# US 2025/0085186 A1 · Method and system for quantitative damage monitoring of reinforced concrete structure

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2025/0085186 A1
- Document ID: US20250085186A1
- Status: Published application
- Kind: A1
- Application number: 18/701,093
- Filed: 2023-08-31
- Published: 2025-03-13
- Earliest claimed: 2023-08-31
- Assignees: Shenzhen University
- Applicants: Shenzhen University
- Inventors: Yingwu ZHOU; Zenghui YE; Xiaoxu HUANG; Feng XING; Zongjun LI; Zhongfeng ZHU; Menghuan GUO
- Web page: https://patentgrep.com/patent/US20250085186A1

## CPC

- G01M 5/0033: {by determining damage, crack or wear}
- G01L 1/242: {the material being an optical fibre}
- G01M 5/0091: {by using electromagnetic excitation or detection}
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)

## Abstract

The present disclosure relates to a method and system for quantitative damage monitoring of a reinforced concrete structure and belongs to the technical field of civil engineering. The method includes: obtaining an optical fiber strain signal and cross-section design parameters of a longitudinal tensile reinforcement of a reinforced concrete beam (101), where the cross-section design parameters include geometric parameters and material performance parameters; the geometric parameters include a cross-section width, a cross-section height, an equivalent cross-section height, a protective layer thickness, and a reinforcement area; establishing a cross-section analysis model based on the cross-section design parameters (102), where the cross-section analysis model includes a concrete damage stress-strain relationship model and a reinforcement damage stress-strain relationship model; and inputting the optical fiber strain signal to the cross-section analysis model to obtain a damage indicator and a bending moment-curvature curve of each cross-section (103).

## Claims

### Claim 1

A method for quantitative damage monitoring of a reinforced concrete structure, comprising:
obtaining an optical fiber strain signal and cross-section design parameters of a longitudinal tensile reinforcement of a reinforced concrete beam, wherein the cross-section design parameters comprise geometric parameters and material performance parameters; the geometric parameters comprise a cross-section width, a cross-section height, an equivalent cross-section height, a protective layer thickness, and a reinforcement area; and the material performance parameters comprise a compression peak stress of concrete, an initial tangent modulus of concrete, and an initial tangent modulus of a reinforcement;
establishing a cross-section analysis model based on the cross-section design parameters, wherein the cross-section analysis model comprises a concrete damage stress-strain relationship model and a reinforcement damage stress-strain relationship model; and
inputting the optical fiber strain signal to the cross-section analysis model to obtain a damage indicator and a bending moment-curvature curve of each cross-section;
monitoring damage indicators and mechanical properties of a key member of the reinforced concrete structure in real-time, so as to guarantee and guide a maintenance and a first-aid repair of the key member of the reinforced concrete structure according to the damage indicator and the bending moment-curvature curve of each cross-section;
wherein the inputting the optical fiber strain signal to the cross-section analysis model to obtain a damage indicator and a bending moment-curvature curve of each cross-section specifically comprises:
setting a position of a neutral axis of an xth cross-section at a time t as y0,x(t);
calculating based on the cross-section design parameters, the optical fiber strain signal, and the position of the neutral axis, a curvature of the xth cross-section at the time t by a formula ϕx(t)=εci,x(t)/(y0,x(t)−d), wherein ϕx(t) represents the curvature of the xth cross-section at the time t; εci,x(t) represents the optical fiber strain signal; and d represents the equivalent cross-section height;
calculating, based on the curvature, a strain distribution of concrete fibers of the xth cross-section at the time t and a strain distribution of compressive reinforcement fibers of the xth cross-section at the time t,
calculate, based on the strain distribution of the concrete fibers of the xth cross-section at the time t, a stress distribution and a damage indicator of the concrete fibers of the xth cross-section at the time t using the concrete damage stress-strain relationship model;
calculating, based on the strain distribution of reinforcement fibers of the xth cross-section at the time t, a stress distribution and a damage indicator of the reinforcement fibers of the xth cross-section at the time t using the reinforcement damage stress-strain relationship model, wherein the strain distribution of the reinforcement fibers of the xth cross-section at the time t comprises a strain distribution of tensile reinforcement fibers of the xth cross-section at the time t and the strain distribution of the compressive reinforcement fibers of the xth cross-section at the time t;
calculating a resultant force of axial forces based on the stress distribution and the damage indicator of the concrete fibers of the xth distribution at the time t and the stress distribution and the damage indicator of the reinforcement fibers of the xth distribution at the time t;
determining whether the resultant force of the axial forces is zero;
if the resultant force of the axial forces is zero, calculating and outputting the damage indicator and the bending moment-curvature curve of the xth cross-section at the time t, and
if the resultant force of the axial forces is not zero, returning to “setting a position of a neutral axis of the xth cross-section at a time t as y0,x(t)”.

