Concrete Compressive Strength – Factorial DoE Analysis

Introduction

This report analyzes a 2³ full factorial experiment designed to understand how water–cement ratio, curing time, and additive type affect concrete compressive strength.

Experimental Design

• Factor A: Water–Cement Ratio (0.40 low, 0.55 high)
  
• Factor B: Curing Time (7 vs 28 days)
  
• Factor C: Additive (None vs Plasticizer)
  
• Response: Compressive strength (MPa)
  
• Design: Full factorial 2³ with 2 replicates (16 total runs)

Data

The dataset is provided separately as concrete_strength_sim.csv.

df <- read.csv("concrete_strength_sim.csv")
head(df)

Model Fitting

df$A <- df$A_coded
df$B <- df$B_coded
df$C <- df$C_coded

model <- lm(Strength_MPa ~ A * B * C, data=df)
summary(model)

library(car)
Anova(model, type=2)

Diagnostic Plots

par(mfrow=c(2,2))
plot(model)

shapiro.test(resid(model))

Predicted Means & Optimal Settings

newdat <- expand.grid(A=c(-1,1), B=c(-1,1), C=c(-1,1))
newdat$pred <- predict(model, newdat)

transform(newdat,
   A_wcr = ifelse(A==-1, 0.40, 0.55),
   B_days = ifelse(B==-1, 7, 28),
   C_additive = ifelse(C==-1, "None", "Plasticizer")
)

Recommendations

• Use w/c = 0.40, 28-day curing, Plasticizer for maximum predicted strength.
• Validate through confirmatory batches.
• Examine workability & durability constraints.
• Consider expansion into RSM for fine-tuning.