Rice University

Civil and Environmental Engineering

CEVE 518 – GROUNDWATER HYDROLOGY AND CONTAMINANT TRANSPORT

HOMEWORK ASSIGNMENT NO. 1

Due Thursday, September 1, 2005

Show all work. Partial credit given generously!

  1. A stream in a 1-mile wide mountain valley has a total watershed area of 50 mi2, an average thickness (b) of 30 m, and an average porosity of 0.35. Streamflow measurements indicate that the stream base flow at the lower limit of the study area is 1 m3/s. The effective precipitation rate in the watershed is 75 cm/yr in rain and snow, of which 30% runs off. Evaporation and transpiration have been measured to be 8 and 16.1 cm/yr, respectively. Groundwater wells near the lower limit of the watershed indicate that the groundwater flux out of the study area is 0.3 m3/m2-d (0.3 m/d). A large industrial facility and a major municipal water well field pump a total of 5 MGD (million gallons per day) from the aquifer.
  2. Write a volumetric water balance equation that represents all of the inflows and outflows to the watershed.
  3. List each inflow and outflow, expressed in units of m3/d.
  4. Calculate the total inflow, total outflow, and net inflow (In – Out) to the aquifer. In the absence of groundwater pumping, is the aquifer system close (within 1%) to being at steady-state?
  5. What is the net recharge to the aquifer from precipitation? (Ans: 28.4 cm/yr)
  6. What is the rate of water level decline in the aquifer? (Hint: consider porosity).
  7. At current pumping rates, in how many years will the groundwater resource be depleted? (Ans: 197 yrs).
  8. Text: Problem 2-1.
  9. Text: Problem 2-2.
  10. In problem 3 above, explain qualitatively what these hydraulic heads indicate about the direction of groundwater flow.
  11. A geologist examining a soil core in the field described the soil as a loamy sand. Subsequent geotechnical analysis indicated the following particle size distribution:

Particle Size / Weight Percent
<0.004 / 10
0.004 – 0.062 / 20
0.062 – 0.25 / 50
0.25 – 1.0 / 15
>1.0 / 5

Was the geologist’s soil description accurate? (Hint: See Table 2.2 in the text and Slide 24 – Particle Size Distribution in your handouts).

  1. A soil has a solids mass density of 2.6 g/cm3 and a dry bulk density of 1.6 g/cm3.
  2. Derive the expression for porosity in terms of the bulk and solid densities of the soil (Hint: Start with the volume balance VT = VS + VV and use the definitions of bulk and solid densities:

)

  1. What is the porosity?
  2. If a moist sample of the same soil has a density of 1.9 g/cm3, what is its volumetric water and air content?
  3. What is its water saturation?
  4. Porosity data is often reported by geotechnical laboratories in terms of the void ratio.
  5. Derive the relationship between porosity and void ratio (Hint: start with the definition of porosity:

and remember that VT = VS + VV.)

  1. A soil has a porosity of 0.4. What is its void ratio?
  2. ASTM Standard D2216 for the calculation of moisture content of soils and rock by mass reports moisture content as the gravimetric water content (w), which is the ratio of the weight (mass) or water contained in the soil to the dray weight (mass) of the soil sample.
  3. What is the algebraic relationship between the gravimetric water content and the volumetric water content?
  4. If a soils sample has a mass of 26.2 g when moist, 22.4 g when dry, and a bulk density of 1.65 g/cm3, what is the gravimetric water content and the volumetric water content of the moist soil sample?
  5. A course sand comprised of uniformly circular particles with a grain diameter of 0.5 mm has a porosity of 0.38. What would the porosity of the sand be if the grain diameter was 1 mm assuming that the packing configuration of the sand grains is the same?
  6. Draw diagrams of two realistic field situations in which three piezometers installed side by side, but bottoming at different depths, would have the same water-level elevation.