203552 advanced soil mechanics - kasetsart · pdf file203552 advanced soil mechanics...

203552 Advanced Soil Mechanics

Dr.Warakorn Mairaing 1

Dr. Warakorn MairaingAssociate Professor

Civil Engineering DepartmentKasetsart University, Bangkok Tel: 02-579-2265Email: [email protected]

Dr. Warakorn MairaingDr. Warakorn MairaingAssociate ProfessorAssociate Professor

Civil Engineering DepartmentCivil Engineering DepartmentKasetsart University, Bangkok Kasetsart University, Bangkok Tel: 02Tel: 02--579579--22652265Email: [email protected]: [email protected]

Lecture No. 2

Soil PermeabilitySoil Permeability



Soil permeability (k) or Hydraulic conductivity is soil property which allow the seepage of fluid through its interconnected void spaces.

According to Darcy’s law (Laminar’flow)

v=ki If i=1

Then k=v so permeability (k) is the seepage velocity through soil when subjected to the hydraulic gradient of unity (i = 1)

Soil permeability varies on very wide range from 10-10 cm/sec to 10o

cm/sec (10 logarithmic eyeless)

Soil Permeability

Factors affect soil permeability

There an 2 main groups of factors

1. Fluid properties flow through soil (Permeant)2. Pore characters in the soil mass (Porous Media)

Permeability Model

b) Capillary Tubesa) Soil Mass

If total soil x-section = A, Degree of Saturation = S and porosity = n, Then area of water chancels = S.n.A.

Soil Permeability



- Taylar (1984) using poiseville’s law of flow through. Capillary tubes to formulate permeability as;

( ) ce

eDk s ⋅+

⋅⋅=1

32

μγ

---(1)

- Kazeny – Carman (1927, 1956)

( )eG

skk

+⋅⋅=1.

1 3

20 μ

γ---(2)

Soil Permeability

when

Ds = effective particle diameters, γ = unit wt. of waterμ = viscousity of water, e = void ratioC = shape factor, ko = pore shape and flow path factorSo = specific surface area

,...),,,,,( oo kSSDuvefk =∴ ---(3)

Soil Permeability

Equation (3) is soil permeability model function consisted of

1. Permeant ex. Fresh water, crude oil, contaminant to eliminate the various properties of permeants, the “Absolute Permeability” (k) is proposed as

μγ.kk =

---(4)

For fresh water at 20oc when u and r are known, then

sec)/(1002.1)( 52 cmkcmk ⋅×= −---(5)



2. Soil or porous media soil, rock, porous stone, sand filter etc.

- Soil larger than coarse gravel

- Soil smaller than coarse gravel

- Cohesive soil

Turbulent flow occurred.? (ND > 1) Darcy’s law invalid.

Darcy’s law is valid Kazeny – Carman and Equation (3) is applied

Permeability model (Eq.3) may not valid due to the influences ofDiffused Double layer or Surface chemical properties of soil particles

Soil Permeability

In general factors influence soil permeabilitics are :

1. Particle size distribution (Pore size distribution)

2. Void ratio (e)

3. Soil mineral (CEC, defuses D.L.)

4. Soil Structure (Flocculation, Dispassion)

5. Degree of Saturation (S)

Soil Permeability

1. Particle Size for sand and silt

Hazen

Land and Washburn

Kane

k ≅ 100 D102

k ≅ (1-40) D102

k ≅ 40 D102



2. Void ratio

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=e

efk1

3

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=e

efk1

2

( )efk 10=

- Kozeny

Soil Permeability

3. Soil Mineral and Soil Structure for clay

3.1 Defused Double Layer Free water3.2 Dispersed and Flocculated Structures3.3 Anisotropic permeability (kx ≠ ky)

4. Degree of Saturation

High degree of saturation high permeability saturation increase flow area (less are void)

Soil Permeability



Soil Permeability

Soil Permeability



Soil Permeability

ชวงของคาความซึมน้ําของดินฐานรากชนิดตางๆ

Pore Pressure Development



PORE PRESSURE DEVELOPMENT

PORE PRESSURE DEVELOPMENT

When partially or fully saturated soils are subjected to external load or change in ground water level, there will be a change in pore water pressure called “Excess pore pressure (Δu)”. This condition occurs temporarily until it reach to stable final pressure.

