Tensile Strain Capacity Research Articles

Hydration mechanism and mechanical properties of a developed low-carbon and lightweight strain-hardening cementitious composites

Strain-hardening cementitious composites (SHCC) have been widely studied due to their high toughness and durability. The high cement content increases a huge burden on the cost and CO2 emissions of SHCC. To reduce the environmental impacts of SHCC, this study first develops low-carbon and lightweight SHCC by using high-volume recycled concrete powder (RCP) as supplementary cementitious materials and cenosphere waste as lightweight aggregate. The influence of RCP content (0%, 15%, 30%, and 45% by mass) on the hydration mechanism, mechanical properties, and sustainability of low-carbon and lightweight SHCC was investigated. The results showed that the incorporation of RCP in the SHCC matrix resulted in a decrease in hydration heat with increasing RCP content. The filling and pozzolanic effects of RCP were significantly lower than those of cement. The increased porosity and the presence of the interface transition zone due to RCP incorporation led to reduced compactness of the SHCC, which consequently led to decreased compressive strength and fracture toughness of the cement matrix. While the fracture toughness of the cement matrix was reduced, the SHCC still exhibited remarkable bending toughness and tensile ductility. The developed low-carbon and lightweight SHCC containing 45% RCP showed a density of 1482.5 kg/m3, a tensile strength of 3.94 MPa, and a tensile strain capacity of 6.80%, which successfully pushed the performance of low-carbon and lightweight SHCC. The replacement of cement with high-volume RCP in the low-carbon and lightweight SHCC resulted in a significant reduction in embodied carbon compared to conventional SHCC. Therefore, SHCC combines the advantages of lightweight, low-carbon, and highly ductile, making it a promising material for widespread utilization in concrete structures.

Comparison of tensile strain capacity models of oil and gas pipelines

In the field of strain-based pipeline design, the widely used pipeline tensile strain capacity models mainly include CSA Z662, PRCI-CRES, and EXXON MOBIL. In this paper, the methods for calculating the ultimate tensile strain, toughness, and other key parameters of various models are emphatically introduced, and their applicable ranges are compared. Ninety-six sets of full-scale test and curved wide plate test data are collected in this paper. The prediction accuracy of various tensile strain capacity models under different steel grades is compared and verified by the test results. The CSA Z662 model has few parameters to consider, the TSC prediction value is relatively low, and EXXON MOBIL has more nonconservative situations when the strain is less than 4%. The PRCI-CRES model has the highest prediction accuracy.

Experimental Study on the Mutual Influence of Fly Ash, Silica Fume & Fibers on Strength Enhancement of Portland Cement

Abstract: Mineral additives have a wide range of applications today because of their benefits such as waste evaluation for ecological balance and improving the physical and mechanical qualities of cement or concrete. Fly ash and silica fume are two of the wastes. These raw materials were subjected to physical, chemical, mineralogical, and molecular analysis for this purpose. Engineered cementitious composites (ECC) with excellent tensile strain capacity and repeated cracking often contain fly ash (FA) as a key component. Silica fume can either be "added" (added individually at the concrete mixer) or mixed with a composite cement that is manufactured in a factory. This essay examines the advantages and usefulness of using fly ash and silica fume. Silica fume can typically be used with chemical admixtures, and it is typically used with a super-plasticizer, just like with conventional concretes. Tests should be conducted to determine the right dose levels as the performance of admixtures may depend on the unique characteristics of the source of the cementation's material (as with OPC cement). Supplementary cementing materials (SCMs) are utilized in concrete to partially replace the Portland cement component and exhibit pozzolanic and/or cementitious qualities. High-performance concrete contains an essential component called supplemental cementing material. In particular, when great strength and durability turn out to be the most desired attributes of high-performance concrete, the insertion of supplemental cementing material is crucial. Several well-known supplemental cementing materials, including fly ash, silica fume, and powdered granulated blast-furnace slag, are presented in this work. The impact of using steel fibers, fly ash, silica fume, and various combinations of them are evaluated in this paper. This study aims to ascertain how fly ash, silica fume, and fibers interact with Portland cement to increase concrete strength, reduce internal cracks, and increase tensile strength.

