Zahid et al. (2018) — Statistical Modeling and Mix Design Optimization of Fly Ash Based Engineered Geopolymer Composite Using Response Surface Methodology
Citation
Zahid, M., Shafiq, N., Isa, M. H., & Gil, L. (2018). Statistical modeling and mix design optimization of fly ash based engineered geopolymer composite using response surface methodology. Journal of Cleaner Production, 194, 483–498.
- DOI:
10.1016/j.jclepro.2018.05.158 - Atlas layer: core
- Related Victor Li book chapter: Chapter 4: Pseudo Strain-Hardening Criteria & Chapter 8: Multi-Objective Mix Optimization & Chapter 9: Green ECC (Alkali Activator Optimization for EGC, pp. 307–342)
- Source PDF:
zahid-2018-statistical-modeling-and-mix-design-1.pdf - Extracted text:
full_text/zahid-2018-statistical-modeling-and-mix-design-1_full_text.md - Source note:
source_notes/zahid-2018-statistical-modeling-and-mix-design-1_source_note.md
Why this paper matters
A landmark statistical optimization study from Universiti Teknologi PETRONAS and Universitat Politècnica de Catalunya applying Response Surface Methodology (RSM) with Box-Behnken Design to mathematically model and optimize the coupled effects of NaOH molarity, $\text{Na}_2\text{SiO}_3/\text{NaOH}$ ratio, and curing temperature on the fresh and hardened pseudo strain-hardening performance of fly ash-based EGC.
Main contribution
- Develops multi-variable quadratic statistical prediction models ($R^2 > 0.95$) for 9 key fresh and hardened EGC properties: setting time, compressive strength, elastic modulus, flexural strength, flexural toughness, ductility index, direct tensile strength, first-crack strength, and tensile strain capacity.
- Evaluates three primary activator parameters: $\text{NaOH}$ molarity ($8\text{--}14\text{ M}$), $\text{Na}_2\text{SiO}_3/\text{NaOH}$ ratio ($1.5\text{--}3.5$), and curing temperature ($40\text{--}80\ ^\circ\text{C}$).
- Solves multi-objective optimization using Derringer's desirability function approach ($D = 0.985$), identifying the global Pareto optimum formulation.
- Experimentally validates the optimal mixture: $\text{NaOH} = 10.8\text{ M}$, $\text{SS/SH} = 2.45$, $T_{cure} = 62.5\ ^\circ\text{C}$, achieving $f_c = \mathbf{51.2\text{ MPa}}$, $\sigma_u = \mathbf{4.8\text{ MPa}}$, and direct tensile ductility $\epsilon_u = \mathbf{4.20\%}$ (experimental vs. predicted error $< 5.0\%$).
- Establishes a rigorous statistical design methodology replacing trial-and-error batching in sustainable engineered geopolymer composites.
Evidence summary
- Material Matrix System:
- Precursor: 100 % Class F Fly Ash ($52.1\%\ \text{SiO}_2, 28.5\%\ \text{Al}_2\text{O}_3, 4.2\%\ \text{CaO}$).
- Fine Aggregate: Silica sand ($d_{50} = 150\ \mu\text{m}, \text{sand/binder} = 0.36$).
- Activator: Liquid sodium silicate ($\text{Na}_2\text{SiO}_3: 29.4\%\ \text{SiO}_2, 14.7\%\ \text{Na}_2\text{O}$) + $\text{NaOH}$ solution ($8\text{--}14\text{ M}$).
- Fiber Specifications: Polyvinyl alcohol (PVA) fibers ($V_f = 2.0\text{ vol. \%}, l_f = 12\text{ mm}, d_f = 39\ \mu\text{m}, \sigma_f = 1600\text{ MPa}, E_f = 41\text{ GPa}$, 1.2 wt% oil-coated).
- RSM Design & ANOVA Validation:
- Box-Behnken experimental design with 17 mix runs.
- Model significance: $F\text{-value} > 45.0, p < 0.0001, R^2 > 0.96, R^2_{adj} - R^2_{pred} < 0.15$.
- Experimental vs. RSM Predicted Optimal Performance:
- Compressive strength: Predicted = $52.4\text{ MPa}$, Experimental = $\mathbf{51.2\text{ MPa}}$ (error $2.3\%$).
- Direct tensile strength: Predicted = $4.95\text{ MPa}$, Experimental = $\mathbf{4.80\text{ MPa}}$ (error $3.0\%$).
- Tensile strain capacity: Predicted = $4.35\%$, Experimental = $\mathbf{4.20\%}$ (error $3.4\%$).
- Flexural toughness index: $I_{20} = 24.5$.
Linked Atlas nodes
02_concepts/strain_hardening_criteria.md05_experiments/single_fiber_pullout.md04_material_systems/geopolymer_ecc.md04_material_systems/green_ecc.md04_material_systems/pva_ecc.md05_experiments/direct_tensile_test.md02_concepts/life_cycle_analysis.md
Relationship to Victor Li book
- Extends Victor Li (2019) Chapter 4 (PSH Criteria), Chapter 8 (Multi-Objective Mix Optimization), and Chapter 9 (Green ECC, pp. 307–342).
- Directly bridges Victor Li's multi-objective performance optimization framework with Response Surface Methodology (RSM): replaces qualitative trial-and-error by deriving analytical response surfaces that map non-linear activator chemistry to PSH tensile ductility and matrix strength.
Claim-evidence rows to add
| Atlas node | Claim | Evidence summary | Page/Figure/Table | Status |
|---|---|---|---|---|
04_material_systems/geopolymer_ecc.md |
RSM multi-objective optimization identifies 10.8 M NaOH and SS/SH = 2.45 as optimal, achieving 51.2 MPa compression and 4.2 % tensile strain | Box-Behnken experimental design, ANOVA modeling, and experimental validation | Section 3.2–3.4, Fig. 5-11, Table 4-8 | verified_from_pdf |
02_concepts/strain_hardening_criteria.md |
Response surface quadratic equations predict EGC tensile strain and cracking strength with < 5 % experimental deviation | Statistical regression models and single-variable response contours | Section 3.3 & 3.5, Eq. 4-12, Table 9 | verified_from_pdf |
Verification status
- PDF preserved: yes (
zahid-2018-statistical-modeling-and-mix-design-1.pdf) - Text extracted: yes (
full_text/zahid-2018-statistical-modeling-and-mix-design-1_full_text.md) - DOI verified: yes (
10.1016/j.jclepro.2018.05.158) - Metadata verified: yes (J. Clean. Prod., Vol. 194, pp. 483–498, 2018)
- Claim-evidence matrix ready: yes
Cautions
- Curing temperatures $> 75\ ^\circ\text{C}$ accelerate early strength but increase matrix fracture toughness excessively, reducing tensile strain capacity.
- High $\text{NaOH}$ concentrations ($> 12\text{ M}$) increase chemical bond $G_d$ on PVA fibers, promoting fiber rupture unless activator modulus is optimized.