Methods for predicting a stability of a steel cylinder against tilt

A method for predicting a stability of a steel cylinder against tilt comprising:

• Step 1, obtaining water level line information, soil layer information, and external load data of burial environment of the steel cylinder, the soil layer information including a thickness (hi) of a soil layer, a density (γi) of the soil layer, a cohesive force (Ci) of the soil layer, a friction angle (φi) of the soil layer, and a friction coefficient (δ1) between a soil body and the steel cylinder;
• Step 2:
• in response to determining that the steel cylinder is tilted towards a seaward side, assuming that a coordinate of a rotation point (O) at which the steel cylinder is tilted is (Rxi, Ryi), then a soil body outside the steel cylinder at a land side above the rotation point (O) and a soil body outside the steel cylinder at the seaward side below the rotation point (O), are active soil pressures (Pa1) and (Pa2) respectively, and a soil body outside the steel cylinder at the land side below the rotation point (O) and a soil body outside the steel cylinder at the seaward side above the rotation point (O), are passive soil pressures (Pp1) and (Pp2), respectively;
• in response to determining that a burial soil of the steel cylinder is cohesionless soil and a slope surface of filled soil at the land side is horizontal, determining the active soil pressures and the passive soil pressures outside the steel cylinder by using Rankin theory;
• Step 3:
• determining a filler pressure inside the steel cylinder, including:
• 3(i):
• dividing an interior of the steel cylinder into three sections from top to bottom, the three sections including an AB section, a BC section, and a CD section, respectively, wherein
• a height of the AB section is denoted as
• h
• 1
• =
• D
• 0
• ·
• tan
• ⁡
• (
• 45
• +
• φ
• 2
• -
• δ
• )
• ,
• a height of the CD section is denoted as
• h
• 3
• =
• D
• 0
• ·
• tan
• ⁡
• (
• 45
• -
• φ
• 2
• )
• ,
• a height of the BC section is denoted as h2=H−h1−h3,
• wherein, φ denotes a friction angle of a filler inside the steel cylinder, δ denotes a friction angle between the steel cylinder and the filler, D0 denotes a diameter of the steel cylinder;
• 3(ii):
• determining a filler pressure of the section AB, wherein
• a vertical pressure (σy) of the filler inside the steel cylinder is denoted as σy=γAm+q0e−y/A
• A
• =
• D
• 0
• 4
• ⁢
• K
• ⁢
• K
• =
• λ
• 0
• ⁢
• tan
• ⁡
• (
• δ
• )
• wherein γ denotes a volume weight (kN/m3) of the filler inside the steel cylinder, m=1−e−y/A, y denotes a calculated depth (m), e denotes a natural logarithm, q0 denotes an external load, A denotes a parameter to be determined, and
• λ
• 0
• =
• 1
• 1
• +
• 2
• ⁢
• tan
• ⁢
• φ
• ⁢
• tan
• ⁢
• δ
• +
• 2
• ⁢
• (
• tan
• 2
• ⁢
• φ
• +
• 1
• )
• ⁢
• (
• tan
• ⁢
• φ
• ⁢
• tan
• ⁢
• δ
• -
• tan
• 2
• ⁢
• δ
• )
• ,
• wherein λ0 denotes a thrust coefficient at a side of the filler;
• and
• a horizontal pressure (σx) of the filler against an inner wall of the AB section of the steel cylinder is denoted as σx=λ0σy;
• 3(iii):
• determining a filler pressure of the BC section, wherein
• the filler pressure of the BC section is considered to be equal pressure, a filler pressure (σBx) at a point (B) is calculated according to the formula σx=λ0σy in step 3.2, and a filler pressure at another position of the BC section is equal to the filler pressure (σBx) at the point B;
• 3(iv):
• determining a filler pressure of the CD section, including:
• determining filler pressures at a point (C) and a point (D), and obtaining a linear formular for a variation of the filler pressure of the CD section with a depth for the CD section, wherein
• the filler pressure at the point (C) is equal to the filler pressure (σBx) at the point (B);
• the filler pressure at the point (D) is calculated using the following formula:
• σDx=λ0(σmid−σx), wherein σmid is an average pressure at a bottom of the steel cylinder;
