📄 chemistry

Probabilistic Reliability Assessment of Biochar-Modified Cementitious Composites Using Monte Carlo Simulation

This study employs a Monte Carlo reliability framework to analyze 240 paired compressive-strength records from 30 studies, revealing that while biochar dosages between 2.5% and 5% generally offer the highest reliability, no universal optimum exists due to significant variability driven by matrix design, feedstock, and curing conditions.

Original authors: Syaiful Osman, Mohd. Nazarudin Zakaria, Siti Hazifah Mokhtar, Rosmamuhamadani Ramli

Published 2026-06-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Syaiful Osman, Mohd. Nazarudin Zakaria, Siti Hazifah Mokhtar, Rosmamuhamadani Ramli

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to bake the perfect loaf of bread, but instead of flour, you are mixing biochar (a type of charcoal made from plants) into cement to make stronger, greener building materials.

For years, scientists have been baking these "biochar breads" in different labs. Some say adding a little bit makes it stronger; others say a lot makes it weaker. The problem is that everyone uses different recipes, different ovens (curing conditions), and different types of charcoal. When you try to compare their results, it's like comparing a sourdough loaf from Paris to a baguette from Tokyo and trying to decide which one is "better" just by looking at the average weight.

This paper is the authors' attempt to stop guessing and start measuring how likely these biochar mixes are to actually work, even when the recipes vary.

Here is the breakdown of their study using simple analogies:

1. The Problem: Too Many Different Recipes

The researchers looked at 30 different studies containing 240 pairs of test results. In every pair, there was a "control" (regular cement) and a "treatment" (cement with biochar).

The issue was that many of these studies didn't report how much their results varied. It's like a chef saying, "My cake weighs 500 grams," but not telling you if it could actually be anywhere between 400 and 600 grams. Without knowing that "wiggle room" (uncertainty), it's hard to know if the biochar really helped or if the result was just a lucky fluke.

2. The Solution: The "What-If" Simulator

To fix this, the authors used a computer tool called Monte Carlo Simulation.

Think of this like a video game simulator for building materials.

Instead of just looking at one average number, the computer runs the experiment 100,000 times for every single study.
It adds random "noise" to the results based on how much variation is usually seen in construction (or guesses a reasonable amount if the study didn't say).
It asks a simple question for every single run: "Did the biochar mix beat the regular mix?"

At the end, they get a Reliability Score (a probability from 0 to 1).

0.50 is a coin flip (50/50 chance).
0.80 means the biochar mix wins 8 out of 10 times.
0.10 means it almost never wins.

3. The Findings: It's Not About "How Much," It's About "How"

The big surprise wasn't finding a "magic number" of biochar to add. Instead, they found that the answer depends entirely on what kind of building material you are making.

The "Sweet Spot" (2.5% to 5%): This dosage range had the highest reliability. It was the most likely to beat regular cement. However, the authors found a catch: many of these wins came from specialized systems, like concrete that is cured with carbon dioxide or "foamed" concrete (like a sponge).
The "Too Little" Zone (<1%): Adding a tiny pinch of biochar usually didn't do much. The results were so close to regular cement that it was hard to tell if it was actually an improvement or just random noise.
The "Too Much" Zone (>10%): When they added a lot of biochar, the reliability dropped significantly. It became very likely that the material would be weaker than regular cement.
The "System Matters" Rule: The study showed that you can't just say "Add 3% biochar to everything."
- If you are making foamed concrete or using carbonation curing, 3% might be a winner.
- If you are making standard concrete, that same 3% might be a loser.
- It's like saying, "Running shoes are great." They are great for a marathon, but terrible for swimming. The context changes the result.

4. The "Leave-Out" Test

To make sure they weren't being fooled by a few lucky studies, the authors did a "leave-out" test. They removed the studies with the best results (the specialized ones) and re-ran the simulation.

Result: The "sweet spot" (2.5–5%) still looked good, but it wasn't as amazing as before. This proved that while the dosage range is promising, it relies heavily on those special, high-tech methods to work perfectly.

5. The Bottom Line

The authors conclude that there is no universal "best" amount of biochar to add to cement.

Don't look for a magic number: You can't just tell a builder, "Add 4% biochar," and expect it to work everywhere.
Look at the whole picture: Whether biochar helps depends on the type of cement, how it's processed, and how it's cured.
Better data is needed: The study highlights that future scientists need to report not just the average strength, but also the "wiggle room" (standard deviation) and sample sizes. Without this, we are just guessing.

In short: This paper didn't find a single "best recipe." Instead, it built a reliability map. It tells us that while biochar can be a great ingredient, it's a picky one. It works best in specific, well-designed recipes, and adding too much of it usually backfires. The key to success isn't just the amount of biochar; it's the entire system it's mixed into.