Feasibility study of engineered geopolymer composites based high-calcium fly ash and micromechanics analysis

Engineered geopolymer composites (EGC) have attracted much attention as green construction materials, characterized by strain-hardening behavior and multiple cracking capabilities. Nevertheless, the current utilization of low-calcium fly ash in EGC preparation poses a challenge in terms of long hardening time, which substantially affects the feasibility of applying EGC in engineering projects. The purpose of this study is to assess the potential for developing EGCs using high-calcium fly ash (HFA), explore the impact of sodium silicate (SS)-to-sodium hydroxide (SH) ratio on material properties, and perform a comparative analysis between EGCs fabricated with low-calcium fly ash (LFA) and HFA. SEM analysis elucidates that an increase in the SS-to-SH ratio exerts a favorable influence on matrix density, thereby augmenting overall strength. Nevertheless, this enhancement is accompanied by a notable reduction in tensile strain capacity. It was observed that EGC based on HFA (HFA-EGC) outperforms LFA-based EGC (LFA-EGC) in various aspects of mechanical properties. The effects of SS-to-SH ratio, LFA, and HFA on the mechanical properties were analyzed at the microscale using XRD and SEM, and combined with micromechanical parameters, establishing a multi-scale connection for material performance. The study offers a comprehensive analysis of how varying precursor and activator compositions affect the tensile properties.

Micromechanical and mineralogy analyses on extremely ductile engineered geopolymer composites with different activator pretreatments

In this study, the effects of activator pretreatments on properties of fly ash-based extremely ductile engineered geopolymer composites (ED-EGCs) were investigated. Two ED-EGC mixtures were designed using the same binder system and polyethylene fiber reinforcement, but different pretreated activators. A sequence of experiments including mechanical testing, micromechanical analysis, and chemical characterization was performed. The test results indicate that ED-EGCs were lightweight with density values lower than 1.7 g/cm3, had moderate compressive strengths over 21 MPa, and exhibited extremely ductile behavior with tensile strain capacities over 11 %. Overall, the warming pretreatment was beneficial to improve strengths but less effective to enhance tensile ductility of ED-EGCs. In contrast, the ED-EGC mixture adopting the cooling pretreatment showed tensile strain capacity up to 18.6 %, which has been unprecedented in the literature. The micromechanical analysis explained the extremely ductile behavior of ED-EGCs. SEM observation also confirmed that the fibers were robustly embedded into the geopolymer matrix. Through chemical analysis using EDS, it was found that N-A-S-H gel was the dominant geopolymeric product of ED-EGCs.

Using special coarse aggregate to enhance the tensile strain capacity of engineered cementitious composites

This study introduced fly ash cold-bonded coarse aggregate (CA) to produce a special kind of engineered cementitious composites (CA-ECC). Four mixtures of ECC with different particle sizes of coarse aggregate were fabricated at a constant water-to-binder ratio. Experimental and analytical studies including mechanical behaviors, micro-mechanical analysis, microstructure analysis, and chemical characterization of CA-ECC were conducted from macro-, meso-, and micro-scales. The results showed that CA-ECC can achieve the characteristic of strain-hardening with high ductility. Remarkably, ECC with aggregate size ranging from 5 to 8 mm achieved tensile strain capacity up to 11 %. The mechanism of over-saturated cracking and high ductility behaviors were explained by pseudo-strain-hardening index and microstructure analysis. By calculating the materials sustainability index (MSI) of all mixtures, the CA-ECC was proven to possess environmental advantages over conventional ECC. The present study extends the fundamental knowledge for developing ECC materials.

Novel Prediction Model of Tensile Strain Capacity for Pipelines with Corrosion Defects

Novel Prediction Model of Tensile Strain Capacity for Pipelines with Corrosion Defects

Enhancement of in-plane shear performance in masonry walls strengthened with high-performance fiber-reinforced cementitious composites

This study aims to design a high-performance fiber-reinforced cementitious composite (HPFRCC) material for reinforcing masonry walls and assess its impact on in-plane shear performance. Different specimens were compared, including an unreinforced one, a conventional mortar-reinforced one, and HPFRCC-reinforced specimens of varying thicknesses ranging from 10 mm to 20 mm. Aspects such as failure modes, shear stress–strain curves, pseudo-ductility, and energy dissipation were evaluated. Test results indicated that the unreinforced and mortar-reinforced masonry walls demonstrated brittle failure with wide cracks on both sides, whereas HPFRCC-reinforced walls exhibited ductile failure with controlled crack propagation owing to the excellent mechanical properties of HPFRCC, such as an average tensile strength of 7.32 MPa and a tensile strain capacity of 4.60 %. The HPFRCC significantly enhanced the shear strength and modulus of the masonry walls. The wall reinforced with 20 mm-thick HPFRCC showed a remarkable 26-fold increase in the energy dissipation capacity compared to the unreinforced one, and the 10-mm-thick and 15 mm-thick strengthening demonstrated 4.0- and 5.7-times improvement, respectively. The ideal HPFRCC overlay thickness was found to be between 15 mm and 20 mm. Beyond this thickness, gravitational flow and stiffness asymmetry negatively impacted shear performance.