### Claim 2

(canceled)

### Claim 3 (depends on 2)

The method for quantitative damage monitoring of a reinforced concrete structure according to claim 2, wherein the calculating a resultant force of axial forces based on the stress distribution and the damage indicator of the concrete fibers of the xth cross-section at the time t and the stress distribution and the damage indicator of the reinforcement fibers of the xth cross-section at the time t specifically comprises:
calculating the resultant force of the axial forces by the following formula:
∑
Nx
⁡
(
t
)
=
∑
i
=
1
n
⁡
(
x
)
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
σ
ci
,
x
(
ε
ci
,
x
(
t
)
)
⁢
A
c
,
i
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
s
,
x
(
t
)
)
⁢
A
s
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
sc
,
x
(
t
)
)
⁢
A
s
′
wherein ΣNx(t) represents the resultant force of the axial forces; Dci,x(εci,x(t)) represents a damage indicator of an ith concrete fiber of the xth cross-section at the time t, and Ds,x(εsc,x(t)) represents a damage indicator of the compressive reinforcement fibers of the xth cross-section at the time t; Ds,x(εs,x(t)) represents a damage fiber of the tensile reinforcement fibers of the xth cross-section at the time t; Ac,i=(bh/n(x)) represents an area of the ith concrete fiber; b represents the cross-section width; h represents the cross-section height; As represents an area of the tensile reinforcement fibers; As′ represents an area of the compressive reinforcement fibers; σs,x(εsc,x(t)) represents a stress distribution of the compressive reinforcement fibers of the xth cross-section at the time t; σs,x(εs,x(t)) represents the strain distribution of the tensile reinforcement fibers of the xth cross-section at the time t; σci,x(εci,x(t)) represents a stress of the ith concrete fiber in the xth cross-section at the time t; and n(x) represents a number of the concrete fibers in the xth cross-section.

### Claim 4 (depends on 2)

The method for quantitative damage monitoring of a reinforced concrete structure according to claim 2, wherein the calculating the damage indicator and the bending moment-curvature curve of the xth cross-section at the time t specifically comprises:
calculating the damage indicator of the xth cross-section at the time t by a formula
D
sec
,
x
(
t
)
=
1
-
A
-
B
2
/
C
A
′
-
B
′2
/
C
′
,
wherein,
A
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
2
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
(
d
-
A
′
=
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
2
+
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
2
+
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
2
,
B
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
,
B
′
=
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
+
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
,
C
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
′
,
C
′
=
∑
i
=
1
n
⁡
(
x
)
⁢
E
0
⁢
A
c
,
i
+
E
s
⁢
A
s
+
E
s
⁢
A
s
′
;
Dci,x(εci,x(t)) represents the damage indicator of the ith concrete fiber of the xth cross-section at the time t; Ds,x(εs,x(t)) represents the damage indicator of the compressive reinforcement fibers of the xth cross-section at the time t; Ds,x(εs,x(t)) represents the damage indicator of the tensile reinforcement fibers of the xth cross-section at the time t; h represents the cross-section height; As represents the area of the tensile reinforcement fibers; As′ represents the area of the compressive reinforcement fibers; σs,x(εsc,x(t)) represents the stress distribution of the compressive reinforcement fibers of the xth cross-section at the time t; ∝s,x(εs,x(t)) represents the strain distribution of the tensile reinforcement fibers of the xth cross-section at the time t; σci,x(εci,x(t)) represents the stress of the ith concrete fiber in the xth cross-section at the time t; E0 represents the initial tangent modulus of concrete; d′ represents the protective layer thickness; Es represents the initial tangent modulus of the reinforcement; Ac,i represents the area of the ith concrete fiber; n(x) represents the number of the concrete fibers in the xth cross-section;
calculating a bending moment Mx(t)=Mcx(t)+Msx(t) of the xth cross-section based on a sum of products of axial forces of the concrete fibers and distances of centers of the concrete fibers from the neutral axis y0,x(t) and a sum of products of axial forces of the reinforcement fibers and distances of centers of the reinforcement fibers from the neutral axis y0,x(t), wherein Mcx(t) represents a bending moment of the concrete fibers of the xth cross-section at the time t, Mcx(t)=yi,x(t) represents a distance of a center of the ith concrete fiber in the xth cross-section at the time t from the neutral axis; and Msx(t) represents a bending moment of the xth cross-section at the time t,
Msx
⁡
(
t
)
=
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
s
,
x
(
t
)
)
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
sc
,
x
(
t
)
)
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
;
and
obtaining the bending moment-curvature curve based on the bending moment and the curvature.