Technical Summary: Probabilistic Reliability Assessment of Biochar-Modified Cementitious Composites

Problem Statement
Biochar-modified cementitious composites are increasingly investigated as lower-carbon construction materials capable of storing biomass-derived carbon while modifying hydration, pore structure, and matrix packing. However, the literature presents a significant challenge for design-oriented interpretation: published strength results are highly heterogeneous. Variations in matrix type, feedstock, pyrolysis temperature, particle size, moisture conditions, curing regimes, and dosage strategies make direct comparisons difficult.

A recurring limitation in existing studies is the reliance on deterministic treatment-control mean values to draw conclusions. This approach often fails to account for experimental variability, potentially exaggerating weak improvements or obscuring the specific mechanisms (e.g., carbonation curing, internal curing) that drive performance in specialized systems. Furthermore, formal meta-analysis is frequently hindered by incomplete reporting of standard deviations, sample sizes, or raw data in the broader biochar-cement literature, making inverse-variance weighting inappropriate for many records.

Methodology
To address these gaps, this study developed a reproducible, literature-derived Monte Carlo reliability framework. The analysis utilized a curated database of 240 paired 28-day compressive-strength records extracted from 30 primary studies.

Data Extraction: Records were included only if they contained a matched control, an extractable 28-day compressive strength mean for the biochar-modified mixture, and a clear dosage level. Treatment means were sourced from tables/text or digitized from figures.
Uncertainty Handling: A critical component of the methodology was the explicit treatment of uncertainty.
- Where source papers reported standard deviations (SD), standard errors, or visible error bars, these were converted to SD values.
- For the 123 records lacking usable uncertainty values, SD was imputed using Coefficient of Variation (CV) assumptions of 5%, 10%, 15%, and 20%. The CV10 (10%) scenario served as the reference case.
Simulation: For each paired record, treatment and control strengths were simulated using zero-truncated normal distributions ( $X_{T,i} \sim N(\mu_{T,i}, \sigma_{T,i}^2)$ and $X_{C,i} \sim N(\mu_{C,i}, \sigma_{C,i}^2)$ ).
Reliability Metric: The primary output was $P(\text{treatment} \geq \text{control})$ , representing the probability that the biochar-modified mixture equals or exceeds its matched control under the selected uncertainty scenario. Simulations were run for 100,000 iterations per record.
Sensitivity Analysis: A "leave-out" check was performed on the >2.5–5% dosage bin to assess the influence of specialized systems (specifically carbonation-cured mortar and foamed concrete/internal-curing records).

Key Results
Under the CV10 reference scenario, the study found that reliability is not uniform across dosage levels and is heavily dependent on system type:

Optimal Dosage Bins: The >2.5–5% dosage bin demonstrated the highest overall reliability ( $n=75$ ; mean $P=0.610$ ; median $P=0.678$ ), followed closely by the 1–2.5% bin ( $n=75$ ; mean $P=0.583$ ; median $P=0.666$ ).
Low and High Dosages:
- The <1% bin showed low reliability ( $n=22$ ; mean $P=0.331$ ), suggesting changes at very low dosages often fall within experimental scatter.
- The >5–10% bin was more heterogeneous ( $n=57$ ; mean $P=0.479$ ).
- The >10% bin remained generally unfavorable for compressive-strength reliability ( $n=11$ ; mean $P=0.113$ ; median $P=0.002$ ).
System Dependence: The high reliability observed in the >2.5–5% bin was partially driven by specialized systems. Removing carbonation-cured mortar records (Chen et al.) and foamed concrete records (Song et al.) from the dataset reduced the mean probability for this bin from 0.610 to 0.450. This indicates that the apparent "optimum" is not a universal rule but is contingent on matrix design and curing mechanisms.
Data Quality: Of the 240 records, 170 (70.8%) required digitization from figures, and 123 required CV-based uncertainty imputation, highlighting the current limitations in reporting standards within the field.

Significance and Claims
The paper positions its contribution not as the identification of a universal optimum biochar dosage, but as a transparent screening method for evaluating strength-maintenance reliability under heterogeneous evidence conditions.

Complement to Meta-Analysis: The framework complements formal meta-analysis. While meta-analysis is preferable when complete effect-size and uncertainty data are available, this Monte Carlo approach is designed for broad, heterogeneous, and partly incomplete literature where traditional pooling is not feasible.
Shift in Perspective: The study argues that performance should be understood in terms of mechanism-dependent reliability rather than a single dosage target. The same nominal dosage can yield different reliability outcomes depending on whether the biochar acts as a cement replacement, filler, internal-curing agent, or part of a specialized curing strategy.
Reporting Needs: The authors conclude that stronger quantitative synthesis requires better reporting of mean strength, standard deviation, sample size, mixture design, and biochar characteristics.
Limitations: The authors explicitly state that the results are screening-level estimates, not formal pooled inferential estimates. They caution against generalizing findings across different cementitious matrices (e.g., conventional concrete vs. engineered cementitious composites) without considering specific mix designs and mechanisms. High-dose biochar may still offer benefits for shrinkage reduction, thermal performance, or carbon storage, but these require endpoint-specific reliability assessments rather than inferences based solely on compressive strength.