# US 12,180,668 B2 · Methods for predicting a stability of a steel cylinder against tilt

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- Number: US 12,180,668 B2
- Document ID: US12180668B2
- Status: Granted
- Kind: B2
- Application number: 18/644,065
- Filed: 2024-04-23
- Published: 2024-08-22
- Granted: 2024-12-31
- Earliest claimed: 2022-04-15
- Assignees: Tianjin Port Engineering Institute Co., Ltd. of Cccc First Harbor Engineering Co., Ltd.; Cccc First Harbor Engineering Co., Ltd.; Tianjin Port Engineering Quality Testing Center Co., Ltd.
- Applicants: Tianjin Port Engineering Institute Co., Ltd. of Cccc First Harbor Engineering Co., Ltd.; Cccc First Harbor Engineering Co., Ltd.; Tianjin Port Engineering Quality Testing Center Co., Ltd.
- Inventors: Changyi Yu; Wei Pan; Yiyong Li; Naishou Zhang; Yonghua Cao; Aimin Liu; Changxi Yue; Xiaoqiang Kou; Zhijun Chen; Binbin Xu
- Web page: https://patentgrep.com/patent/US12180668B2

## CPC

- E02D 33/00: Testing foundations or foundation structures (testing methods and apparatus, see the relevant subclasses of class G01; testing structures or apparatus as regards function, in general, G01M; testing or determining chemical or physical properties, in general G01N)
- G06F 30/27: using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
- G06F 2119/02: Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
- G06F 2119/14: Force analysis or force optimisation, e.g. static or dynamic forces
- E02D: FOUNDATIONS; EXCAVATIONS; EMBANKMENTS (specially adapted for hydraulic engineering E02B); UNDERGROUND OR UNDERWATER STRUCTURES {(tunnels, tunnelling, mining E21)}
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Method for predicting a stability of a steel cylinder including: in response to the steel cylinder tilting toward a seaward side at an arbitrary rotation point, obtaining a safety factor for the steel cylinder tilting toward the seaward side by determining an anti-tilt moment and a tilt moment when the steel cylinder is tilted to the seaward side; under a same rotation point, in response to determining that the steel cylinder is rotated toward a land side, determining the safety factor for the steel cylinder tilting toward the land side; taking a smaller safety factor as the safety factor under the rotation point; re-selecting a new rotation point, determining a safety factor corresponding to the new rotation point, and taking a safety factor with a smallest value among all rotation points as a final safety factor; and generating, based on the final safety factor, an anti-tilt instruction.

## Claims

### Claim 1

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.

### Claim 2 (depends on 1)

The method of claim 1, wherein the step 2 comprises:
2(i): determining the active soil pressures
e
a
⁢
x
⁢
i
⁢
1
=
K
a
⁢
x
⁢
i
⁢
∑
1
i
-
1
γ
i
⁢
h
i
⁢
e
a
⁢
x
⁢
i
⁢
2
=
K
a
⁢
x
⁢
i
(
∑
1
i
-
1
γ
i
⁢
h
i
+
γ
i
⁢
h
i
)
⁢
K
a
⁢
x
⁢
i
=
tan
2
(
4
⁢
5
-
φ
i
2
)
⁢
E
a
⁢
x
⁢
i
=
e
a
⁢
x
⁢
i
⁢
1
+
e
axi
⁢
2
2
⁢
h
i
wherein φi denotes the friction angle of the soil layer i, δ denotes the friction angle between the steel cylinder and the soil, hi denotes the thickness of the soil layer i, γi denotes a volume weight of the soil layer i, a natural volume weight is used for soil above a water level, and a floating volume weight is used for soil below the water level, Kaxi denotes an active soil pressure coefficient of the soil layer i, eaxi1 denotes an active soil pressure at a top of the soil layer i, eaxi2 denotes an active soil pressure at a bottom of the soil layer i, Eaxi denotes a resultant force of the active soil pressures of the soil layer i, a sum of resultant forces of the active soil pressures Eaxi of all soil layers i outside the steel cylinder at the land side above the rotation point (O) is the active soil pressure (Pa1), and a sum of resultant forces of the active soil pressures Eaxi of all the soil layers i outside the steel cylinder at the seaward side below the rotation point (O) is the active soil pressure (Pa2);
2(ii): determining the passive soil pressures
e
pxi
⁢
1
=
K
pxi
⁢
∑
1
i
-
1
γ
i
⁢
h
i
⁢
e
pxi
⁢
2
=
K
pxi
(
∑
1
i
-
1
γ
i
⁢
h
i
+
γ
i
⁢
h
i
)
⁢
K
pxi
=
tan
2
(
45
+
φ
i
2
)
⁢
E
pxi
=
e
pxi
⁢
1
+
e
pxi
⁢
2
2
⁢
h
i
wherein Kpxi denotes a passive soil pressure coefficient of the soil layer i, epxi1 denotes a passive soil pressure at the top of the soil layer i, epxi2 denotes a passive soil pressure at the bottom of the soil layer i, Epxi denotes a resultant force of the passive soil pressures of the soil layer i, a sum of resultant forces of the passive soil pressures Epxi of all the soil layers i outside the steel cylinder at the land side below the rotation point (O) is the passive soil pressure (Pp1), and a sum of resultant forces of the passive soil pressures (Epxi) of all the soil layers i outside the steel cylinder at the seaward side above the rotation point (O) is the passive soil pressure (Pp2).

### Claim 3 (depends on 1)

The method of claim 1, further comprising:
in step 3(ii), to simplify calculations, taking a variation of the filler pressure of the AB section as a linear variation, and calculating the filler pressure (σBx) at the point B according to a formula σx=λ0σy, wherein a filler pressure at a point (A) is set to be 0.

### Claim 4 (depends on 1)

The method of claim 1, wherein the step 5 comprises:
5(i): the vertical reaction force of the foundation bed against the steel cylinder, wherein
the average pressure of the vertical reaction force of the foundation bed against the steel cylinder is denoted as q=9·Cu, wherein Cu denotes an undrained shear strength of a foundation soil body, the vertical reaction force of the foundation bed against the steel cylinder is denoted as Fq=q*Lq, wherein Lq denotes a distance Lq between the rotation point and the tilt side, and Lq is calculated based on coordinates of the rotation point and the diameter of the steel cylinder; and
5(ii): the horizontal resistance force of the foundation bed against the steel cylinder, wherein
the horizontal resistance force of the foundation bed against the steel cylinder is denoted as F=π/4·D0·D0·Cu.