Enhanced tensile performance of ultra-high-performance alkali-activated concrete using surface roughened steel fibers

To improve the mechanical performance of ultra-high-performance alkali-activated concrete (UHP-AAC), the surface of steel fiber was modified using an electrolyte solution containing ethylenediaminetetraacetic acid (EDTA). The longer the steel fiber was exposed to the EDTA-electrolyte solution, the more the longitudinal peeling of the steel fiber surface was induced and the surface roughness increased. By exposing the specimens to the solution for up to 6 h, the highest fiber bond strength (11.96 MPa) and a maximum tensile strength of UHP-AAC (14.7 MPa) were obtained. The mechanical properties of UHP-AAC were also investigated using conventional long straight and twisted steel fibers. The increase in bond strength due to the triangular cross-sectional shape and untwisting torque of the twisted fiber had an overall positive effect on the mechanical properties of UHP-AAC. However, the best tensile performance of UHP-AAC, in terms of tensile strength and energy absorption capacity, was obtained when the straight steel fibers surface-refined by the EDTA-electrolyte solution for 6 h were adopted. Based on the Pearson correlation coefficient, the Weibull distribution was applied as a crack width prediction model. The results showed that the median microcrack widths formed in UHP-AAC were marginally influenced by the surface treatment using EDTA-electrolyte solution. However, the longer straight and twisted steel fibers produced wider microcracks than their counterparts. The greatly increased tensile strain capacity of UHP-AAC by using the surface-refined steel fibers was thus caused by the formation of more microcracks rather than the increase in the microcrack width.

Mechanical property, volume stability and microstructure of lightweight engineered cementitious composites (LECC) containing high-volume diatomite

Due to the requirement of sustainable development, the number of coal-fired power plants has gradually decreased, resulting in insufficient supply of traditional supplementary cementitious materials (SCMs). In this study, diatomite is proposed to replace fly ash in the lightweight engineered cementitious composites (LECC), and mechanical properties, shrinkage deformation and microstructure of diatomite-modified LECC (D-LECC) are investigated. The results show that the incorporation of diatomite reduces compressive strength, tensile strength and tensile strain capacity of LECC because of reduction of hydration degree and increase of porosity. Meanwhile, incorporating extra water (EW) into diatomite further increases the amount of hydration products and compactness of D-LECC, so the D-LECC with EW has higher compressive strength, tensile strength and less tensile strain capacity in comparison without EW. Besides, compared to reference specimen, autogenous shrinkage of D-LECC increases due to the reduction of mixing water. As the EW is absorbed in diatomite, the autogenous shrinkage of D-LECC reduces because of the internal curing effect of EW. The 14-d autogenous shrinkage of F50E is 1151 μm/m, which reduces by 68.3 % of the autogenous shrinkage of F50. In the microstructure, incorporating diatomite decreases hydration degree and increases the porosity of sample. Meanwhile, incorporating EW into diatomite improves hydration degree and refines pore structure of D-LECC sample. Therefore, it is found that diatomite absorbing EW has a great potential to be incorporated into the LECC for solving the shortage reserves of traditional SCM.