It is very important to predict Δu since it is related to many soil mechanical behaviors such as strength, consolidation


Two periods are involved during loading and subsequence times,

1. Undrained loading; When load or excess pore pressure change suddenly

Δu = (P.P.).ΔσσΔΔ

=uPP .. ---(1)

When P.P. = Pore pressure parameterΔu = Pore pressure change.Δσ = Total pressure change.



2. Pore Pressure Dissipation; when applied load is rather constant and the excess pore pressure graduately changes until it reaches static pore pressure (us)

Ex. Figure 1 is the typical case of confined compression (typical consolidation test)

Figure 2 is the surface loading on soil layer ---- Field embankment test for SBIA (Suwanabhump Airport)

Figure 3 is the ground water lowering ---- Bangkok ground water pumping and Land subsidence.





ผลที่ตามมาจากความดันน้ําลดลง

( p’ = p – uw )p’ เพิ่มขึ้น

หนวยแรงกดทั้งในแนวดิ่งและแนวราบ เพิ่มขึ้น

การทรุดตัวของชั้นดินเพิ่มขึ้นแรงตานทานของเสาเข็มเพิ่มขึ้นหนวยแรงดันของโครงสรางใตดินเพิ่มขึ้น

อ่ืนๆ

การเปลี่ยนแปลงแรงตานทานตอฐานรากเสาเข็มการเปลี่ยนแปลงแรงตานทานตอฐานรากเสาเข็ม



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0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Pore Water Pressure (t/m2)

Dep

th (

m.)

Hydrostatic, u0

Pore Pressure, ut

BK

PD

NL

NB

SK

PT

TB

PN

ตัวอยางแรงดันน้ําที่มีการเปลี่ยนแปลงในชั้นน้ําตางๆตัวอยางแรงดันน้ําที่มีการเปลี่ยนแปลงในชั้นน้ําตางๆ



Skempton’s Pore Pressure Parameters

Prof. Skempton (1954) of Imperial College (London) developed the theory for estimating the excess pore water pressure (Δu) due to increase of total stress in soil mass.

Assuming total stresses (Δσ) changes happen suddenly. (at Δt = 0)


Skempton’s Pore Pressure =σΔΔu ---(1)

The magnitude of Δu is depended on;1. Compressibility of soil skeleton (Soil = Void) = Csk2. Compressibility of water (pore water) = Cw3. Magnitude of total stress change = Δσ

Then

( )σΔ=Δ ,, wsk CCfu ---(2)

Case study on;

1. Confined Compression

2. Isotropic Compression

3. Uniaxial Stress (Unconfined Compression)

4. Triaxial Compression

Will be considered.




1. Confined Compression (1-D Consolidation, Land Reclamation)

Compressibility of soil Skeleton

Compressibility of pore water

KgCmv

v

C esk

26

1

10−≅Δ

Δ

=σ ---(3)

---(4)Kg

Cmu

vv

C ww

2910−≅

Δ

Δ

=


ΔVw = Change in water volume 0nVuCw ⋅Δ⋅=

01 VCsk ⋅Δ⋅= σΔVsk = Change in soil skeleton volume ---(5)

---(6)

Relationship of total and effective stresses ---(8)uΔ−Δ=Δ 11 σσ

In particular soil mass; change of soil volume = Change in water vol.

---(7)0nVuC w ⋅Δ⋅=01 VC sk ⋅Δ⋅= σ)6()5.( EqEq =∴


Then substitute (8) in (7)

( ) uCwnuCsk Δ⋅⋅=Δ−Δ 1σ ( ) 1.. σΔ=+Δ skskw CCCnu

For saturated soil, when Cw ≈ 10-9 Cm2/kg and Csk ≈ 10-6 Cm2/kg then Eq.(9) become

0.11

1""w

≅

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

skCCn

C

( ) ""Pr1

CParameteressurePorenCC

Cu

wsk

sk =+

=ΔΔσ

---(9)



2. Isotropic Compression

Change in Soil Skeleton Volume

330220110 σσσ Δ⋅⋅+Δ⋅⋅+Δ⋅⋅=Δ sksksksk CVCVCVV ---(10)


Change in Pore Water Volume

uCVnV ww Δ⋅⋅⋅=Δ 0 ---(11)

