mohanad.alfach (1)

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of Dynamic Analysis Shallow and Machine
Foundations

• Dr.Mohanad Alfach
• Ph.D. in Earthquake Geotechnical Engineering

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Contents

• Fundamentals
• Dynamic Waves Propagation in the Soils.
• Dynamic Properties of Soil
• Dynamic Bearing Capacity of Shallow Foundations
• Dynamic Analysis of Machine Foundations

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Waves

Rayleigh wave

Vertical component
Horizontal component
Relative amplitude
Shear wave


-
-
r -1

Compression wave

r
r -1
Shear window
Wave Type Percentage of Total Energy
Rayleigh 67
Shear 26
Compression 7
Waves
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Waves
Rayleigh, R Surface
Shear,S Secondary
Compression, P Primary
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Material P wave Velocity (m/s) S wave Velocity (m/s)
Air 332  
Water 1400-1500  
Petroleum 1300 - 1400  
Steel 6100 3500
Concrete 3600 2000
Granite 5500 5900 2800 - 3000
Basalt 6400 3200
Sandstone 1400 4300 700 - 2800
Limestone 5900 6100 2800 3000
Sand (Unsaturated) 200 1000 80 - 400
Sand (saturated) 800 2200 320 - 880
Clay 1000 2500 400 - 1000
Glacial Till (Saturated) 1500 2500 600 - 1000
Yawing
Where Vp Compression Wave Velocity.Shear
Wave Velocity Vs ? density of the medium µ
Shear Modulus ? Bulk Modulus
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Dynamic Properties of Soil
Saturated Clay
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Sand
According to Several Triaxial test results on
different dry sands
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Foundation Movement
Z
Vertical
Y
Yawing
?
Pitching
f
X
Lateral
Rocking
?
Longitudinal
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Failure Mechanism of Shallow Foundations
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Static Bearing Capacity of Shallow Foundations
The static ultimate bearing capacity of shallow
foundation subjected to vertical loading can be
given by the equation
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The values of Nq and N? can be represented by the
following equations
Shape Factors
Depth Factors
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Seismic Bearing Capacity and Settlement in
Granular Soil
In 1993, Richards et al. developed a seismic
bearing capacity theory.
According to this theory, the ultimate bearing
capacities for continuous foundations in granular
soil are
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And
Where
and,
Where
The following table provide the values of bearing
capacity factors Nq , N?
bearing capacity factors
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Example
Solution
From next left figure,
, and From next right figure,
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From This figure,
,Also, from the next table
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Machine Foundation Analysis
In the design of machine foundations , the
following general rules may be kept in mind to
avoid possible resonance conditions
1- The resonant frequency of foundation-soil
system should be less than half the operating
.frequency for high-speed machines (that is
operating frequency )
2- For slow-speed machineries (speed less than
about 350-400 Cpm ), the resonant frequency of
the foundation-soil system should be at least two
times the operation frequency.
3- In all types of foundations, the increase of
weight will decrease the resonant frequency.
4- An increase of will increase the resonant
frequency of the foundation.
5- An increase of shear modulus of soil will
increase the resonant frequency of the foundation.
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Design Questions

• How Does It Fail?
• Static Settlement
• Dynamic Motion Too Large (0.02 mm is large)
• Settlements Caused By Dynamic Motion
• Liquefaction
• What Are Maximum Values of Failure?
  (Acceleration, Velocity, Displacement)

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Fundamentals-Modeling-Properties-Performance
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Calculation Procedure for foundation response-
Vertical Vibration
The general procedure is outlined by this steps
A. Resonant Frequency
1- Calculation of natural frequency
2- Calculation of damping ratio
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3- Calculation of the resonance frequency
for constant force type excitation
for the case of
for rotating mass-type excitation
for the case of
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B. Amplitude of vibration at resonance
For constant force type excitation
Where
and
so
For rotating mass-type excitation
Where
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C. Amplitude of vibration at frequency other than
resonance
For constant force type excitation
For rotating mass-type excitation
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Example
Solution
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