Dynamic compressive behavior of polyethylene fiber reinforced high strength and high ductility concrete over wide ranges of strain rate

High strength and high ductility concrete (HSHDC) possesses extraordinary mechanical properties, including high compressive strength (123.3 MPa), high tensile strength (9.1 MPa), and ideal tensile strain capacity (6.6%), and exhibits promising application prospects in structures against dynamic loadings. This study systematically explored the dynamic compressive behavior of Polyethylene (PE) fiber reinforced HSHDC over wide ranges of strain rates (10−5–102 s−1) using the hydraulic servo-controlled testing machine and split Hopkinson pressure bar device. The dynamic stress-strain relations and failure patterns of HSHDC were obtained, based on which the dynamic compressive strength, peak compressive strain, and specific energy absorption (SEA) were analyzed in detail. It indicated that the compressive strength increased moderately at low strain rates (2.4 × 10−5–2.4 × 10−2 s−1) and obviously at high strain rates (105.8–258.8 s−1) with the increase of strain rate. To describe the dynamic compressive strength, several dynamic increase factor (DIF) formulae in the literature were evaluated, and an experimentally fitted DIF formula was proposed. The peak compressive strain remained almost constant at low strain rates, while it decreased significantly with the increase of strain rate at high strain rates. Besides, the dynamic SEA shows a bilinear growth law with the increasing strain rate and has a more obvious strain rate effect than the dynamic compressive strength. Finally, a nonlinear viscoelastic constitutive model was established, which satisfactorily predicts the compressive stress-strain relationship of HSHDC at different strain rates.

Development of a glass microbubble-based lightweight strain hardening cementitious composite (LW-SHCC): Experiment and numerical simulation

In this study, lightweight strain hardening cementitious composites (LW-SHCC) was developed through mix proportion design and experimental tests. The modified Andreasen and Andersen (A&A) model was applied for dry materials mixture proportioning and micromechanics for the fiber-reinforced composites were applied for designing the materials achieving multiple cracking and strain hardening characteristics. Four types of 3M™ glass microbubbles were considered as lightweight aggregates to achieve the lightweight of the composites. The designed SHCC mixes were tested in the lad, including tensile test and compressive test, to optimize the mixture design of the SHCC. Results showed the developed LW-SHCC exhibited tensile strain capacities of 3.05–4.07 % at the densities of 1.20–1.44 g/cm3. A numerical simulation was conducted to predict the tensile behavior of LW-SHCC based on the micromechanics model, which can simulate the initial and peak values of stress and strain of SHCC materials. Simulation results indicated that the tensile response could be reasonably predicted using the proposed numerical model and glass microbubbles acting as artificial flaws were an ideal material to develop the tensile strain hardening and multiple cracking behavior of the composites.

Design-oriented stress-strain model for FRP-confined engineered cementitious composites

Engineered cementitious composites (ECC) is known for its enhanced tensile performance compared with normal concrete. Ductile strain hardening behavior, multiple cracking beahvior as well as large tensile strain capacity can be achieved for ECC under tensile loadings. For the compressive performance, using lateral fiber-reinforced polymer (FRP) confinement is an effective approach to improve the compressive strength and strain. However, the research work on design models of FRP-confined ECC, especially on the stress-strain relationship, is limited at the current stage. To address this aspect, this study focuses on developing the design-oriented stress-strain model for FRP-confined ECC under axial compression. A test database on FRP-confined ECC was firstly assembled. Existing design equations on FRP-confined concrete were evaluated and found not be able to provide satisfactory predictions for FRP-confined ECC. New design equations on ultimate conditions, including the ultimate compressive strength and ultimate axial strain, were then proposed and verified with the test results. Finally, the design-oriented stress-strain model for FRP-confined ECC was developed, which consists of the formulated form of a stress-strain model for FRP-confined normal concrete and the new design equations on ultimate conditions proposed for FRP-confined ECC. Predictions of stress-strain curve show close agreements with test results, indicating the good performance of the developed design-oriented stress-strain model.

Pore structure characteristics and mechanical property of engineered cementitious composites (ECC) incorporating recycled sand

The mechanical properties of recycled sand (RS) modified ECC are intimately linked to its pore structure characteristics, but the internal pore size and distribution of RS modified ECC and its impact mechanism on the mechanical properties are still unclear. This study employed mercury intrusion porosimetry (MIP) and low field nuclear magnetic resonance (LF-NMR) techniques to analyze the pore structure of ECC incorporating RS. Furthermore, compression and tension mechanical experiments were conducted to investigate the correlation between the evolution of pore structure and mechanical properties of ECC incorporating RS. The findings demonstrate that the addition of RS increases the porosity of ECC. When replacement ratio of RS is 100 %, the volume fraction of pores decreases within the range of 10 nm to 100 nm, whereas it exhibits an increasing trend within a ranging from 100 nm to 1 μm. The incorporation of RS results in a decrease of the volume fraction of gel pores and the increase of capillary pores in ECC owing to its high-water absorption and porous, as well as the reduction of calcium-silicate-hydrate (C-S-H) due to the surface attached old mortar. Therefore, addition of RS lead to a reduction in both the compressive strength and tensile strength of ECC. However, as a result of the pore structural flaw inherent in the recycled fine aggregate, the occurrence of multi-crack cracking, induced by interfacial imperfections between the recycled fine aggregate and matrix, contributing to development of cracks in ECC and thus enhancing its tensile strain capacity.

