工学类地盘工学特论

工学类地盘工学特论

工学类地盘工学特论.txt
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地盤工学特論 第10回
Stress, Strain, Elasticity and Plasticity
廣岡 明彦 ahirooka@civil.kyutech.ac.jp
http://geo.civil.kyutech.ac.jp
1 2004/6/23
地盤工学特論
前回の講義のまとめ前回の講義のまとめ-1
粘土の排水せん断強度
– エネルギー補正
dy τl =τ ?σ dx
(σ1 ?σ3 )l
地盤工学特論
dε1 + 2dε3 ? ? = (σ1 ?σ3 ) +σ3? ? ? dε1 ? ?
2 2004/6/23
前回の講義のまとめ前回の講義のまとめ-2
排水せん断強度 σ1 f ?σ3 f = 2cd cosφd + (σ1 f +σ3 f )sin φd
φd ≒φ′
cd ≒c′
圧密非排水三軸試験で 求めた φ と圧密排水 三軸試験で求めた φd と の比較
3 2004/6/23
地盤工学特論
前回の講義のまとめ前回の講義のまとめ-3
粘土の残留強度
一面せん断 あるいは リングせん断試験における 応力～変位関係の特徴
地盤工学特論
4 2004/6/23
前回の講義のまとめ前回の講義のまとめ-4
Stress, Strain, Elasticity and Plasticity
model : physical representation in the sense of a scale model ? a conceptual idea or a number of mathematical equations
For Soils mathematical models :
based on theories of elasticity, plasticity, and friction
Critical State Model
地盤工学特論
Schofield and Wroth, 1968 Atkinson and Bransby, 1978
5 2004/6/23
前回の講義のまとめ前回の講義のまとめ-5
Plain Strain
Axial Symmetry
Special case: Solid cylinders of soil in triaxial tests σ’2 = σ’3 δε2 = δε3
Soil : an aggregate of mineral grains with a fluid filling the pore spaces dry ; pore fluid is air alone saturated ; pore fluid is water alone
地盤工学特論 6 2004/6/23
前回の講義のまとめ前回の講義のまとめ-6
effective stress σ’ = σ – u controls soil behavior The principle of effective stress (stated by Terzaghi 1936) ?All measurable effects of a change of stress, such as compression, distortion, and a change of shearing resistance, are due exclusively to changes of effective stress. Mathematical models for soil behavior must be written in terms of effective stress, not total stress.
地盤工学特論 7 2004/6/23
1.3 Analysis of Deformation and Strain
δσ’v, δσ’h
: stress increment δv, δh : small change of dimensions
Mode of deformation. (a) Stresses on a plane element. (b) Continuous straining. (c) Discontinuous slipping. (b) no discontinuities in the element. the behavior in each and every part of the el
ement is the same. (c) all deformations are due to very large strain within the slip zone. → Slip Plane ( in the limit , the zone: zero thicknes

工学类地盘工学特论

s) (b) and (c) often occur simultaneously， but (b) or (c) usually predominates.
8 2004/6/23
地盤工学特論
Increment of plane displacement
(δh) δεx = ? ?x ?(δv) δεz = ? ?z 1 ??(δv) ?(δh) ? δεxz = ? ? + ? 2 ? ?x ?z ?
(δv) ?(δh)? + δγxz = 2δεxz = ?? ? ?z ? ? ?x
the engineer’s shear strain
地盤工学特論 9 2004/6/23
Increment of strain (a) increments of strain in a plane element (positive) (b) principal strain
counterclockwise shear strains :positive
P : pole
地盤工学特論
Mohr’s circle of plane strain corresponding to the increments of strain above
10 2004/6/23
Planes of zero strain increment.
ψ : an angle of dilation
(δε1 +δε3 ) sinψ = ? (δε1 ?δε3 )
δεγ = δε1 ?δε3 δεv = δε1 +δε3
εγ : maximum shear strain εv : volumetric strain (if ε2=0)
P : pole
地盤工学特論
γ = 45°－ ψ / 2
the increment of minor principal strain is negative and tensile 11
2004/6/23
δεv sinψ = ? δεγ
, in the limit,
dεv sinψ = ? dεγ
For the special case of axial symmetry (δε2= δε3)
2 δv δεs = (δε1 ?δε3 ) , δεv = δε1 + 2δε3 = ? 3 v v =1+ e : specific volume 1 1 δγn = (δε1 ?δε3 ) cosψ 2 2
, in the limit,
δεv tanψ = ? δγn
地盤工学特論
dεv tanψ = ? dγ n
12 2004/6/23
Directions of zero strain Increment
δεn = δεv the same value for δγn : the plane of zero
A strain increment From the geometry, the tangent to the point A makes an angle ψ to the δε axis.
P : pole
β = 45°＋ ψ / 2
地盤工学特論
13 2004/6/23
all deformations and strains are contained within slip line ? discontinuous slipping
δm δγn = ? δy δn δεv = ? δy δn dn tanψ = = δm dm
地盤工学特論
Analysis of discontinuous slipping
14 2004/6/23
1.4 Analysis of State of Stress
State of stress in two dimensions
Mohr’s circle of stress corresponding to the state of stress above
P : pole
地盤工学特論
1 ′ (σ1′ ?σ3 ) ′= 2 sin ρ 1 ′ ′ 15 (σ1 +σ3 )2004/6/23 2
stress parameters t’ s’ mobilized angle of shearing resistance : ρ’
1 ′ ′ t′ = (σ1 ?σ3 ) 2 1 ′ ′ s′ = (σ1 +σ3 ) 2 t′ sin ρ′ = s′
For the special case of axial symmetry (σ’2 = σ’3 )
1 ′ ′ ′ ′ q′ = (σ1 ?σ3 ) , p′ = (σ1 + 2σ3 ) 3 q′ η= p′
地盤工学特論 16 2004/6/23
the planes for discontinuous slipping
Stress on planes for which tangents from the origin touch the Mohr’s circle
1 ′ ′ ′ τn = (σ1 ?σ3 ) cos ρ′ 2 1 ′ = (σ1 +σ3 ) cos2 ρ′ ′
′ σn 2 ′ τn tan ρ′ = ′ σn
P : pole
ρ′ α = 45° +
2
17 2004/6/23
地盤工学特論
′ τ n =τ n t′ = t q′ = q
′ σn = σn ? u s′ = s ?u p′ = p ?u
ρ

工学类地盘工学特论

′ ≠ ρ η′ ≠η
Mohr’s circles of total and effective stress
地盤工学特論 18 2004/6/23
1.5 Relationships between stress and strain
Coaxiality condition : principal plains of stress and principal plains of strain and strain increment coincide （共軸） ; …… 此处隐藏：10710字，全部文档内容请下载后查看。喜欢就下载吧 ……