Beam Bending Test Research Articles

Investigation on the anti-aging properties enhancement mechanism of graphene on RA based on size effect

The application of rubber powder to modify asphalt has become one of the main ways of resourceful and harmless utilization of waste tire rubber. However, rubber powder is prone to degradation during service, and this deficiency limits its further development. To solve the problem of insufficient aging resistance of RA, multi-layer graphene with different sizes was adopted to modify it. The aging resistance of modified asphalt was evaluated by high-temperature dynamic shear test(DSR), low-temperature bending beam test (BBR), and Brookfield rotational viscosity test (RV), and the microscopic mechanism was investigated by Fourier infrared spectroscopy (FTIR) and Four-component analysis(SARA). Furthermore, the aging model of modified asphalt was established by combining the content of asphalt components and the number of oxidation functional groups using MD technology, to reveal the size effect and anti-aging mechanism of graphene from a molecular perspective. In the molecular simulation section, the radial distribution function (RDF), mean square displacement (MSD), glass transition temperature (TG), and viscosity of the model were compared and analyzed. Macroscopic tests showed that graphene could improve the rheological properties and viscosity of RA, and the graphene with a smaller size has a more obvious improvement of asphalt anti-aging properties. Comparing the carbonyl index and carboxyl index of the four components before and after asphalt aging, it can be found that, graphene mainly relies on the inhibition of the oxidation of saturated phenols to improve the aging resistance of asphalt. In further simulation analysis, the glass transition behavior and viscosity simulation of the asphalt model confirmed the above conclusion and further revealed that the modification mechanism of graphene is related to its size. The high surface of small-sized graphene adsorbs more light components and forms a "micelle core", which inhibits the tendency of resin, aromatic, and asphaltene rearrangement during aging. In addition, graphene increases the energy within asphalt molecules and decreases the energy between asphalt molecules, which leads to more active intermolecular motion and promotes uniform dispersion of asphalt micelles in the dispersion medium. This research can offer a theoretical guideline for optimizing the use of graphene in modified asphalt.

Theoretical analysis on the measurement accuracy of embedded strain sensor in asphalt pavement dynamic response monitoring based on FEM

Embedded strain sensors are the primary measurement device for strain in the tensile layer of asphalt pavement. The favorable deformation compatibility between embedded strain sensor and asphalt layer is the key to ensure the precise measurement of mechanical response. However, the good deformation coordination may be difficult to maintain under different environments due to the viscoelasticity of asphalt mixture. In this study, 4-point bending beam tests were performed to investigate deformation compatibility between embedded strain sensor and asphalt mixture under different temperature. Then, a quasi-static finite element model (FEM) was employed to simulate static mechanical response of asphalt pavement, and the design requirements for embedded strain sensor were proposed considering deformation coordination. In addition, the rationality of the design requirements of the sensor was further validated in the dynamic response monitoring. The results indicate that the deformation compatibility between embedded strain sensor and pavement material changes at different temperatures. In order to ensure favorable deformation compatibility, the reinforcement of the protective housing should be eliminated and the equivalent modulus (EM) of the sensitive element shall be the same as that of the asphalt mixture. Considering the viscoelasticity of asphalt mixture, the strain sensor with lower EM is recommended in the dynamic response monitoring of pavement structure. This study provides a basis for optimizing the embedded strain sensor of asphalt pavement from the perspective of deformation compatibility.

Study on Low-Temperature and Fatigue Performance of High RAP Content Hot Recycled Asphalt Mixture Based on the Degree of Blending (DOB).

This paper selected three kinds of AC-20 hot-mix recycled asphalt mixtures with high RAP content (30%, 40%, and 50%). It obtains a mixture of different degrees of miscibility by changing RAP preheating temperatures and mixing temperatures. The calculation formula of the degree of blending (DOB) of RAP asphalt interface recycling is proposed. The DSR test quantitatively characterized the DOB mixture's low temperature, and fatigue properties were tested by beam bending test and four-point bending fatigue test. The prediction models of the recycled mixture's low temperature and fatigue properties were proposed. The RAP preheating temperature is the most critical factor that dominates both transfers of RAP asphalt to the surface of new aggregate and the effective blending of old and new asphalt. DOB has a significant great influence on low-temperature performance and fatigue performance. The DOB of recycled asphalt can be improved by adjusting and optimizing the process parameters of plant hot recycled mixture to effectively improve the recycled mixture's low-temperature crack resistance and fatigue lifetime. The optimal RAP dosage and mixing process of required performance can be obtained based on the prediction models to save experimental time and cost.

