10. Groundwater in geotechnical problems

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Chester Owen
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1 . Goundwate in geotechnical poblems Goundwate plays a key ole in many geotechnical poblems. We will look at; - land subsidence - dewateing open pits - Consolidation of sediments Remembe the stoage of wate in sediments. 3 P and M w incease In the step 3, solid gains eaange themselves to make oom fo wate. Poosity (n) inceases. A evese step, 3, is called consolidation. In many cases elated to goundwate, the majoity of consolidation is vetical (land subsidence, diagenesis, etc.). In othe wods, only the thickness of sediments changes. Consolidation is induced by loading exta weight (building, glacie, etc.). But loading alone cannot cause consolidation.

2 Effective stess - Suppose an imaginay plane at some depth. It is pushed fom the above by the weight of wate and sediments. This foce pe unit aea is total stess (σ T ). σ e σ T P The plane is pushed fom the below by solid gains and wate. The foce suppoted by solid gains pe unit aea is effective stess (σ e ). P is the pessue of wate (poe pessue). Effective stess keeps solid gains togethe, and poe pessue pushes them apat. load wate In the vetical theoy of consolidation, σ T σ e + P and dσ T dσ e + dp [-] A change in total stess may cause no change in effective stess, if dσ T dp. On the othe hand, a significant incease in σ e may happen without any change in σ T, if fluid pessue deceases. load ai

3 Calculation of total stess and effective stess Suppose a -m column of soil. What ae the total stess (σ T ) and effective stess (σ e ) at the bottom? Assumptions Hydostatic condition Wet bulk density (ρ wb ) of the soil is; 9 kg/m 3 above the wate table kg/m 3 below the wate table σ T (weight of the entie column)/( m ) m. m 3. m -3 σ T? σ e? P ρ w gψ σ e σ T - P Now the soil column is satuated to the top. What ae σ T and σ e at the bottom? 4. m What ae the effects of wate-table ise on the mechanical stength of the soil? σ T? σ e?

4 Compessibility and stess-stain elationship -4 Let s define compessibility (α) in the context of consolidation. Conside a slab of satuated sediments. We change the poe pessue in the slab unde constant load (dσ T ). dσ T dσ e + dp o dσ e -dp One-dimensional stain (ε) is defined by: b db ε b The elastic behavio of the slab is given by a linea stess-stain elationship (Hooke s law): db ε αdσ e α [-] b dσ e Suppose that the base aea of the slab is A (constant). Adb dv α Ab dσ V dσ e Noting that the volume (V) change is pimaily caused by the compaction o expansion of void volume (V void ), dv void α V dσ e dv void Substituting dσ e -dp, α [-3] V dp e σ e Compae this to the equation in page 4-6. We now see that Eq.[-3] is a special case (i.e. constant load) of [-].

5 Land subsidence -5 When an aquife is pumped fo a long time, poe pessue goes down (dp < ) while total stess is constant (dσ T ). As we saw in Section 9, pumping induces dawdown in the aquife. This ceates hydaulic gadient between the aquife and the confining clay layes. Wate is squeezed out of the clay layes and h in the clay layes goes down. Recall that dh d(ψ + z) dψ dp/ρg clay sand clay at a fixed location. Reaanging Eq. [-], we have db -αbdσ e But dσ e - dp -ρgdψ -ρgdh db bαρg dh [-4] Theefoe, dawdown (dh < ) in confining layes esults in consolidation (db < ). Clays geneally have lage α, and db can become vey lage. Fo example, long-tem pumping in the confined aquife unde vey thick lacustine clays in the Mexico City caused sevee land subsidence (> 9 m). Land subsidence can be explained using a sping model. Suppose we open the valve slightly and let wate leak. Fluid pessue gadually deceases and solid gains (spings) suppot moe and moe load. This causes the top plate to go down. load

6 If we inject wate in the sping model, it will bounce back to the oiginal position. Howeve, clay is not a pefect sping, and they do not bounce back completely when wate pessue goes back to the oiginal value. Consolidation is an ievesible pocess. Note also that consolidation of thick clay layes may take yeas o decades because goundwate flow in clay is vey slow. -6 Consolidation by ice sheet Suppose the load suddenly inceases. If the valve is closed, the majoity of exta load is suppoted by wate (dσ T dp). dσ e Nothing happens to the top plate. The exta pessue (dp) is called excess poe pessue. If the valve is opened, wate stats to leak and excess poe pessue slowly dissipates. In the end, pessue goes back to the oiginal value (dp ) and the exta load is completely suppoted by the spings: dσ T dσ e This pocess took place duing the last glacial peiod. Afte the ice sheet eteated fom the Geat Plains, the total stess dopped and the glacial till stated ebounding. Howeve, because consolidation is ievesible, the glacial tills did not fully bounce back to the initial thickness. This phenomena is called oveconsolidation.

7 Dewateing ditches and pits -7 Suppose we want to excavate a ditch paallel to a ive. d x z x Flow lines have both vetical and hoizontal components, but they ae mostly hoizontal. In such case, we may assume that the flow is stictly hoizontal and make a ough estimate of flow ate. By doing so, we ae implying that thee is no vetical gadient of hydaulic head (h), o h is independent of depth. Suppose an impemeable bedock at some depth, and define z at the bedock suface. The h at the WT is numeically equal to the distance (d) between the WT and the bedock suface. Since h does not change vetically h(x) d(x) at any depth. Hydaulic conductivity (K) deceases dastically in the unsatuated zone, and the majoity of flow occus in the zone below the WT. Suppose that the ditch has a length w. The volumetic flow ate () enteing the ditch is; dh dh wd K wkh [-5] dx dx This is called Dupuit-Fochheime (D-F) equation.

8 Reaanging Eq. [-5], dx wkhdh -8 Integating both sides fom x to x L, d(x) h(x) x h h We can gain some physical insight by noting; L dx wk ( hl + h )( hl h ) ( hl + h ) ( hl h ) wk wk L L What does this mean? h h L hdh hl h ( L ) wk wk ( ) hl h [-6] L x L h h L The D-F equation and its solution [-6] ae commonly used in geotechnical applications and also in studies of steamgoundwate inteaction. Note that h is measued fom the bed ock suface and that the following is equied. () The flow diection is mostly hoizontal. () The system is at steady state in an appoximate sense. (3) The majoity of flow occus between the WT and the bedock suface.

9 Now, we look at a simila poblem fo a cicula pit. Let be the adius of the pit. Suppose, fo now, that h h at some distance ( ) away fom the cente of the pit. -9 d() h() h h h h Volumetic flow ate into a cylinde having an abitay is At steady state, is independent of and is equal to the amount of seepage into the pit. Upon eaanging, πk Integating both sides fom to, πk d d dh πh K πkh d hdh πk ( h ln( h h h / ) hdh ) [-7] π K This is the D-F solution in cylindical coodinates. Note the similaity between [-7] and Thiem equation in page 9-. ln dh d ( h h )

Water flows through the voids in a soil which are interconnected. This flow may be called seepage, since the velocities are very small.

Water flows through the voids in a soil which are interconnected. This flow may be called seepage, since the velocities are very small. Wate movement Wate flows though the voids in a soil which ae inteconnected. This flow may be called seepage, since the velocities ae vey small. Wate flows fom a highe enegy to a lowe enegy and behaves