Sand Replacement Method Calculation Example

Sand Replacement Method Formulas:

\[ V_h = \frac{W_1 - W_4 - W_2}{\gamma} \] \[ \text{Wet density} = \frac{W_s}{V_h} \] \[ \text{Dry density} = \frac{\text{Wet density}}{1 + w} \]

W1 (Weight of sand before pouring):

W4 (Weight of sand after pouring):

W2 (Weight of sand in cone):

γ (Unit weight of sand):

kg/m³

Ws (Weight of soil from hole):

w (Water content):

decimal

Volume of hole (Vh):

Wet density:

Dry density:

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1. What is the Sand Replacement Method?

The sand replacement method is a field method for determining the in-situ density of natural or compacted soils. It involves excavating a small hole in the ground, measuring the weight of the excavated soil, and determining the volume of the hole by filling it with sand of known density.

2. How Does the Calculation Work?

The calculation uses these formulas:

\[ V_h = \frac{W_1 - W_4 - W_2}{\gamma} \] \[ \text{Wet density} = \frac{W_s}{V_h} \] \[ \text{Dry density} = \frac{\text{Wet density}}{1 + w} \]

Where:

\( V_h \) — Volume of hole (m³)
\( W_1 \) — Weight of sand before pouring (kg)
\( W_4 \) — Weight of sand after pouring (kg)
\( W_2 \) — Weight of sand in cone (kg)
\( \gamma \) — Unit weight of sand (kg/m³)
\( W_s \) — Weight of soil from hole (kg)
\( w \) — Water content (decimal)

Explanation: The method calculates the volume of the hole by measuring how much sand is needed to fill it, then uses this volume to determine the density of the soil.

3. Importance of Density Measurement

Details: Measuring in-situ density is crucial for quality control in earthworks, assessing compaction of fills, and evaluating the bearing capacity of soils.

4. Using the Calculator

Tips: Enter all weights in kg, unit weight of sand in kg/m³, and water content as a decimal (e.g., 0.12 for 12%). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What type of sand should be used?
A: Uniform, dry, clean sand with known and consistent unit weight should be used. Calibrated sand is typically used.

Q2: How big should the test hole be?
A: Typically 100-150mm diameter and depth, but depends on maximum particle size of soil.

Q3: What are typical values for dry density?
A: Varies by soil type - clay might be 1600-2000 kg/m³, well-compacted sand might be 1800-2200 kg/m³.

Q4: When is this method not suitable?
A: Not suitable for very soft soils that won't hold the hole shape, or soils with large voids or particles.

Q5: How accurate is this method?
A: With proper procedure, accuracy is typically within 1-2% of actual density.