Three-point bending of thin-walled arched beams with square sections

Arched structures can fully make use of the compression properties of structural materials and significantly improve their energy absorption performances under transverse loads. On the basis of this inspiration, the bending behaviors of a type of thin-walled arched beams (abbreviated as AB) with square section are studied. Static and dynamic three-point bending tests of thin-walled straight beams (SB) and AB are firstly performed. The deformation modes show that there are primarily three energy absorbing mechanisms during the bending of AB, including indentation, bending, and axial deformation, while SB is mainly subject to bending deformation. Both the crushing force efficiency (CFE) and the specific energy absorption (SEA) of AB are found to very much better than those of SB. Numerical simulations of the tests are then carried out by using the finite element code LS-DYNA, and the simulated force responses are in good agreement with the tests. The influence of critical influencing factors on the response of both AB and SB specimens are then analyzed numerically. The factors including the boundary conditions, material failure, impact velocity, geometric parameters and sectional shape. Results show that AB outperforms SB for cylinder or L-shapes supports, but it may be superior or inferior to SB for fixed boundaries with the variation of geometric and loading conditions. Arched and straight beams with square sections generally show much better energy absorption efficiency than those with circular sections. Finally, thickness enhancement of the arc segment is employed to further improve the crashworthiness of AB.

Fracture Mechanical Properties of Steel Fiber Reinforced Self-Compacting Concrete under Dry–Wet Cycle Sulfate Attack

Sulfate attack is the most common form of the durability damage of hydraulic concrete, and the performance degradation of cracked structural components is more significant at the position of water level change. Fly ash, a widely utilized supplementary cementitious material, can effectively improve the durability of concrete. In this paper, fly ash was used to partially replace Portland cement at 0 w%, 40 w%, 50 w%, 60 w%, and 70 w%, respectively. Through the three-point bending beam test with notch and the dry–wet cycle of sulfate attack, the change law of the fly ash content on the fracture mechanical properties of steel fiber reinforced self-compacting concrete (SFSCC) and its degradation mechanism under sulfate attack was studied. The results show that the load–crack mouth opening displacement curve of SFSCC changed from a steamed bread peak to a sharp peak under 30 dry–wet cycles of sulfate attack. The fracture toughness, peak load, and fracture energy of SFSCC with a high-volume fly ash increased with the increase in the fly ash content, while they reversed after sulfate attack. When the percentage of fly ash was 70 w%, the retention ratio of the fracture parameters was lower than that of SFSCC without incorporating fly ash, and when the percentage of fly ash was 50 w%, SFSCC had good bearing capacity, fracture mechanical properties, and corrosion resistance. The corrosion product of the reference SFSCC with 30 dry–wet cycles of sulfate attack was ettringite, whereas the SFSCC with a high-volume fly ash had no obvious corrosion products and the microstructure became looser.

Assessment of interfacial fracture of asphalt mortar-aggregate system at low temperature: A study based on four-point bending test of sandwich beams

• Focus on the bonding region of asphalt mortar-aggregate system at low temperature. • Four-point bending test with mortar-aggregate-mortar sandwich beam is executed. • Failure mode of asphalt mortar-aggregate system is changed with temperatures. • Effects of material types, aging level and aggregate roughness are considered. The bonding properties of the asphalt mortar-aggregate interface at low-temperatures are investigated in this study. A novel method based on mortar-aggregate-mortar sandwich beam and four-point bending test is established. The effects of temperature, loading speed, material type, asphalt aging level and aggregate surface roughness on the bonding properties of the mortar-aggregate interface are methodically examined. Three cracking indexes, including peak bending stress, fracture energy and interface stiffness, are considered for the evaluation. It is concluded that the proposed testing method can effectively distinguish the low-temperature bonding performance of the asphalt mortar-aggregate system under different conditions. The obtained results reveal that the fracture energy can be increased by 700 % with the failure mode changing from brittle failure (−6 °C) to ductile failure (0 °C), and the positive correlation between loading speed and asphalt-mortar system fracture resistance at low temperature is verified. Additionally, the bonding properties are apparently affected by the type of asphalt and aggregate, aging level of the specimen, and aggregate surface roughness. Specimens composed of the styrene butadiene styrene (SBS) modified asphalt and basalt have the best bonding properties. The moderate aging of the specimen or increasing surface roughness of the aggregates has a positive incorporation into the bonding properties of the asphalt mortar-aggregate system, but severe aging or over-dense grooving act adversely.