• Step 4:
• determining an external friction (t2) and an internal friction (t1) of the steel cylinder when the steel cylinder is tilted to the seaward side, respectively, including:
• 4(i):
• determining a friction between the soil layer and an exterior of the steel cylinder, wherein
• a friction between the soil layer (i) and the exterior of the steel cylinder is denoted as Eyi=tan(δi)·Eaxi or Eyi=tan(δi)·Epxi;
• and
• the above formula depends on whether the soil layer (i) is involved in an active soil pressure calculation or a passive soil pressure calculation, and in response to determining that the soil layer (i) is involved in the active soil pressure calculation, Eyi=tan(δi)·Eaxi, and in response to determining that the soil layer (i) is involved in the passive soil pressure calculation, Eyi=tan(δi)·Epxi;
• 4(ii):
• determining a friction between the filler and the interior of the steel cylinder, wherein
• for the interior of the steel cylinder, a friction that the AB section is subjected to is denoted as Eyt1AB=tan(δ)·σBx·h1·0.5;
• for the interior of the steel cylinder, a friction that the BC section is subjected to is denoted as Eyt1BC=tan(δ)·σCx·h2;
• for the interior of the steel cylinder, a friction that the CD section is subjected to is denoted as Eyt1CD=tan(δ)·(σCx+σDx)·h3·0.5;
• Step 5:
• determining a vertical reaction force and a horizontal resistance force of a foundation bed against the steel cylinder when the steel cylinder is tilted toward the seaward side, respectively;
• Step 6:
• determining an anti-tilt moment (Mr) and a tilt moment (Ms) when the steel cylinder is tilted to the seaward side, wherein
• the active soil pressures on the exterior of the steel cylinder provides the tilt moment, the passive soil pressures, the vertical reaction force of the foundation bed against the steel cylinder, the horizontal resistance force of the foundation bed against the steel cylinder, the internal friction of the steel cylinder, and the external friction of the steel cylinder provide the anti-tilt moment, and the external load is used to calculate and provide, according to a moment direction, the anti-tilt moment or the tilt moment;
• Step 7:
• determining a safety factor (Kl) for the steel cylinder tilting toward the seaward side, wherein
• Kl
• =
• M
• r
• M
• s
• ;
• Step 8:
• at the same rotation point (O), in response to determining that the steel cylinder rotates toward the land side, the soil body outside the steel cylinder at the seaward side above the rotation point (O), and the soil body outside the steel cylinder at the land side below the rotation point (O), are active soil pressures;
• and
• the soil body outside the steel cylinder at the seaward side below the rotation point (O), and the soil body outside the steel cylinder at the land side above the rotation point (O), are passive soil pressures, wherein
• under a condition that the steel cylinder rotates to the land side, the active soil pressures outside the steel cylinder, the passive soil pressures outside the steel cylinder, the vertical reaction force of the foundation bed against the steel cylinder, the horizontal resistance force of the foundation bed against the steel cylinder, the internal friction of the steel cylinder, and the external friction of the steel cylinder are re-determined according to steps above;
• the anti-tilt moment and the tilt moment are determined under a condition that the steel cylinder is tilted toward the land side, and a safety factor (Kr) for of the steel cylinder tilting toward the land side is determined;
• Step 9:
• comparing (Kl) and (Kr), and taking a smaller value of (Kl) and (Kr) as a safety factor (Fi) below the rotation point;
• and
• Step 10:
• re-selecting a new rotation point, determining a safety factor corresponding to the new rotation point according to steps above, and taking a safety factor with a smallest value among all rotation points as a final safety factor (Fmin) under a working condition.