Settlement of the bottom liner of a landfill

[BrianQ]

I am trying to determine settlement of the bottom liner of a landfill. It is irregularly shaped roughly 2000 ft by 4000 ft. As you would suspect it is imposes an irregular load ranging from almost nothing at the edges to over 18,750psf (900kPa) at the center. The foundation soils vary in thickness and type across the site, but consist of saturated sand, saturated clay, and partially saturated clay. I know how to calculate the consolidation of the saturated clay, but I don’t know how to calculate the immediate settlement for the sand and the partially saturated clays. All the references I have are for structures. Does anyone have a suggestion of a formula to use or a reference?

 

[fattdad]

Make a profile of modulus values to depth.
Calculate the change in effective stress to depth (to where the change in stress is less than 10 percent of the overburden pressure).
Integrate the change in stress profile with respect to depth and divide by the modulus value for that layer.
Voilla!

Let's say you have a layer that's 100 ft thick and it experiences an average stress increase of 8,000 psf.
Let's say it's underlain by another 100 ft layer that has an average stress increase of 4,000 psf. (I'm using a very simplifed example, eh?)

Let's say the modulus value of the upper layer is 200 tsf and the modulus value for the lower layer is 400 tsf.

Upper layer:

Let's integrate:
8,000 psf*100=800,000 lb/ft (400 t/ft),
Let's divide:
400/200=2 ft

Lower layer:
4,000*100=400,000 lb/ft (200 t/ft)
200/400=0.5 ft

Add for totals: 2 1/2 ft!

Notes:
You'll need good control on your soil modulus values
You'll need more sublayers
You may need to consider hyperbolic modulus values (i.e., change in modulus as a function of confining stress). It's unlikely that you'll actually get data to the full depth of the seat of settlement.
I'd model the clay as an elastic solid also unless the stresses actually exceed Pp.

Hope this helps.

yes this works.

f-d




¡papá gordo ain’t no madre flaca!

 

[VAD]

BrianQ
Are you digging a hole in the ground for landfill or are you placing landfill on the existing ground surface. I am presuming the former but this does not make sense based on what you are calculating, hence it must be the latter. Can you confirm?.

 

[BrianQ]

The facility has 3H to 1V interior slopes that are excavated down about 20 ft, and the waste slopes are also 3H to 1V and go up about 200 ft above the surface. The leachate pipes that conveys the contaminated water to the sumps are constructed at a 0.8% slope are about 1900ft long and I have to determine if it maintains at least a 0.5% slope. The sump is on rock. The center of the landfill has a load of 18,750psf is underlain from the bed rock up by about 10 ft of loose saturated sand (N60 =5 – 8), 5 ft of soft saturated silty clay (N60 =0 – 4), and 10 ft of partially saturated silty clay (N60 =7 – 12). The far end of the leachate pipe is loaded with about 3,000psf and is underlain from the bed rock up by about 15 ft of loose saturated sand (N60 =5 – 8), 5 ft of soft saturated silty clay(N60 =0 – 4), and 15 ft of partially saturated silty clay (N60 =7 – 12).

 

[fattdad]

I assigned the following: Es=100 tsf for the N=5-8 interval; 50 tsf for the N=0-4 interval and 150 tsf for the N=7-12 interval. At the location where the stress increase is 9.375 tsf (18,750 psf), I'd get about 2 1/2 ft of settlement. At the location where the stress increase is 1.5 tsf, I'd get about 0.5 ft of settlement. I'd discount settlement at the sump location (i.e., on bedrock).

You can do the math on the slope or otherwise figure out the soil modulus values. You can also look at primary consolidation for the soft clay, which I just overlooked (i.e., 50 tsf is pretty much like mud).

Good luck.

f-d

¡papá gordo ain’t no madre flaca!