Evaluation of fracture performance of Polyvinyl Alcohol fiber reinforced hot mix asphalt

• Fracture performance of reinforced HMA was significantly affected by Gradation type, binder grade, and PVA fiber dosage. • Coarse graded reinforced HMA exhibited 25% higher strength than fine graded HMA at 0.3% fiber content. • FE and FI doubled for lower grade asphalt reinforced HMA than control. • Coarse graded HMA showed higher fracture growth rate. • SEM and DIC analyses revealed effective crack bridging and enhanced strain distribution due to fiber reinforcement. Several studies have been conducted over the past two decades to evaluate the fracture and fatigue performance of hot mix asphalt (HMA) reinforced with different fiber types, dosages, and aspect ratio. However, a few studies focused on the impact of aggregate gradation and binder grades on the fracture performance of fiber reinforced mixtures. This study adopted a systematic approach to evaluate the impact of three different coarse and fine aggregate gradations with different nominal maximum sizes using three different binder grades and varying Polyvinyl Alcohol (PVA) fiber content. Semicircular bending beam (SCB) test was performed to evaluate several fracture characteristics of PVA fiber reinforced HMA. Experimental results revealed that binder grades and gradation significantly affect the fracture performance of such mixtures. Total fracture energy, flexibility index, and stiffness of 0.3% PVA reinforced PG 58-22 mixtures were doubled relative to control ones. However, fiber reinforced PG76-22 mixtures exhibited up to 50% improvements. The fracture growth rate reduced by 250% at 0.3% fiber content in coarse graded mixture while cumulative energy per unit crack length increased by 190% in fine graded mixture. Digital Imaging Correlation analyses revealed more twisted and convoluted fracture path and higher strain distribution in lower grade asphalt reinforced mixtures with lower nominal maximum size gradation. Scanning electron microscopy micrographs showed proper fiber coating of asphalt and effective fiber bridging across the cracks indicating enhanced resistance to post-peak deformation under load.

Flexural behaviour of cold-formed steel square and rectangular hollow sections with moderate heat-treatment

This paper discusses the flexural behaviour of cold-formed square and rectangular hollow steel sections (SHSs and RHSs) with subsequent heat-treatment through experimental and numerical investigations. Firstly, an experimental programme comprising tensile coupon tests on flat and corner regions and three-point bending beam tests were conducted. A total of 12 specimens were tested under monotonic bending loads, covering a variety of section slenderness. Failure modes, moment-rotation curves and plastic hinge lengths have been evaluated highlighting the effect of the web-flange interaction on rotation capacity. Successively, experimental results were combined with numerical FE results to assess the corresponding moment and deformation capacities. Current cross-section classification limits given in Eurocode 3 and AISC 360–16 were assessed and new limits has been proposed.

A Design Method of Styreneic Methyl Copolymers Normal Temperature Modified Asphalt Mixture Based on Performance Balance.

The objective of this research was to develop a solution for the deterioration effect on the high-temperature rutting performance and water stability of SMC. This research proposed a method for designing an SMC normal temperature modified asphalt mixture based on the existing findings, experimental research and the performance balance. First, the power function curve model of the aggregate gradation was put forward. The 0.075 mm, 4.75 mm and nominal maximum particle size were the key points of the aggregate gradation, and their passing rate was about 6%, 30%, and 95% respectively. Then, on the basis of the quadratic curve model, a method for determination of the optimum asphalt aggregate ratio of SMC normal temperature modified asphalt mixture was put forward, considering the skeleton-density structure. Last, rutting tests, small beam bending tests, freeze-thaw split tests, permeability coefficient tests, texture depth tests and pavement roughness tests were conducted, and the test results all met the performance requirements of the specifications for the construction of highway asphalt pavement in China perfectly, especially the high-temperature and water stability properties, which indicated that the design method for SMC normal temperature modified asphalt mixtures based on performance balance presented in this paper was reasonable and practical.

