Let's break down the problem and solve it step by step: ### Given: - **Length of road section**: 200 m - **Terrain**: Undulating (survey data is referenced but not provided—I'll explain the general process and what to do with typical data) - **Road Gradient**: Uniform, rising, 1 in 150 (i.e., for every 150 m horizontally, the road rises 1 m vertically) - **Fixed Road Formation RL at Chainage 100 m**: 100.00 m - **Task**: Determine if earthwork is balanced, or if additional fill (embankment) or cut (excavation) is required. --- ## 1. **Calculate the Formation Levels Along the Road** The **gradient** is **1 in 150, rising**. **Gradient = Rise / Run = 1 / 150 = 0.006667 (unitless)** ### **Chainages:** - Starting at **Chainage 100 m** (RL = 100.00 m) - Ending at **Chainage 300 m** (since section is 200 m long: 100 + 200 = 300 m) #### **Formation RL at any chainage (x):** \[ \text{Formation RL at chainage } x = 100.00 + \frac{(x-100)}{150} \] - At **Chainage 100 m**: \( 100.00 + \frac{0}{150} = 100.00 \) m - At **Chainage 200 m**: \( 100.00 + \frac{100}{150} = 100.00 + 0.6667 = 100.67 \) m - At **Chainage 300 m**: \( 100.00 + \frac{200}{150} = 100.00 + 1.3333 = 101.33 \) m --- ## 2. **Interpretation with Survey Data** To determine if earthwork is balanced (i.e., cut = fill), **you need to compare the formation levels (designed road RLs) to the natural ground levels (surveyed RLs) at each chainage**. **Typical process:** 1. **List the surveyed ground RLs** at each chainage (e.g., at 100m, 120m, 140m, ..., 300m). 2. **Calculate the difference** at each chainage: \[ \text{Difference} = \text{Formation RL} - \text{Ground RL} \] - **Positive** value: **Fill** needed (formation above ground) - **Negative** value: **Cut** needed (formation below ground) 3. **Calculate the area** of cut and fill at each interval (using cross-sections). 4. **Calculate volumes** (typically with the trapezoidal or prismoidal formula). --- ### **What to Do With Your Survey Data** Since you haven't provided the ground RLs, here's how to proceed when you have them: | Chainage (m) | Ground RL (m) | Formation RL (m) | Difference (Fill +ve, Cut -ve) | |--------------|---------------|------------------|-------------------------------| | 100 | X1 | 100.00 | 100.00 - X1 | | 120 | X2 | 100.13 | 100.13 - X2 | | 140 | X3 | 100.27 | 100.27 - X3 | | ... | ... | ... | ... | | 300 | Xn | 101.33 | 101.33 - Xn | - **If the result is mostly positive**: **More fill is required**. - **If mostly negative**: **More cut is needed**. - **If the sum of Cut ≈ Fill**: **Balanced earthwork**. --- ### **Example (Hypothetical Data)** Suppose the ground RLs are as follows: | Chainage | Ground RL | Formation RL | Difference (Fill +ve, Cut -ve) | |----------|-----------|--------------|--------------------------------| | 100 | 99.80 | 100.00 | +0.20 (fill) | | 120 | 99.95 | 100.13 | +0.18 (fill) | | 140 | 100.10 | 100.27 | +0.17 (fill) | | 160 | 100.30 | 100.40 | +0.10 (fill) | | 180 | 100.60 | 100.53 | -0.07 (cut) | | 200 | 100.80 | 100.67 | -0.13 (cut) | | ... | ... | ... | ... | | 300 | 101.50 | 101.33 | -0.17 (cut) | - **Sum up the positive values** (total fill required) - **Sum up the negative values** (total cut required) - **Net result** tells you if you need to import fill or dispose of excess spoil. --- ## **Conclusion/Interpretation** **Without actual ground RL data, the answer is:** > **To determine whether earthwork is balanced or if additional fill or cut is required, compare the formation RLs at each chainage (according to the rising gradient) to the surveyed ground RLs. If the net volume of fill (formation RL above ground RL) exceeds the net volume of cut, additional fill will be required, and vice versa. If they are approximately equal, the earthwork is balanced.** **If you provide the ground RLs, I can do the specific calculations for you.** --- ### **Summary Table for Your Report** | Chainage (m) | Ground RL (m) | Formation RL (m) | Difference (Fill +ve, Cut -ve) | |--------------|---------------|------------------|-------------------------------| | 100 | | 100.00 | | | 120 | | 100.13 | | | ... | | ... | | | 300 | | 101.33 | | --- **Please provide your actual survey data for a specific calculation!**