Numerical model of tensile behavior of textile reinforced concrete (TRC) based on stress field analysis

Textile reinforced concretes (TRCs) are cementitious composites featuring excellent tensile strength and strain capacity. While previous studies have discussed the relationship between TRC tensile performance and textile/matrix interaction, the detailed mechanism has yet to be comprehensively investigated. In this study, a numerical model to simulate the overall stress–strain relation of TRC is developed. The model takes into account interfacial friction, chemical bond, and weft yarns’ anchorage effect to derive the stress transferred from textiles to matrix at various distances from a crack. Additionally, non-uniform matrix strength from X-ray CT-derived flaw structure is compared with the matrix stress field to determine new crack locations, while inconsistent yarn strength is incorporated for textile fracture description. The model provides a prediction tool for TRC’s mechanical behavior, and the stress–strain relation aligns with experimental results. Overall, the findings from this model can facilitate the design of TRCs with high performance for various applications.

Improving the material sustainability of strain-hardening magnesium-silicate-hydrate composite by incorporating aggregates

The existing strain-hardening magnesium-silicate-hydrate composites (SHMSHCs) utilize a magnesium-silicate-hydrate (MSH) paste-based cementitious matrix, using significant binder content, thus prone to higher embodied energy and carbon footprint. In this study, authors have explored the feasibility of incorporating aggregates without compromising the mechanical performance to improve the material sustainability of SHMSHCs. For this purpose, SHMSHCs utilizing microsilica sand and river sand with a median particle size of 0.18 mm and 1.10 mm, at varying sand-to-MgO weight ratios from 0 to 1.60, were experimentally investigated. The compressive strength of the SHMSHC was increased with the addition of aggregates. The initial cracking strength of the MSH cementitious matrix also increased with the addition of aggregates. All the SHMSHCs with microsilica sand and river sand showed strain-hardening behavior. The SHMSHCs with river sand demonstrated higher tensile strain capacity than microsilica sand SHMSHCs, whereas the effect on the ultimate tensile strength was the opposite. The residual crack widths of the SHMSHCs increased with the addition of aggregates. The beneficial effect of aggregate incorporation was reflected in the lower embodied carbon and energy in the SHMSHCs.

Mechanical performances and micro-level properties of basalt and PVA fiber reinforced engineered cementitious composite after high temperatures exposure

After high-temperature exposure, synthetic fibers with low melt temperature tend to exert negative influence on mechanical performance of engineered cementitious composite (ECC) and its elements. Basalt and PVA fiber reinforced hybrid-fiber ECC (basalt/PVA HF-ECC) is a promising way to address such drawback, due to the low cost, sustainability and high-temperature stability of basalt fiber. However, relevant researches only focus on fiber replacement and are still on primary stage, meanwhile their results show further performance improvements are required. In present study, basalt/PVA HF-ECC with superimposed basalt fiber content is proposed. Mechanical and micro-level related tests were conducted to investigate the effect of superimposed basalt fiber content after high-temperature exposure. Compressive test results showed basalt fiber could increase compressive strength at elevated temperatures. The optimal basalt fiber volume fraction was 0.8%, whereby compressive strength was higher than that of control PVA-ECC by 62.05%, 55.45% and 37.24% at 400 °C, 600 °C, and 800 °C. Tensile test results exhibited that stress-strain curves of basalt/PVA HF-ECC showed brittle behavior when PVA fiber melted at elevated temperatures, and first cracking strength also showed continuous increase as basalt fiber content increased. The optimal basalt fiber volume fraction was 1.2%, whereby first cracking strength was higher than that of control PVA-ECC by 48.43%, 42.38%, 36.30% and 50.41% at 23 °C, 400 °C, 600 °C, and 800 °C. Mercury intrusion porosimetry (MIP) tests showed basalt fiber reduced average pore diameter at elevated temperatures, while hardly exerted influence on porosity. At 600 °C and 800 °C, 0.8% and 1.2% content of basalt fiber decreased average pore diameter of control PVA-ECC by 13%–37%, and deduced peak heights of pore size distribution curves. SEM observation discussed and proved the basalt fiber contribution to strength improvement after high-temperature exposure. Rupture space related analysis was also used to discuss the tensile strain capacity deterioration at elevated temperatures. The present study investigates high-temperature mechanical performances and micro-level properties of basalt/PVA HF-ECC with superimposed basalt fiber content, thus promotes development of heat-resistant ECC with much reliable performances.

