Strength Analysis in Geomechanics Part 1 ppsx
Strength Analysis in Geomechanics Part 1 ppsx
... of structures
Strength Analysis in
Geomechanics
Serguey A. Elsoufiev
With 15 8 Figures and 11 Tables
Contents
1 Introduction: Main Ideas 1
1 .1 Role of Engineering Geological Investigations . ... . . . . . . . . . . . . . . 16 6
1
Introduction: Main Ideas
1. 1 Role of Engineering Geological Investigations
An estimation of conditions of buildings and structures installation...
Strength Analysis in Geomechanics Part 9 ppsx
... 2ψ)
+cotχ(g
µ
sin 2ψ) + 4 (1 − µ)g
µ
cos 2ψ. (5 .11 6)
Putting (3 .11 5) into (2.78) we derive
(g
µ
sin 2ψ)
+(g
µ
sin 2ψ)
cot χ +(9µ (1 − µ) − 1/ sin
2
χ)g
µ
sin 2ψ
+ 2(2 − 3µ)(g
µ
cos 2ψ)
=0.
(5 .11 7)
Combining ... (5 .12 9)
σ
θ
=p (1 µ)(b/r)
µ
/ (1 − β
µ 1
) (5 .13 1)
where β = b/a. Putting σ
θ
into (2.66) we find for the dangerous (internal)
surface
e
−αε
ε =3β (1 − µ)
m
Ω(t...
Strength Analysis in Geomechanics Part 2 ppt
... compression and torsion (Fig. 1. 13) the solution of (1. 18),
(1. 19) can be presented in form
(M/M
∗
)
2
+F/F
∗
= 1 (1. 20)
16 1 Introduction: Main Ideas
F
M
l
2r
M
F
Fig. 1. 13. Circular bar under compression ... The
1. 4 Main Properties of Soils 11
Ot
1
2
3
S
Fig. 1. 9. Combined in uence of time and loading
Combined In uence of Time and Loading
At small loads F the settli...
Strength Analysis in Geomechanics Part 4 potx
... −(2p/π)
1
1
(y
2
+(x− η)
2
)
−2
dη
or after integration
σ
y
=p(υ
1
− υ
2
+0.5(sin 2υ
1
− sin 2υ
2
))/π. (3.52)
Similarly we find
σ
x
=p(υ
1
−υ
2
+0.5(sin 2υ
2
−sin2υ
1
))/π, τ
xy
= p(sin
2
υ
1
−sin
2
υ
2
)/π. ... σ
r
=(K
1
/
√
2πr) (1 + sin
2
(θ/2)) cos(θ/2),
τ
rθ
=(K
1
/2
√
2πr) sin θcos(θ/2), τ
e
=(K
1
/2
√
2πr) sin θ,
(3.90)
u
r
=(K
1
/G)
r/2π(0.5(κ +1) − cos
2
(θ...
Strength Analysis in Geomechanics Part 5 potx
... again can see that τ
e
in (3 .10 6), (3 .11 0) differ by a constant multiplier.
3.2 .13 Inclined Crack in Tension
By a combination of the solutions in Sects. 3.2.7, 3.2 .11 a strength of a body
with inclined ... =r/aandz=0are
u
z
(ρ, 0) = 4 (1 −ν
2
)pa
1 − ρ
2
/πE(ρ ≤ 1) ,
σ
z
= 2p (1/
ρ
2
− 1 − sin
1
(1/ ρ))/π (ρ > 1) .
(3 .15 0)
Since near the crack edges the first me...
Strength Analysis in Geomechanics Part 6 ppt
... k
1
1 − (k
1
)
2
− sin
1
k
1
= (1 k
1
)(−p − (1 − k
1
)l/4h). (4 .18 )
Then we take integral equilibrium equation at contact surface as
2Q = τ
yi
(1 + k
1
)l
which gives 1 + k
1
= 2q where q ... rigid plates.
Putting in (4 .12 )
τ = τ
e
sin 2ψ, σ
r
− σ
θ
=2τ
e
cos 2ψ (4 .13 )
a) b)
P
Fig. 4.4. Slip lines
4.2 Plane Deformation 10 3
0
1
1
2
1
0
11
0
0 45 90 13...
Strength Analysis in Geomechanics Part 7 pdf
... 11 7
we have
R
1
=P
1
sin α
1
− P
1
cos α
1
tan ϕ
1
− c
1
L
1
,
R
2
=P
2
sin α
2
− P
2
cos α
2
tan ϕ
2
− c
2
L
2
+R
1
cos(α
1
− α
2
)
or
R
i
=P
i
sin α
i
− P
i
cos α
i
tan ϕ
i
− c
i
L
i
+R
i 1
cos(α
i 1
− ... supposing tan(C − θ)=
√
x we receive
4dln(f/D) = (1 −
(m + 1)
2
+ 4mx)dx/x (1 + x). (5.5)
and after integration we find
f=D((
√
− m +1) /(
√
+m− 1) )
(m 1) /...
Strength Analysis in Geomechanics Part 8 docx
... m
J=0.5K
m +1
m(2m + 1) /f
(π)/
m 1
f
(π)
1
0
( (1 −ξ)/ξ)
1/ (1+ m)
dξ.
Using equation J = J
1
we have
K=((κ +1) πσ
2
l/4GΩ
1
(t)I
1
(m))
1/ (1+ m)
.
Here
I
1
(m) = (2m +1) (m +1) /f
(π)/
m 1
f
(π)Γ((2m +1) /(m +1) )Γ((2+m)/ (1+ m))
and ... σ
θ
=Kr
1/ (m +1)
s(s 1) f, τ
rθ
=Kr
1/ (m +1)
(1 −s)f
(5.92)
and
ε
θ
= −0.5Ω
1
(t)K
m
r
−m/(m +1)
F
m 1
(f
...
Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 1 ppsx
... 1, 0)
(9, 4, 0) (59, 6, 5, 4, 3, 1, 0)
(10 , 3, 0) (60, 1, 0)
(11 , 2, 0) ( 61, 5, 2, 1, 0)
(12 , 6, 4, 1, 0) (62, 6, 5, 3, 0)
(13 , 4, 3, 1, 0) (63, 1, 0)
(14 , 5, 3, 1, 0) (64, 4, 3, 1, 0)
(15 , 1, ... single full-word exclusive-or operation:
#define IB1 1 Powers of 2.
#define IB2 2
#define IB5 16
#define IB18 13 1072
#define MASK (IB1+IB2+IB5)
int irbit2(unsigned long...
A Complete Guide to Programming in C++ part 1 ppsx
... 0-7637 -18 17-3
1. C++ (Computer program language) I. Kirch-Prinz, Ulla. II. Title.
QA76.73.C153 P73 713 20 01
005 .13 '3—dc 21 20 010 29 617
2090
Chief Executive Officer: Clayton Jones
Chief Operating ... string, which is used to repre-
sent strings. In addition to defining strings, the chapter looks at the various methods of
string manipulation. These include inserting and erasin...