184 Ground improvement by deep vibratory methods
2. Earthquake input values.
• Number of equivalent stress cycles (N eq )
• Relevant duration of shaking time (t d )
3. Improvement factor β for the chosen stone column grid is calculated
according to Section 4.3.2. The increase of the overall soil stiffness as
represented by the β-value is calculated with the Priebe method and is
responsible for the reduction of the vertical deformations. It is implied
that it reduces in the same amount the horizontal shear stresses by an
equivalent increase of the shear modulus G.
4. Determination of layer-dependent cyclic stresses during the design
earthquake using SHAKE 2000. The original acceleration time history at bedrock level is introduced and the τ σ
/ ′ 0 ratio (CSR) is calculated
for each soil layer using Equation 3.7. The acceleration is than scaled to
reach design peak ground acceleration (PGA) of 0.5 g for the structures
according to the design requirement.
5. Stress ratio reduction. The improvement factor β (here calculated by
the Priebe method) is applied on the shear modulus of the unimproved
soil between the piles and a reduced CSR is calculated.
6. Number of cycles to cause liquefaction (N l ). The N l value is preferably
established in the laboratory by undrained cyclic simple shear or triaxial
tests on the in-situ soils. It can, however, alternatively, be estimated using
published results as by Finn et al. (1971), provided comparability of the
in-situ soil characteristics can be ensured.
7. Reduction of liquefaction potential by improved drainage. With the
method described in Section 4.3.4 the time factor T ad is calculated
for the chosen drain configuration using Equation 4.45. With the
earthquake severity ratio N eq /N l now being established the respective
chart in Figure 4.24 can be chosen. The intersection of the d/d e value
(relative stone column spacing) represented by the drain configuration
with the calculated time factor T ad in the chart gives the greatest pore
pressure ratio r g = u g v
/ ′
σ allowed in the design.
For the 80 cm diameter stone columns placed in square pattern of 2.1 m
within the 100 cm diameter bored piles a time factor T ad = 21 was calculated for the upper sand layers. With an earthquake severity ratio N eq /
N l = 39/11 = 3.4 the lower right graph in Figure 4.24 is chosen where the
intersection of T ad = 21 with d/d e = 0.34 gives r g = 0.6. Defining the safety
against liquefaction of a specific layer as
η = 1/r g
(4.100)
We see that for the silty sand layer considered in this instance a safety factor of 1.67 against liquefaction exists. This calculation has to be carried out
for all soil layers which are likely to liquefy during an earthquake event.
2. Earthquake input values.
• Number of equivalent stress cycles (N eq )
• Relevant duration of shaking time (t d )
3. Improvement factor β for the chosen stone column grid is calculated
according to Section 4.3.2. The increase of the overall soil stiffness as
represented by the β-value is calculated with the Priebe method and is
responsible for the reduction of the vertical deformations. It is implied
that it reduces in the same amount the horizontal shear stresses by an
equivalent increase of the shear modulus G.
4. Determination of layer-dependent cyclic stresses during the design
earthquake using SHAKE 2000. The original acceleration time history at bedrock level is introduced and the τ σ
/ ′ 0 ratio (CSR) is calculated
for each soil layer using Equation 3.7. The acceleration is than scaled to
reach design peak ground acceleration (PGA) of 0.5 g for the structures
according to the design requirement.
5. Stress ratio reduction. The improvement factor β (here calculated by
the Priebe method) is applied on the shear modulus of the unimproved
soil between the piles and a reduced CSR is calculated.
6. Number of cycles to cause liquefaction (N l ). The N l value is preferably
established in the laboratory by undrained cyclic simple shear or triaxial
tests on the in-situ soils. It can, however, alternatively, be estimated using
published results as by Finn et al. (1971), provided comparability of the
in-situ soil characteristics can be ensured.
7. Reduction of liquefaction potential by improved drainage. With the
method described in Section 4.3.4 the time factor T ad is calculated
for the chosen drain configuration using Equation 4.45. With the
earthquake severity ratio N eq /N l now being established the respective
chart in Figure 4.24 can be chosen. The intersection of the d/d e value
(relative stone column spacing) represented by the drain configuration
with the calculated time factor T ad in the chart gives the greatest pore
pressure ratio r g = u g v
/ ′
σ allowed in the design.
For the 80 cm diameter stone columns placed in square pattern of 2.1 m
within the 100 cm diameter bored piles a time factor T ad = 21 was calculated for the upper sand layers. With an earthquake severity ratio N eq /
N l = 39/11 = 3.4 the lower right graph in Figure 4.24 is chosen where the
intersection of T ad = 21 with d/d e = 0.34 gives r g = 0.6. Defining the safety
against liquefaction of a specific layer as
η = 1/r g
(4.100)
We see that for the silty sand layer considered in this instance a safety factor of 1.67 against liquefaction exists. This calculation has to be carried out
for all soil layers which are likely to liquefy during an earthquake event.