems. In the present CDDA, simple polynomial interpolations are defined at the deformable block elements, and a link element is employed to connect the adjacent block elements. The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures. The SIFs (stress intensity factors) for various types of cracks, such as kinked cracks or curved cracks, can be easily computed in the CDDA by using the virtual crack extension technique (VCET). Both the formulation and implementation of the VCET in CDDA are simple and straightforward. Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes, and can automatically simulate the crack propagation without degrading accuracy.
A brief overview of vortex-induced vibration (VIV) of circular cylinders is first given as most of VIV studies have been focused on this particular bluff cross-section. A critical literature review of VIV of bridge decks that highlights physical mechanisms central to VIV from a renewed perspective is provided. The discussion focuses on VIV of bridge decks from wind-tunnel experiments, full-scale observations, semi-empirical models and computational fluids dynamics (CFD) perspectives. Finally, a recently developed reduced order model (ROM) based on truncated Volterra series is introduced to model VIV of long-span bridges. This model captures successfully salient features of VIV at “lock-in” and unlike most phenomenological models offers physical significance of the model kernels.
With increasing environmental pressure to reduce solid waste and to recycle as much as possible, the concrete industry has adopted a number of methods to achieve this goal by replacement of waste glass with concrete composition materials. Due to differences in mixture design, placement and consolidation techniques, the strength and durability of Self Compacting Concrete (SCC) may be different than those of conventional concrete. Therefore, replacement of waste glass with fine aggregate in SCC should deeply be investigated compared to conventional concretes. The aim of the present study is to investigate the effect of glass replacement with fine aggregate on the SCC properties. In present study, fine aggregate has been replaced with waste glass in six different weight ratios ranging from 0% to 50%. Fresh results indicate that the flow-ability characteristics have been increased as the waste glass incorporated to paste volume. Nevertheless, compressive, flexural and splitting strengths of concrete containing waste glass have been shown to decrease when the content of waste glass is increased. The strength reduction of concrete in different glass replacement ratios is not remarkable, thus it can be produced SCC with waste glass as fine aggregate in a standard manner.
This paper presents an efficient hybrid control approach through combining the idea of proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) control algorithm. The proposed LQR-PID controller, while having the advantage of the classical PID controller, is easy to implement in seismic-excited structures. Using an optimization procedure based on a cuckoo search (CS) algorithm, the LQR-PID controller is designed for a seismic- excited structure equipped with an active tuned mass damper (ATMD). Considering four earthquakes, the performance of the proposed LQR-PID controller is evaluated. Then, the results are compared with those given by a LQR controller. The simulation results indicate that the LQR-PID performs better than the LQR controller in reduction of seismic responses of the structure in the terms of displacement and acceleration of stories of the structure.
Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g., the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g., peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.
This paper reports on modern developments related to nanotechnology of cement and concrete. Recent advances in instrumentation and design of advanced nano-composite materials is discussed. New technological directions and historical milestones in nanoengineering and nanomodi?cation of cement-based materials are presented. It is concluded that there is a strong potential of nanotechnology to improve the performance of cement-based materials.
In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.
The concept of structural robustness and relevant design guidelines have been in existence in the progressive collapse literature since the 1970s following the partial collapse of the Ronan Point apartment building; however, in the more general context, research on the evaluation and enhancement of structural robustness is still relatively limited. This paper is aimed to provide a general overview of the current state of research concerning structural robustness. The focus is placed on the quantification and the associated evaluation methodologies, rather than specific measures to ensure prescriptive robustness requirements. Some associated concepts, such as redundancy and vulnerability, will be discussed and interpreted in the general context of robustness such that the corresponding methodologies can be compared quantitatively using a comparable scale. A framework methodology proposed by the authors is also introduced in line with the discussion of the literature.
Bridge girders exposed to aggressive environmental conditions are subject to time-variant changes in resistance. There is therefore a need for evaluation procedures that produce accurate predictions of the load-carrying capacity and reliability of bridge structures to allow rational decisions to be made about repair, rehabilitation and expected life-cycle costs. This study deals with the stability of damaged steel I-beams with web opening subjected to bending loads. A three-dimensional (3D) finite element (FE) model using ABAQUS for the elastic flexural torsional analysis of I-beams has been used to assess the effect of web opening on the lateral buckling moment capacity. Artificial neural network (ANN) approach has been also employed to derive empirical formulae for predicting the lateral-torsional buckling moment capacity of deteriorated steel I-beams with different sizes of rectangular web opening using obtained FE results. It is found out that the proposed formulae can accurately predict residual lateral buckling capacities of doubly-symmetric steel I-beams with rectangular web opening. Hence, the results of this study can be used for better prediction of buckling life of web opening of steel beams by practice engineers.