Evaluation of the Low-Temperature Cracking Performance of Recycled Asphalt Mixture: A Development of Equivalent Fracture Temperature

This study aims to develop a new index to evaluate the low-temperature cracking performance (LTCP) of recycled asphalt mixtures. To achieve this, the assumption that fracture energy has limitation in evaluating the LTCP of mixtures was put forward firstly. To reveal this limitation theoretically, a concept of energy absorption rate that characterized the fracture energy of the mixtures was then given. Thirdly, an equivalent fracture temperature (EFT) corresponding to the critical cracking temperature in a thermal stress restrained specimen test (TSRST) was proposed to evaluate the LTCP of mixtures based on a three-point bending beam (3PBB) test. Finally, some data derived from previous work were collected to verify the proposed assumption, and the 3PBB test and TSRST were conducted to investigate the LTCP of five recycled mixtures with different reclaimed asphalt pavement (RAP) material contents and to verify the rationality of the proposed EFT. The results confirmed that fracture energy had some limitations in predicting the LTCP of mixtures. The EFT was as accurate as the critical cracking temperature in evaluating the LTCP of mixtures. Compared to fracture energy and critical cracking temperature, EFT had bigger absolute change and relative change between different mixtures, meaning it was better to differentiate the LTCP of mixtures. Compared to failure strain, EFT was also more definite and less variable when processed by different data analysts, meaning it was more objective.

Investigation of Long-Term Performance and Deicing Longevity Prediction of Self-Ice-Melting Asphalt Pavement.

Based on laboratory tests, the objective of this study is to assess long-term road performance and to predict deicing longevity of self-ice-melting asphalt pavements containing salt-storage materials. Dry–wet cycles and freeze–thaw cycles were used to treat the specimens at different durations. The long-term road performance of self-ice-melting asphalt mixtures was evaluated by freeze–thaw splitting tests, high-temperature rutting tests, and low-temperature beam bending tests. In addition, the influences of coefficients of void ratio, temperature, vehicle load, crack, and Mafilon (MFL) content on salt precipitation were quantified by conductivity tests, and single consumption of snow and ice melt was quantified by total dissolved solids (TDS) tests. The results show that the long-term water stability, long-term high-temperature stability, and long-term low-temperature crack resistance of self-ice-melting asphalt pavements tended to decrease as the number of dry–wet cycles and freeze–thaw cycles increased. Freeze–thaw cycles exerted deeper influences on the deterioration of road performance than dry–wet cycles, especially on water stability. With increased void ratio and temperature, salt precipitation was accelerated by 1.1 times and 1.5~1.8 times, respectively. Under vehicle loads and cracks, salt precipitation was accelerated by 1.5 times and 1.65 times, respectively. With decreased MFL content, salt precipitation slowed down by 0.54 times. Finally, based on the proportion of each factor relative to the whole life cycle of the pavement, a dicing longevity prediction model was established considering the above factors.

A damage model based on Tsai–Wu criterion and size effect investigation of pultruded GFRP

This paper presented a progressive damage model of pultruded GFRP based on the Tsai–Wu criterion. The constitution of the damage model was coded by UMAT subroutine in Abaqus. The model shows sufficient accuracy in validating against the tensile and three-point beam bending tests. It was used to obtain the size effect law of pultruded GFRP with varying sizes and fiber volume ratios. The resistance curve was then calculated by using the obtained size effect law, and the effect of composite’s material property on R-curve was discussed. The fracture toughness obtained by size effect law is within the range of typical pultruded GFRP material property, and the fiber volume’s effect on R-curve is also explored. It’s found that the fracture toughness increases from 53.68KJ/m2 to 76.18KJ/m2 as the fiber volume ratio ascends from 50% to 70%.

Seamless coupling of bond- and state-based peridynamic and finite element analyses

This study presents a variational approach to couple PeriDynamic (PD) and Finite Element (FE) analyses to take advantage of their salient features. The PD and FE domains share the same nodes along their interface without an overlap region and any constraint conditions. Therefore, this approach does not require a morphing or a blending function that facilitates coupling over a transition zone. Although this approach is general and not limited to any commercial FE software, the PD interactions for bond-based (BB), ordinary state-based (OSB) and non-ordinary state-based (NOSB) are modeled with MATRIX27 elements native to ANSYS, a commercial software, for the purpose of demonstration. It is a general framework to perform BB, OSB and NOSB PD coupled with traditional elements. It provides the ability to practicing engineers in industry for integrating PD into their FE based design tools. The PD domains can share a boundary with FE domains or be completely embedded in the FE domain. The resulting global system of equations includes the contributions arising from the PD nodes and FE nodes. These equations are solved simultaneously without requiring an iterative procedure through implicit methods. Therefore, it is a direct (seamless) coupling approach without an overlap zone. The results are free of displacement kinks; thus, unphysical stress concentrations do not appear near the interface between the PD and FE regions. Its accuracy is demonstrated by considering isotropic elastic plates subjected to various types of boundary conditions under quasi-static and dynamic loading conditions. Also, its accuracy is demonstrated for quasi-static crack propagation by considering double cantilever beam and three-point bend test specimens. The results from the coupled PD-FE approach agree well with those of FEM for all boundary and loading conditions.

