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

27 Principle of the earth pressure computation in the case of broken terrain β < φ Distribution of earth pressures in case of broken terrain Figures show the procedure of earth pressure

1

Chương 2 TẢI TRỌNG VÀ LỰC TÁC DỤNG

3

4

???

5

7

8

9

K bđ = 1/K cđ ???

Theo Coulomb

11

K bđ = 1/K cđ Theo Rankine

12

Phương pháp Coulomb

13

15

16

Phương pháp Rankine

17

19

20

21

23

24

Phương pháp Coulomb Phương pháp Rankine

25

27

Principle of the earth pressure computation in

the case of broken terrain β < φ

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

28

Principle of the earth pressure computation in the

case of broken terrain for β > φ

29

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

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

31

Alternate loading for calculation of increment of

active earth pressure

32

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

33

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 - angle of internal friction of soil

ε - angle derived from the following formulas

where: β - slope inclination

φ - angle of internal friction of soil

δ - angle of friction structure - soil

α - back face inclination of the structure

c - cohesion of soil

γ - unit weight of soil

h - 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:

35

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