Cementitious materials reinforced with well dispersed multiwall carbon nanotubes (MWCNTs) and carbon nanofibers (CNFs) at the nanoscale were fabricated and tested. The MWCNTs and CNFs were dispersed by the application of ultrasonic energy and the use of a superplasticizer. Mechanical and fracture properties including flexural strength, Young’s modulus, flexural and fracture toughness were measured and compared with similarly processed reference cement based mixes without the nano-reinforcement. The MWCNTs and CNFs reinforced mortars exhibited superior properties demonstrated by a significant improvement in flexural strength (106%), Young’s modulus (95%), flexural toughness (105%), effective crack length (30%) and fracture toughness (120%).
This paper deals with the fatigue crack growth simulations of three-dimensional linear elastic cracks by XFEM under cyclic thermal load. Both temperature and displacement approximations are extrinsically enriched by Heaviside and crack front enrichment functions. Crack growth is modelled by successive linear extensions, and the end points of these linear extensions are joined by cubic spline segments to obtain a modified crack front. Different crack geometries such as planer, non-planer and arbitrary spline shape cracks are simulated under thermal shock, adiabatic and isothermal loads to reveal the sturdiness and versatility of the XFEM approach.
In view of China’s development trend of green building and building industrialization, based on the emerging requirements of the structural engineering community, the development and proposition of novel resource-saving high-performance steel-concrete composite structural systems with adequate safety and durability has become a kernel development trend in structural engineering. This paper provides a state of the art review of China’s cutting-edge research and technologies in steel-concrete composite structures in recent years, including the building engineering, the bridge engineering and the special engineering. This paper summarizes the technical principles and applications of the long-span bi-directional composite structures, the long-span composite transfer structures, the comprehensive crack control technique based on uplift-restricted and slip-permitted (URSP) connectors, the steel plate concrete composite (SPCC) strengthen technique, and the innovative composite joints. By improving and revising traditional structure types, the comprehensive superiority of steel-concrete composite structures is well elicited. The research results also indicate that the high-performance steel-concrete composite structures have a promising popularizing prospect in the future.
Many researches have been carried out to study the fresh and hardened properties of concrete containing crumb rubber as replacement to fine aggregate by volume, yet there is no specific guideline has been developed on the mix design of the rubbercrete. The experimental program, which has been developed and reported in this paper, is designed and executed to provide such mix design guidelines. A total of 45 concrete mixes with three different water to cement ratio (0.41, 0.57 and 0.68) were cast and tested for fresh and mechanical properties of rubbercrete such as slump, air content, unit weight, compressive strength, flexural strength, splitting tensile strength and modulus of elasticity. Influence of mix design parameters such as percentage of crumb rubber replacement, cement content, water content, fine aggregate content, and coarse aggregate content were investigated. Three levels of slump value (for conventional concrete mixes) has been selected; low, medium and high slump. In each slump level, water content was kept constant. Equations for the reduction factors (RFs) for compressive strength, flexural strength, splitting tensile strength and modulus of elasticity have been developed. These RFs can be used to design rubbercrete mixes based on the conventional mix (0% crumb rubber content)
We propose a method to estimate the natural frequencies of the multi-walled carbon nanotubes (MWCNTs) embedded in an elastic medium. Each of the nested tubes is treated as an individual bar interacting with the adjacent nanotubes through the inter-tube Van der Waals forces. The effect of the elastic medium is introduced through an elastic model. The mathematical model is finally reduced to an eigen value problem and the eigen value problem is solved to arrive at the inter-tube resonances of the MWCNTs. Variation of the natural frequencies with different parameters are studied. The estimated results from the present method are compared with the literature and results are observed to be in close agreement.