### Claim 5

A system for quantitative damage monitoring of a reinforced concrete structure, comprising:
a data obtaining module configured to obtain an optical fiber strain signal and cross-section design parameters of a longitudinal tensile reinforcement of a reinforced concrete beam, wherein the cross-section design parameters comprise geometric parameters and material performance parameters; the geometric parameters comprise a cross-section width, a cross-section height, an equivalent cross-section height, a protective layer thickness, and a reinforcement area; and the material performance parameters comprise a compression peak stress of concrete, an initial tangent modulus of concrete, and an initial tangent modulus of a reinforcement;
a model establishment module configured to establish a cross-section analysis model based on the cross-section design parameters, wherein the cross-section analysis model comprises a concrete damage stress-strain relationship model and a reinforcement damage stress-strain relationship model; and
a calculation module configured to input the optical fiber strain signal to the cross-section analysis model to obtain a damage indicator and a bending moment-curvature curve of each cross-section;
the system further configured to monitor damage indicators and mechanical properties of a key member of the reinforced concrete structure in real-time, so as to guarantee and guide a maintenance and a first-aid repair of the key member of the reinforced concrete structure according to the damage indicator and the bending moment-curvature curve of each cross-section;
wherein the calculation module comprises:
a neutral axis assumption unit configured to set a position of a neural axis of an xth cross-section at a time t as y0,x(t);
a curvature calculation unit configured to calculate, based on the cross-section design parameters, the optical fiber strain signal, and the position of the neutral axis, a curvature of the xth cross-section at the time t by a formula ϕx(t)=εs,x(t)/(y0,x(t)−d), wherein ϕx(t) represents the curvature of the xth cross-section at the time t; εs,x(t) represents the optical fiber strain signal, and d represents the equivalent cross-section height;
a strain calculation unit configured to calculate, based on the curvature, a strain distribution of concrete fibers of the xth cross-section at the time t and a strain distribution of compressive reinforcement fibers of the xth cross-section at the time t;
a concrete stress calculation unit configured to calculate, based on the strain distribution of the concrete fibers of the xth cross-section at the time t, a stress destruction and a damage indicator of the concrete fibers of the xth cross-section at the time t using the concrete damage stress-strain relationship model,
a reinforcement stress calculation unit configured to calculate, based on the strain distribution of reinforcement fibers of the xth cross-section at the time t, a stress distribution and a damage indicator of the reinforcement fibers of the xth cross-section at the time t using the reinforcement damage stress-strain relationship model, wherein the strain distribution of the reinforcement fibers of the xth cross-section at the time t comprises a strain distribution of tensile reinforcement fibers of the xth cross-section at the time t and the strain distribution of the compressive reinforcement fibers of the xth cross-section at the time t;
a resultant force calculation unit configured to calculate a resultant force of axial forces based on the stress distribution and the damage indicator of the concrete fibers of the xth cross-section at the time t and the stress distribution and the damage indicator of the reinforcement fibers of the xth cross-section at the time t;
a determination unit configured to determine whether the resultant force of the axial forces is zero;
a first execution unit configured to, if the resultant force of the axial forces is zero, calculate and output the damage indicator and the bending moment-curvature curve of the xth cross-section at the time t; and
return to “setting a positon of a neutral axis of the xth cross-section at the time t as y0,x(t)”.

