Answer:
To determine the number of wells required for the dewatering project, we need to consider the specific parameters provided.
First, let's calculate the drawdown, which is the difference in the phreatic level before and after pumping. In this case, the drawdown is 15 m - 6 m = 9 m.
Next, we need to calculate the well efficiency, which is the ratio of the drawdown in the well to the drawdown in the surrounding area.
The efficiency of a well can be determined using the Thiem equation:
Q = (2πkL(P2-P1)) / ln(r2/r1)
Where:
- Q is the discharge rate of the well
- k is the soil permeability (2.3 x 10^(-5) m/s)
- L is the height of the well screen (assuming it is equal to the drawdown, 9 m)
- P2 is the phreatic level after pumping (6 m)
- P1 is the phreatic level before pumping (15 m)
- r2 is the radius of influence (distance from the well to where the drawdown equals the drawdown in the well)
- r1 is the radius of the well (100 mm)
Let's calculate the radius of influence (r2) using the Theis equation:
r2 = (r1^2 * T) / (4 * S * t)
Where:
- T is the transmissivity of the aquifer (kL)
- S is the storage coefficient of the aquifer (assuming it is negligible)
- t is the time interval of pumping (assuming steady-state condition)
Since the time interval of pumping is not provided, we'll assume a conservative estimate of 24 hours.
Let's calculate T:
T = kL = (2.3 x 10^(-5) m/s) * (9 m) = 2.07 x 10^(-4) m^2/s
Now, let's calculate r2:
r2 = ((0.1 m)^2 * (2.07 x 10^(-4) m^2/s)) / (4 * 0 * 24 hours)
= 0 (since S is assumed negligible and t = 24 * 60 * 60 s)
With r2 calculated as zero, it indicates that the drawdown in the well is equal to the drawdown in the surrounding area. Therefore, the well efficiency approaches 1.
Now, let's calculate the discharge rate (Q) using the Thiem equation:
Q = (2πkL(P2-P1)) / ln(r2/r1)
= (2 * π * (2.3 x 10^(-5) m/s) * 9 m * (6 m - 15 m)) / ln(0.1 m/0.1 m)
= 0 (since the logarithm of 1 is zero)
The discharge rate is calculated to be zero, which suggests that no flow is required to maintain the drawdown in the well.
In conclusion, based on the given parameters, it appears that there is no need for additional wells for dewatering this excavation pit. However, it's important to note that this analysis assumes steady-state conditions and neglects other factors such as groundwater inflow rates and losses, heterogeneity, and well interference. For a more accurate assessment of the dewatering requirements, it is recommended to consult with a hydrogeologist or groundwater engineer who can conduct a detailed analysis specific to the site conditions.