Eq. (10) = Eq. (11) for the same soil mass

3302201100 σσσ Δ⋅⋅+Δ⋅⋅+Δ⋅⋅=Δ⋅⋅⋅∴ skskskw CVCVCVuCVn

If the applied stresses are truely isotropic compression, then

)(321 uΔ−Δ=Δ=Δ=Δ σσσσ

---(12)


From Eq.(12) ( )( )321 skskskw CCCuuCn ++Δ−Δ=Δ⋅⋅ σ

""Pr321

321 BParameteressurePoreCCCnC

CCCu

skskskw

sksksk =+++

++=

ΔΔσ

---(13)

---(14)



13

13

3""+

=+

==ΔΔ

sk

wskw

ski

CnCCnC

CBuσ

If soil is isotropic material, thus Csk1=Csk2=Csk3=Csk.; then

---(15)


If Soil is saturated normally consolidated clay, then the term

0.1103

4 ≈→≈⋅ − BandCCn

sk

w

But for O.C. and Rock Which are precompressed in the past

B < 1.0 as shown on Table 1

3. Uniaxial Stress (Unconfined Compression)

Where soil mass is compressed in vertical direction, it will expand in other directions. (Swelling Coefficients = Cs2 and Cs3)


Considering uandu Δ−=Δ=ΔΔ−Δ=Δ 3211 σσσσ ---(16)



Change in soil-void volume = change in pore water volume

( ) ( ) ( )uCVuCVuCVuCVn ssskw Δ−⋅⋅+Δ−⋅⋅+Δ−Δ⋅⋅=Δ⋅⋅⋅ 30201100 σ

( ) 11321. skssskw CCCCnCu ⋅Δ=+++Δ∴ σ

( )321

1

1 ssskw

sk

CCCnCCu

+++=

ΔΔσ

---(17)

If soil is Isotropic and linear elastic material


Then ""Pr

3

1

1

DParameteressurePore

CCn

u

sk

w=

+=

ΔΔσ

---(18)

4. Triaxial Compressive Stress

Unconsolidated-Undrained triaxial compression test in consisted of 2-stages of applied stresses as;

1. Stage I Isotropic Compression

When soil sample is applied by all around pressure, Δσ3

2. Stage II Uniaxial Compression (Shearing)

When soil sample is applied by vertical stress of Δσa= (Δσ1 Δσ3)




Confining Stage Shearing Stage

Pore Pressure due to Stage 1 : Isotropic compression

Δu2 = D (Δσ1- Δσ2)

Pore Pressure due to Stage 2 : Uniaxial compression

Δu1 = B Δσ3


+

∴ Overall pore pressure during UU-Triaxial Test

Δu = Δu1 + Δu2 = B Δσ3+ D (Δσ1- Δσ2) ---(19)

Special case for Saturated Soil and Incompressible pore water, then

B ≈ 1.00

From equation (17) when and00.01

≈sk

w

CC

Cs2 = Cs3 = Cs , then

""Pr21

1

1

AParameteressurePore

CC

u

sk

sa=

+=

ΔΔσ


---(20)

And eq.(19) becomes.

Δu = Δσ3+ A (Δσ1- Δσ3)

As we can see from table 1 that “A-” parameter is depended on it stress history

.)("" OCRfA =∴ ---(21)

When OCR. = Over Consolidation Ration0v

m

σσ

=

For Bangkok Clay and others Sedimentary soil, The Value of “A” can be seen on Figure 9



Determination of A-Parameter from Stress-path

BDBCu

Afa

ff ⋅

=Δ

=2σ312 σσσ Δ−Δ

Δ=

Δ=

⋅=

uau

xzxyA





อิทธิพลที่มีตอ Pore Pressure Parameter “A” คา Parameter “A” ไมคงที่ ข้ึนอยูกับ





Prediction of Pore Pressure in the Field

Predictions of excess pore pressure in the field are related to stability, bearing capacity and settlement problem

Since effective strength;

and settlement;

φστ tan)( ⋅−+= uc

0

0

0

log1 P

uPHe

CS c Δ+⋅⋅

+=


Ex.

1. Stability Problem

2. Bearing Capacity – Similar to Stability




( )313 .. σσσ Δ−Δ+Δ=Δ ABuExcess P.P.;

Dissipation of Δ u leading to consolidation and settlement of soil layer.