The most critical drawback in currently used steel reinforcement in reinforced concrete (RC) structures is susceptibility to accumulation of plastic deformation under excessive loads. Many concrete structures due to damaged (yielded) steel reinforcement have undergone costly repairs and replacements. This research presents a new type of shape memory alloy (SMA)-based composite reinforcement with ability to withstand high elongation while exhibiting pseudo-elastic behavior. In this study, small diameter SMA wires are embedded in thermoset resin matrix with or without additional glass fibers to develop composite reinforcement. Manufacturing technique of new proposed composite is validated using microscopy images. The proposed SMA-FRP composite square rebars are first fabricated and then embedded in small scale concrete T-beam. 3-point bending test is conducted on manufactured RC beam using a cyclic displacement controlled regime until failure. It is found that the SMA-FRP composite reinforcement is able to enhance the performance of concrete member by providing re-centering and crack closing capability.
Plastic concrete is an engineering material, which is commonly used for construction of cut-off walls to prevent water seepage under the dam. This paper aims to explore two machine learning algorithms including artificial neural network (ANN) and support vector machine (SVM) to predict the compressive strength of bentonite/sepiolite plastic concretes. For this purpose, two unique sets of 72 data for compressive strength of bentonite and sepiolite plastic concrete samples (totally 144 data) were prepared by conducting an experimental study. The results confirm the ability of ANN and SVM models in prediction processes. Also, Sensitivity analysis of the best obtained model indicated that cement and silty clay have the maximum and minimum influences on the compressive strength, respectively. In addition, investigation of the effect of measurement error of input variables showed that change in the sand content (amount) and curing time will have the maximum and minimum effects on the output mean absolute percent error (MAPE) of model, respectively. Finally, the influence of different variables on the plastic concrete compressive strength values was evaluated by conducting parametric studies.
This paper describes an inverse Gaussian process-based model to characterize the growth of metal-loss corrosion defects on energy pipelines. The model parameters are evaluated using the Bayesian methodology by combining the inspection data obtained from multiple inspections with the prior distributions. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to numerically evaluate the posterior marginal distribution of each individual parameter. The measurement errors associated with the ILI tools are considered in the Bayesian inference. The application of the growth model is illustrated using an example involving real inspection data collected from an in-service pipeline in Alberta, Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. Parametric analyses associated with the growth model as well as reliability assessment of the pipeline based on the growth model are also included in the example. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.
A mechanical model recently developed for the shear strength of slender reinforced concrete beams with and without shear reinforcement is presented and extended to elements with uniformly distributed loads, specially focusing on practical design and assessment in this paper. The shear strength is considered to be the sum of the shear transferred by the concrete compression chord, along the crack, due to residual tensile and frictional stresses, by the stirrups and, if they exist, by the longitudinal reinforcement. Based on the principles of structural mechanics simple expressions have been derived separately for each shear transfer action and for their interaction at ultimate limit state. The predictions of the model have been compared to those obtained by using the EC2, MC2010 and ACI 318-08 provisions and they fit very well the available experimental results from the recently published ACI-DAfStb databases of shear tests on slender reinforced concrete beams with and without stirrups. Finally, a detailed application example has been presented, obtaining each contributing component to the shear strength and the assumed shape and position of the critical crack.
The nanoparticles of SiO2 were used in cement systems to modify the rheological behavior, to enhance the reactivity of supplementary cementitious materials, and also to improve the strength and durability. In this research, low-cost nano-SiO2 particles from natural hydrothermal solutions obtained by membrane ultrafiltration and, optionally, by cryochemical vacuum sublimation drying, were evaluated in portland cement based systems. ??The SiO2-rich solutions were obtained from the wells of Mutnovsky geothermal power station (Far East of Russia). The constant nano-SiO2 dosage of 0.25% (as a solid material by weight of cementitious materials) was used to compare the cement systems with different nanoparticles against a reference mortar and a commercially available nano-SiO2. Nanoparticles were characterized by X-Ray Diffraction (XRD), BET Surface Area, Scanning Electron Microscope (SEM) and Fourier Transform Infrared (FTIR) spectroscopy techniques. It was demonstrated that the addition of polycarboxylate ether superplasticizer and the dispersion treatment using an ultrasound processor can be used to facilitate the distribution of nano-SiO2 particles in the mixing water. The effect of nano-SiO2 particles in portland cement mortars was investigated by evaluating the flow, heat of hydration and compressive strength development. It was demonstrated that the use of nano-SiO2 particles can reduce the segregation and improve strength properties.
