Li et al. (2019) — Performance-based design of all-grade strain hardening...

Citation

Linzhi Li, Ziwei Cai, Kequan Yu, Y.X. Zhang, Yao Ding (2019). Performance-based design of all-grade strain hardening cementitious composites with compressive strengths from 40 MPa to 120 MPa. Cement and Concrete Composites, Vol. 97, pp. 202-217.

• DOI: 10.1016/j.cemconcomp.2019.01.001
• Atlas layer: extension
• Related Victor Li book chapter: Chapter 2: Micromechanics; Chapter 5: Advanced ECC; Chapter 9: Design Principles
• Source PDF: li-2019-performance-based-design-of-all-grade-strain.pdf
• Extracted text: atlas/full_text/li-2019-performance-based-design-of-all-grade-strain_full_text.md
• Source note: atlas/source_notes/li-2019-performance-based-design-of-all-grade-strain_source_note.md

Why this paper matters

Landmark paper establishing a comprehensive performance-based design (PBD) framework mapping the dimensionless fiber reinforcement index ($V_f L_f / d_f = 5\text{ to }18$) to tensile strength (4.3 to 17.4 MPa), tensile strain capacity (2.2% to 12.0%), and crack patterns across the entire compressive strength spectrum from 43 to 115 MPa.

Main contribution

• Tested over 120 direct tensile dumbbell specimens spanning 5 matrix strength grades ($w/b = 0.32, 0.22, 0.18, 0.16, 0.14$).
• Demonstrated that $V_f L_f / d_f \ge 15$ unlocks extreme tensile strain capacities ($8.00\%\text{ to }12.00\%$) and strain energy $>1000\text{ kJ/m}^3$ across all compressive strength grades.
• Formulated empirical predictive models linking $V_f L_f / d_f$ to Ultimate Limit State (ULS: $\sigma_{tu}, \varepsilon_{tu}$) and Serviceability Limit State (SLS: $w_c, N_c, s_c$).

Evidence summary

• Tensile properties across grades:
• $w/b = 0.32$ ($f_c = 43\text{ MPa}$): $\sigma_{tu} = 4.3\text{--}6.5\text{ MPa}$, $\varepsilon_{tu} = 3.01\text{--}11.28\%$, $w_c = 155\text{--}201\ \mu\text{m}$
• $w/b = 0.22$ ($f_c \approx 60\text{ MPa}$): $\sigma_{tu} = 5.4\text{--}10.4\text{ MPa}$, $\varepsilon_{tu} = 2.59\text{--}12.00\%$, $w_c = 144\text{--}178\ \mu\text{m}$
• $w/b = 0.16$ ($f_c \approx 95\text{ MPa}$): $\sigma_{tu} = 7.5\text{--}14.8\text{ MPa}$, $\varepsilon_{tu} = 2.61\text{--}10.11\%$, $w_c = 133\text{--}288\ \mu\text{m}$
• $w/b = 0.14$ ($f_c = 115\text{ MPa}$): $\sigma_{tu} = 10.3\text{--}17.4\text{ MPa}$, $\varepsilon_{tu} = 2.20\text{--}8.00\%$, $g_{se} = 1036.3\text{ kJ/m}^3$ (Table 6, pages 207-208).
• Stress drop: Average stress drop per crack is 0.5–1.8 MPa (~10% of peak stress for $V_f = 2\%$).

Linked Atlas nodes

• 02_concepts/extreme_ductility_ecc.md
• 02_concepts/strain_hardening_criteria.md
• 05_experiments/direct_tensile_test.md
• 02_concepts/interface_properties.md

Claim-evidence rows to add

Verification status

• PDF preserved: yes (li-2019-performance-based-design-of-all-grade-strain.pdf)
• Text extracted: yes (atlas/full_text/li-2019-performance-based-design-of-all-grade-strain_full_text.md)
• DOI verified: yes (10.1016/j.cemconcomp.2019.01.001)
• Page/figure/table verified: yes
• Claim-evidence matrix ready: yes

Cautions

• Mixing high fiber index ($V_f L_f / d_f = 18$) in ultra-low $w/b$ (0.14) matrices requires high-shear mixing to prevent fiber clumping.
• Cylinder compressive strengths ($100 \times 200\text{ mm}$) were reported.