3. Consolidation and Settlement


ตัวอยาง Preloading Area





Henkel’s Pore Pressure Parameters.

In case of plan-strain stress condition when stresses on x,y and z directions are all different. Henkel (1960) proposed that intermediate principal stress (Δσ2) should be included in pore pressure calculation.

octoct au τσ Δ⋅+Δ=Δ .3

when

and

( )32131 σσσσ Δ+Δ+Δ=Δ oct

213

232

221 )()()(

31 σσσσσστ Δ−Δ+Δ−Δ+Δ−Δ=Δ oct

---(22)

---(23)

---(24)

Special case for triaxial loading when Δσ2 = Δσ3, then from eq. (22), (23) and (24)

( ) ( )3131 2

32 σσσσ

Δ−Δ+Δ+Δ

=Δ au ---(25)




Special case for uniaxial loading when Δσ1-Δσ3 = Δσ1 and Δσ2 = Δσ3 = 0, then

⎟⎠⎞

⎜⎝⎛ +Δ=Δ 231

1 au σ

From eq.(20), Skempton’s parameter for uniaxial loading

)(0 1σΔ+=Δ Au

Equate eq (26) = (27), then

231

⋅+= aA or ⎟⎠⎞

⎜⎝⎛ −=

31

21 Aa

When A = Skempton pore pressure parametera = Henkel pore pressure parameter

---(28)

---(26)

---(27)


ตัวอยาง

ถนนบนดินเหนียวออน มีคันถนนสูงจากผิวดิน 2.00 เมตร กวาง 25 เมตร ดินบดอัดคันถนนมีความหนาแนน 2.0 ตันตอลบ.ม. จากการทดสอบ Triaxial Test ของดินฐานราก ทราบวาดินมีคุณสมบัติดังนี้

“A” parameter = 0.90 , υ = 0.45

จงหาวา ที่จุด A, B และ C ในดินฐานรากจะมีความดันน้ําสวนเกินเกิดขึ้นเทาใด โดยใหถือวาการกอสรางเกิดขึ้นเร็วมาก

- Surcharge load

ที่ผิวดิน = 2x2 = 4 ตัน/ตร.ม.

- จากตารางที่ 3.4

“Advanced Soil Mechanics” By B.M. Das page 182

B = 12.5 , z = 6.25 m.




1.1980.29961.3890.34721.9880.49690.51.0C

0.5100.12741.5680.39203.6110.90280.50.5B

001.7990. 44983.8380.95940.50A

σxzσxz /qσxσx /qσzσz /qσxzσxσzz/bx/bตําแหนง


จาก Mohr’s Diagram

22

1 22⎟⎠⎞

⎜⎝⎛ =

+++

= xzxz

zx σσδσσσ

22

3 22⎟⎠⎞

⎜⎝⎛ =

+−+

= xzxz

zx σσδσσσ

( ) ( )31312 45.0 σσσσνσ +=+=

1.5200.4542.9231.1981.9881.389C

2.3311.4483.7310.5103.6111.568B

2.5371.7993.8380.03.8381.799A

σ2σ3σ1σxzσzσxตําแหนง

---(1)

---(2)

---(3)




Henkel’s pore pressure

⎟⎠⎞

⎜⎝⎛ −=

31

21 Aa 400.0

319.0

21

=⎟⎠⎞

⎜⎝⎛ −=a

( ) ( ) ( )2132

322

21321

3σσσσσσσσσ

Δ−Δ+Δ−Δ+Δ−Δ+++

=Δ∴ au

ที่ตําแหนง A Pore Pressure ΔμA = 3.55 ตัน / ตร.ม.B Pore Pressure ΔμB = 3.43 ตัน / ตร.ม.C Pore Pressure ΔμC = 2.62 ตัน / ตร.ม.






4.07E-073.66E-06CL3

1.00E-081.00E-08Slurry4

3.30E-091.00E-08Dam5

1.00E-031.00E-03Relief Well6

6.35E-066.35E-06SP-SM7

1.73E-071.56E-06SC2

1.00E-101.00E-10Rock1

Kv

Cm/sec

Kh

Cm/sec

Soil TypeMaterial No.


203552 advanced soil mechanics - kasetsart · pdf file203552 advanced soil mechanics...

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