Thermoelectric ultra-lightweight high-performance ECC using cenospheres and calcined petroleum coke

Conventional high-cost conductive filler as the crucial ingredient of multifunctional concrete might negatively affect the workability and mechanical properties. Petroleum coke as a low-cost by-product was ever used as the conductive filler in cementitious composites, while its mechanical properties were disregarded in the design of cementitious composites due to pore structure. This study demonstrates that calcined petroleum coke (CPC) can effectively improve the mechanical properties, workability, and electrical conductivity of ultra-lightweight engineered cementitious composites (ULW-ECCs). Besides, multifunctional ULW-ECCs were developed by using fly ash cenospheres (FAC) and CPC, which show heat insulation, heat energy harvesting, and self-healing functions. The new ULW-ECCs showed high pseudo-strain-hardening indices due to the dense matrix and had an oven-dry density of 1262–1428 kg/m3, compressive strength of 58.1–76.3 MPa, tensile strain capacity of 8.0–8.8 %, tensile strength of 5.2–6.1 MPa, and flexural strength of 13.1–17.6 MPa. Furthermore, the multiple micro-cracks of ULW-ECCs show excellent self-healing properties. The electrical conductivity, Seebeck coefficient (under different moisture conditions), and thermal conductivity and effusivity were tested. The meso- and micro-structure analyses were conducted to explain the results. The new ULW-ECCs show low thermal conductivity and effusivity due to the use of FAC. The ULW-ECCs incorporating CPC result in a P-type thermoelectric voltage and exhibit a Seebeck coefficient of 4060 μV/°C which is higher than that of cementitious composites using different conductive fillers in previous literature, suggesting that the newly developed ULW-ECCs could be viable thermoelectric composites.

Development of engineered cementitious composite with moderate tensile properties using polyester fibers

In recent years, the use of reinforced cementitious composites has increased manifold for structural rehabilitation purposes. The present study concerns the development of a special variant of ECC, which is low-cost but has moderate tensile strength and ductility. Widely available polyester fiber was chosen, which was about ten times cheaper but about four times weaker than the preferred but expensive PVA fibers. Micromechanics-based mathematical model was used for fiber optimization to attain the multiple and strain hardening phenomena of the ECC. Different ECC mixes were prepared to investigate the effect of the matrix toughness on the tensile properties of ECC. ECC, with a strong matrix, failed to attain multiple cracking after 28-days of tensile testing because the fracture toughness exceeded the fiber bridging energy. The matrix was made weaker by increasing the amount of fly ash, and the desired strain hardening phenomena was achieved after 28-days of tensile testing. A low-cost ECC was developed, which used 3% polyester fiber by volume; the tensile strength and strain capacity of ECC was 2.17 MPa and 1.88%, respectively.

Probabilistic-based investigation on tensile behavior of engineered cementitious composites (ECC): A macro-scale stochastic model

Micromechanics-based models are extensively used to simulate the tensile behavior of engineered cementitious composites (ECC). However, obtaining the micromechanical parameters in these models requires complicated experiments. This study proposes a macro-scale stochastic model to straightforwardly simulate the tensile behavior of ECC based on the strength criterion of strain-hardening. Specifically, the model simulates the multiple cracking of ECC as a stochastic process, in which the strength criterion is used to determine the formation of a crack. The failure probability distribution of the cracks is calculated by using statistical parameters of cracking strength and fiber bridging strength. Afterward, the crack number and tensile strain capacity of ECC are derived from the expectation of the failure probability distribution. Results show that the model predicts the crack number and tensile strain capacity of ECC with errors lower than 9.4% and 14.9%, respectively. Parametric analysis reveals that the crack number increases with the increasing difference value between cracking strength and fiber bridging strength. The stochastic model provides a comprehensive understanding on the multiple cracking of strain-hardening materials.