Asphalt concrete (AC) overlays placed over old asphalt pavement have become an alternative to repairing and reinforcing pavements. The strength contributed by the AC overlay is strongly influenced by the anisotropic properties of the pavement material. This study was conducted to analyze the influence of anisotropy, modulus gradient properties, and the condition of the AC overlay and old pavement contact plane on the mechanical behaviors of AC overlays, as well as to quantify the influence of the degree of anisotropy on the mechanical behaviors of AC overlay by a sensitivity analysis (SA). The mechanical behaviors of the AC overlay were numerically obtained using the three-dimensional finite element method with the aid of ABAQUS, a commercial program. Variations in the AC overlay’s modulus as a function of temperature as well as the contact state between the AC overlay and AC layer were considered. The SA is based on standardized regression coefficients method. Comparing the mechanical behavior in terms of surface deflection, stress, and strain of the anisotropy model against those corresponding to the isotropic model under static loads show that the anisotropic properties had greater effects on the mechanical behavior of the AC overlay. In addition, the maximum shear stress in the AC overlay was the most significant output parameter affected by the degree of anisotropy. Therefore, future research concerning the reinforcement and repair of pavements should consider the anisotropic properties of the pavement materials.
Increasing the bending and shear capacities of reinforced concrete members is an interesting issue in structural engineering. In recent years, many studies have been carried out to improve capacities of reinforced concrete members such as using post and pre-tensioning, Fiber Reinforced Polymer and other techniques. This paper proposes a novel and significant technique to increase the flexural capacity of simply supported reinforced concrete beams. The proposed method uses a new reinforcement bar system having bent-up bars, covered with rubber tubes. This technique will avoid interaction of bent-up bars with concrete. They are located in the zone where compressive and tensile forces act against one another. The compressive force in the upper point of the bent-up bars is exerted to the end point of these bars located under neutral axis. Moreover, the tensile stress is decreased in reinforcements located under the neutral axis. This will cause the Reinforced Concrete (RC) beam to endure extra loading before reaching yield stress. These factors may well be considered as reasons to increase bending capacity in the new system. The laboratory work together with finite element method analysis were carried out in this investigation. Furthermore, bending capacity, ductility, strength, and cracking zone were assessed for the new proposed system and compared with the conventional model. Both the FEM simulation and the experimental test results revealed that the proposed system has significant impact in increasing the load bearing capacity and the stiffness of the RC beams. In the present study, an equation is formulated to calculate bending capacity of a new reinforcement bar system beam.
This study examines the properties of fiber-reinforced reactive powder concrete (FR-RPC). Steel fibers, glass fibers, and steel-glass hybrid fibers were used to prepare the FR-RPC. The non-fibrous reactive powder concrete (NF-RPC) was prepared as a reference mix. The proportion of fibers by volume for all FR-RPC mixes was 1.5%. Steel fibers of 13 mm length and 0.2 mm diameter were used to prepare the steel fiber-reinforced RPC (SFR-RPC). Glass fibers of 13 mm length and 1.3 mm diameter were used to prepare the glass fiber-reinforced RPC (GFR-RPC). The hybrid fiber-reinforced RPC (HFR-RPC) was prepared by mixing 0.9% steel fibers and 0.6% glass fibers. Compressive strength, axial load-axial deformation behavior, modulus of elasticity, indirect tensile strength, and shear strength of the RPC mixes were investigated. The results showed that SFR-RPC achieved higher compressive strength, indirect tensile strength and shear strength than NF-RPC, GFR-RPC, and HFR-RPC. Although the compressive strengths of GFR-RPC and HFR-RPC were slightly lower than the compressive strength of NF-RPC, the shear strengths of GFR-RPC and HFR-RPC were higher than that of NF-RPC.
Using of rubber asphalt can both promote the recycling of waste tires and improve the performance of asphalt pavement. However, the segregation of rubber asphalt caused by the poor storage stability always appears during its application. Storage stability of asphalt and rubber is related to the compatibility and also influenced by rubber content. In this study, molecular models of different rubbers and chemical fractions of asphalt were built to perform the molecular dynamics simulation. The solubility parameter and binding energy between rubber and asphalt were obtained to evaluate the compatibility between rubber and asphalt as well as the influence of rubber content on compatibility. Results show that all three kinds of rubber are commendably compatible with asphalt, where the compatibility between asphalt and cis-polybutadiene rubber (BR) is the best, followed by styrene-butadiene rubber (SBR), and natural rubber (NR) is the worst. The optimum rubber contents for BR asphalt, SBR asphalt, and NR asphalt were determined as 15%, 15%, and 20%, respectively. In addition, the upper limits of rubber contents were found as between 25% and 30%, between 20% and 25%, and between 25% and 30%, respectively.