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Chương 2 TẢI TRỌNG VÀ LỰC TÁC DỤNG
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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
of
developed
Figures show the procedure of earth pressure analysis in the case of sloping terrain. The resulting earth shape pressure distribution acting on the construction is obtained triangular from the sum of distributions 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: resultant due to surface or concentrated load - F
- 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: resultant due to surface or concentrated load - F
distance of loading from the back of wall - a
- 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: angle of internal friction of soil - φ angle derived from the following formulas - ε
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where: slope inclination
angle of internal friction of soil
- β φ - - angle of friction structure - soil δ - back face inclination of the structure
α 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: slope inclination - β - angle of internal friction of soil φ - angle of friction structure - soil δ - back face inclination of the structure α
The resultant of the increment of active earth pressure due to line loading f is provided by:
where: angle of critical slip plane -
- angle of internal friction of soil ϑa φ - angle of friction structure - soil
δ f - magnitude of line surcharge