Evaluating fatigue and crack resistance of asphalt mixture containing zinc tailing aggregates

Roads as one of the most important components of the transportation system involve a large quantity of construction aggregate. Limitation in natural-aggregates sources makes it necessary to use alternative materials as a substitute to natural-aggregates. To achieve this goal, the by-products tailings of zinc soil separation and concentration process named zinc tailings were used as an aggregate in asphalt mixture. In this research study, the fatigue, low-temperature, and moisture susceptibility performance of fabricated asphalt mixtures using limestone, siliceous and tailing aggregates were investigated. For this purpose, the four-point bending beam (4PB),semi-circular bending (SCB), and indirect tensile strength (ITS)tests were employed. Findings from 4PB tests indicate that asphalt mixture containing zinc tailings as aggregates have longer fatigue life than the mixture fabricated with limestone aggregates at the strain level of 600 microstrain. However, caution needs to be exercised at higher strain levels. Based on SCB test results, the fracture energy values for mixture with tailing aggregates were almost constant at temperatures of − 6, − 10, and − 12 °C while the results show fracture energy reduction for other mixtures at a lower temperature. Moreover, the cracking resistance index (CRI) indicates that the tailing aggregates fabricated mixture has acceptable low-temperature performance. Finally, the TSR values show that mixture containing zinc tailing aggregates are more resistant to moisture damage compared with siliceous fabricated mixture.

Low Temperature Crack Resistance of Stone Mastic Asphalt Affected by Its Nominal Maximum Size and Asphalt Binders

To study the effect of nominal maximum particle size (NMS) of stone mastic asphalt (SMA) gradation and a mixed modified asphalt binder on the low temperature crack resistance of SMA, SMA asphalt mixtures with three different NMS, two styrene-butadiene-styrene (SBS) and crumb rubber modifier (CRM) hybrid-modified asphalt binders were designed.Thermal strength restrained specimen test (TSRST) and bending beam test (BBT) were performed on the mixtures. The freezing-fracture temperature and strength from TSRST, bending tensile strain and stiffness from BBT at low temperature were evaluated. Finally, an intrinsic relationship was established between these properties obtained from the two tests. The results showed that the following: (1) the SMA-5, the best of all the three NMS, has a freezing-fracture temperature of −31.5 °C, which is 18.9% and 48.6% lower than those of SMA-10 and SMA-13, respectively, while its freezing fracture strength is 6.15 MPa, which is 95.2% and 243.6% higher than those of SMA-10 and SMA-13, respectively; (2) the bending failure strain of SMA-5 is 4649 με, which is higher than those of SMA-10 and SMA-13 by 11.3% and 21.9%, respectively; (3) increased CRM dose in the SBS-modified SMA improves the crack resistance at low temperature; (4) the bending failure strain of the SMA has the best correlation with the freezing-fracture temperature, with a correlation coefficient of about 0.8.

Effect of Hot Mixing Duration on Blending, Performance, and Environmental Impact of Central Plant Recycled Asphalt Mixture

When using a high concentration of reclaimed asphalt pavement (RAP) in a recycled hot-mix asphalt mixture (RHMA), the degree of blending of the reclaimed asphalt binder significantly affects the performance of the RHMA. Hence, it is essential to know the degree of blending of the RAP and its effect on the performance and the environmental impact of RHMA in order to determine the optimal mixing duration. To this end, the dispersion of reclaimed asphalt was observed using artificial RAP and the image analysis method, and the blending of reclaimed asphalt in RHMA with different mixing durations was also evaluated using physical properties tests, a rheometer test, a Fourier-transform infrared spectroscopy (FTIR) test, a gel permeation chromatography (GPC) test, and an atomic force microscope (AFM) test. The performance of RHMA with the different mixing durations in the plant and in the laboratory was tested using a Marshall stability test, rutting resistance test, freeze–thaw splitting test, and low-temperature bending beam test. In addition, the environmental impact of RHMA at different mixing durations was evaluated, and the optimal mixing duration was determined. The results showed that the mixing duration had a significant influence on the dispersion and blending of reclaimed asphalt in RHMA. The longer the mixing duration was, the higher the dispersion and the degree of blending of the reclaimed asphalt in the RHMA were. With the increase in the mixing duration, the properties, chemical composition, and micromorphology of the blended asphalt binder tended to become similar to those of reclaimed asphalt. The performance of RHMA was improved with the increase in mixing duration; however, the energy consumption and CO2 emissions for the RHMA increase significantly with the increase in mixing time. The recommended optimal mixing durations in the mixing plant and in the laboratory were found to be 60 s and 90 s, respectively, considering the environmental impact, the RHMA production efficiency, and the performance of the RHMA.

