Bài giảng Thủy công: Chương 2 (Tải trọng và lực tác dụng) TS. Trần Văn Tỷ (p3)

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Chương 2

TẢI TRỌNG VÀ LỰC TÁC DỤNG

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???

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Theo Coulomb

Kbđ = 1/Kcđ ???

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Theo Rankine

Kbđ = 1/Kcđ
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Phương pháp Coulomb

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Phương pháp Rankine

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Phương pháp Coulomb

Phương pháp Rankine

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Distribution of earth pressures in case of
broken terrain
Figures show the procedure of
earth pressure analysis in the
case of sloping terrain. The
resulting shape of earth
pressure distribution acting on
the construction is obtained
from the sum of triangular
distributions developed by
individual effects acting on the

construction.

Principle of the earth pressure computation in
the case of broken terrain β < φ

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Principle of the earth pressure computation in the
case of broken terrain for β > φ
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Concentrated surcharge
The concentrated load (resultant F due to surface or concentrated
load – see figure) is transformed into a line load with a limited
length. If the width of surface loading b is smaller than the
distance a from the back of wall (see figure) the alternate line
loading f having length 1+2*(a+b) receives the form:

where:

F

-

resultant due to surface or concentrated load

a

-

distance of loading from the back of wall

l

-

length of load

b

-

width of surface loading

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If the width b of surface loading is greater than the distance a
from the back of wall (see figure) the alternate line loading f
having length 1+2.(a+b) and width (a+b) reads:

where:

F

-

resultant due to surface or concentrated load

a

-

distance of loading from the back of wall

l

-

length of load

b

-

width of surface loading

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Alternate loading for calculation of increment of
active earth pressure

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Line surcharge
Vertical infinitely long line loading f acting on the ground
surface parallel with structure leads to a triangular increment of
active earth pressure applied to the structure over a given
segment hf– see figure:

Diagram of increment of active earth pressure due to vertical
line loading acting on ground surface
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Action of the line surcharge is deterimened such that two lines
are drawn from the point of application following angles
φandϑa(corresponding to the critical slip surface), which is
provided by:

where:

φ

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angle of internal friction of soil

ε

-

angle derived from the following formulas

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where:

β

-

slope inclination

φ

-

angle of internal friction of soil

δ

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angle of friction structure - soil

α

-

back face inclination of the structure

c
γ
h

-

cohesion of soil
unit weight of soil
assumed depth

For non-homogeneous soil and inclination of ground surfaceβsmaller than the
angle of internal friction of the soil φ the value of the angle ε is given by:

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where:

β

-

slope inclination

φ

-

angle of internal friction of soil

δ

-

angle of friction structure - soil

α

-

back face inclination of the structure

The resultant of the increment of active earth pressure due to line loading f
is provided by:

where:

ϑa

-

angle of critical slip plane

φ

-

angle of internal friction of soil

δ

-

angle of friction structure - soil

f

-

magnitude of line surcharge
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