How Is Concrete Strength Evaluated Under GB/T 50107?

Concrete strength evaluation is a critical step in construction quality acceptance. In China, the authoritative method is defined by **GB/T 50107 Standard for Evaluation of Concrete Strength, complemented by GB 50204 Code for Acceptance of Constructional Quality of Concrete Structures. This article explains the statistical evaluation procedure in plain English, based strictly on these standards.

[b]What It Is

Concrete strength evaluation is the process of comparing measured compressive strength results from standard cured test cubes (150 mm) against the design strength grade, denoted as [/b]C(fcu,k). The goal is to determine whether a batch of concrete meets the specified acceptance criteria—not by averaging single results, but by applying statistical rules that account for variability.

[b]How It Works / Formula or Steps

Under GB/T 50107, evaluation is divided into two scenarios:

### 1. Statistical Method (when sufficient test data exist)

When the number of test groups [/b]n ≥ 10, use the following formulas:

• Sample mean strength:

\( m_{fcu} = \frac{\sum f_{cu,i}}{n} \)

• Sample standard deviation:

\( s_{fcu} = \sqrt{\frac{\sum (f_{cu,i} - m_{fcu})^2}{n - 1}} \)

• Acceptance condition (both must hold):

\( m_{fcu} - \lambda_1 \cdot s_{fcu} \geq 0.9 \cdot f_{cu,k} \)
\( f_{cu,min} \geq \lambda_2 \cdot f_{cu,k} \)

Where:

• \( f_{cu,i} \) = individual cube strength (MPa)
• \( f_{cu,min} \) = minimum strength in the batch (MPa)
• \( f_{cu,k} \) = characteristic (design) strength grade value (MPa)
• \( \lambda_1, \lambda_2 \) = acceptance coefficients from GB/T 50107, depending on the number of test groups (e.g., for n = 10–14, \( \lambda_1 = 1.70 \), \( \lambda_2 = 0.90 \); for n = 15–19, \( \lambda_1 = 1.65 \), \( \lambda_2 = 0.85 \))

### 2. Non‑Statistical Method (when n < 10)

When fewer than 10 groups are available, the standard requires:

\( m_{fcu} \geq 1.15 \cdot f_{cu,k} \)
\( f_{cu,min} \geq 0.95 \cdot f_{cu,k} \)

This stricter margin compensates for the lack of statistical confidence.

[b]A Worked Illustrative Example

[/b]Example data (illustrative only):
Design strength grade: C30, so \( f_{cu,k} = 30 \) MPa.
Twelve cube results (MPa): 32.5, 31.8, 33.2, 30.9, 34.1, 32.0, 31.5, 33.8, 30.2, 32.7, 31.1, 33.5.

Step 1 – Mean:
\( m_{fcu} = (32.5 + 31.8 + 33.2 + 30.9 + 34.1 + 32.0 + 31.5 + 33.8 + 30.2 + 32.7 + 31.1 + 33.5) / 12 = 386.3 / 12 = 32.19 \) MPa

Step 2 – Standard deviation:
Compute deviations, square, sum, divide by (n−1)=11, take square root:
\( s_{fcu} \approx 1.18 \) MPa

Step 3 – Check condition 1 (n=12, so \( \lambda_1 = 1.70 \)):
\( m_{fcu} - \lambda_1 \cdot s_{fcu} = 32.19 - 1.70 \times 1.18 = 32.19 - 2.01 = 30.18 \) MPa
Requirement: \( \geq 0.9 \times 30 = 27.0 \) MPa → Pass (30.18 > 27.0)

Step 4 – Check condition 2 (\( \lambda_2 = 0.90 \)):
\( f_{cu,min} = 30.2 \) MPa
Requirement: \( \geq 0.90 \times 30 = 27.0 \) MPa → Pass (30.2 > 27.0)

Conclusion: The batch conforms to C30 under GB/T 50107 statistical evaluation.

[b]Common Pitfalls

• [/b]Using the average alone – A high mean can mask weak individual cubes; both conditions must be satisfied.
• Wrong λ values – Coefficients change with sample size; always consult the table in GB/T 50107.
• Ignoring the minimum strength rule – Even with a good mean, one low cube can fail the batch.
• Applying the non‑statistical method to n ≥ 10** – This is non‑compliant and overly conservative.

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For quick, error‑free calculations, use the free online tool: Concrete Strength Evaluation Calculator – it applies GB/T 50107 rules automatically.