A Damage Model of Concrete including Hysteretic Effect under Cyclic Loading.

A novel damage model for concrete has been developed, which can reflect the complex hysteresis phenomena of concrete under cyclic loading, as well as other nonlinear behaviors such as stress softening, stiffness degradation, and irreversible deformation. The model cleverly transforms the complex multiaxial stress state into a uniaxial state by equivalent strain, with few computational parameters and simple mathematical expression. The uniaxial tensile and compressive stress–strain curves matching the actual characteristics are used to accommodate the high asymmetry of concrete in tension and compression, respectively. Meanwhile, an unloading path and a reloading path that can reflect the hysteresis effect under cyclic loading of concrete are established, in which the adopted expressions for the loading and unloading characteristic points do not depend on the shape of the curve. The proposed model has a concise form that can be easily implemented and also shows strong generality and flexibility. Finally, the reliability and correctness of the model are verified by comparing the numerical results with the three-point bending beam test, cyclic loading test, and a seismic damage simulation of the Koyna gravity dam.

An Active Anti-Aging Technology for Asphalt Mixture

For aged asphalt, as the content of light component gets smaller with the passing of time, the performance of the asphalt mixture would degrade accordingly. This study aims to develop an anti-aging material that can supplement light component to asphalt pavement during its service process, thereby suppressing the aging of asphalt and prolong the service life of the road surface. At first, this study carried out four-component separation test to measure the loss mass of light component; then in the experiment, the oil shale wastes were impregnated in light component to determine its adsorption capacity to the light component. After that, according to the loss of asphalt light component after long-term aging and the adsorption ratio of anti-aging materials with different particle sizes for light component, the amount of anti-aging material to be added was determined; moreover, via rutting test, beam bending test, and freeze-thaw splitting test, the high-temperature stability, low-temperature crack resistance, and water stability of the asphalt mixture modified by the proposed anti-aging material had been verified, and the results proved that the proposed anti-aging material can well suppress the aging of asphalt mixture.

Effect of Rest Period and Temperature on the Estimation of Fatigue Life of Bituminous Mixture

This paper reports the experimental investigation conducted to study the influence of temperature and rest period on different methods of estimation of fatigue life of the bituminous mixture. Four-point beam bending tests were conducted on the bituminous mixture prepared with one unmodified binder and two different modified binders (crumb rubber modified and elastomer modified binder). The test was conducted at 20 °C and 0 °C using continuous loading and a rest period between two load cycles. The fatigue life was estimated using stiffness modulus and energy dissipation. The performance of three different bituminous mixtures was ranked—ranking a bituminous mixture based on the fatigue performance varied with temperature and loading condition. In addition, the ranking also varied with different post-processing methods adopted.

Phase-field modeling of fracture in high performance concrete during low-cycle fatigue: Numerical calibration and experimental validation

The development of an elasto-plastic phase-field model is presented which is able to predict nonlinear behavior of high performance concrete (HPC) during low-cycle fatigue. An elasto-plastic damage model which follows the Drucker–Prager yield criterion is formulated. For the modeling of unsymmetric tension–compression behavior of HPC two different continuous stepwise linearly approximated degradation functions for HPC in tension and in compression are used. The experimental three-point bending tests at low-cycle using notched beams of pure HPC are performed. Load–CMOD (crack mouth opening displacement) curves are plotted using the measured experimental data and residual stiffness–CMOD curves are calculated using these experimental Load–CMOD curves. The data used for the interpolation of degradation functions are calibrated using the experimental results for three-point bending tests. For that purpose the uniaxial tension and uniaxial compression tests and three-point bending beam test for HPC are simulated numerically. The accuracy of the proposed numerical model using the presented integration algorithm is verified by comparing the degradation of stiffness in numerical and experimental results.