### Claim 6

(canceled)

### Claim 7 (depends on 6)

The system for quantitative damage monitoring of a reinforced concrete structure according to claim 6, wherein the resultant force calculation unit comprises:
a resultant force calculation subunit configured to calculate the resultant force of the axial forces by the following formula:
∑
Nx
⁡
(
t
)
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
σ
ci
,
x
(
ε
ci
,
x
(
t
)
)
⁢
A
c
,
i
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
s
,
x
(
t
)
)
⁢
A
s
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
sc
,
x
(
t
)
)
⁢
A
s
′
ΣNx(t)=, wherein ΣNx(t) represents the resultant force of the axial forces; Dci,x(εci,x(t)) represents a damage indicator of the ith concrete fiber of the xth cross-section at the time t, and Ds,x(ϵs,x(t)) represents a damage indicator of the compressive reinforcement fibers of the xth cross-section at the time t; Ds,x(εs,x(t)) represents a damage fiber of the tensile reinforcement fibers of the xth cross-section at the time t; Ac,i=(bh/n(x)) represents an area of the ith concrete fiber; b represents the cross-section width; h represents the cross-section height; As represents an area of the tensile reinforcement fibers; As′ represents an area of the compressive reinforcement fibers; σs,x(εs,x(t)) represents a stress distribution of the compressive reinforcement fibers of the xth cross-section at the time t; σs,x(εs,x(t)) represents the strain distribution of the tensile reinforcement fibers of the xth cross-section at the time t; σci,x(εci,x(t)) represents a stress of the ith concrete fiber in the xth cross-section at the time t; and n(x) represents a number of the concrete fibers in the xth cross-section.

### Claim 8 (depends on 6)

The system for quantitative damage monitoring of a reinforced concrete structure according to claim 6, wherein the first execution unit comprises:
a damage indicator calculation subunit configured to calculate the damage indicator of the xth cross-section at the time t by a formula
D
sec
,
x
(
t
)
=
1
-
A
-
B
2
/
C
A
′
-
B
′2
/
C
′
,
wherein
A
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
2
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
(
d
-
A
′
=
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
2
+
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
2
+
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
2
,
B
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
,
B
′
=
E
0
⁢
A
c
,
i
⁢
y
i
,
x
(
t
)
+
E
s
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
E
s
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
,
C
=
∑
i
=
1
n
⁡
(
x
)
⁢
(
1
-
D
ci
,
x
(
ε
ci
,
x
(
t
)
)
)
⁢
E
0
⁢
A
c
,
i
+
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
E
s
⁢
A
s
′
,
C
′
=
∑
i
=
1
n
⁡
(
x
)
⁢
E
0
⁢
A
c
,
i
+
E
s
⁢
A
s
+
E
s
⁢
A
s
′
;
Dci,x(εci,x(t)) represents the damage indicator of the ith concrete fiber of the xth cross-section at the time t; Ds,x(εs,x(t)) represents the damage indicator of the compressive reinforcement fibers of the xth cross-section at the time t; Ds,x(εs,x(t)) represents the damage indicator of the tensile reinforcement fibers of the xth cross-section at the time t; h represents the cross-section height; As represents the area of the tensile reinforcement fibers; As′ represents the area of the compressive reinforcement fibers; σs,x(εs,x(t)) represents the stress distribution of the compressive reinforcement fibers of the xth cross-section at the time t; σs,x(εs,x(t)) represents the strain distribution of the tensile reinforcement fibers of the xth cross-section at the time t; σci,x(εci,x(t)) represents the stress of the ith concrete fiber in the xth cross-section at the time t; E0 represents the initial tangent modulus of concrete; d′ represents the protective layer thickness; Es represents the initial tangent modulus of the reinforcement; Ac,i represents the area of the ith concrete fiber; n(x) represents the number of the concrete fibers in the xth cross-section;
a bending moment calculation subunit configured to calculate a bending moment Mx(t)=Mcx(t)+Msx(t) of the xth cross-section based on a sum of products of axial forces of the concrete fibers and distances of centers of the concrete fibers from the neutral axis y0,x(t) and a sum of products of axial forces of the reinforcement fibers and distances of centers of the reinforcement fibers from the neutral axis y0,x(t), wherein Mcx(t) represents a bending moment of the concrete fibers of the xth cross-section at the time t, Mcx(t)=yi,x(t) represents a distance of a center of the ith concrete fiber in the xth cross-section at the time t from the neutral axis; and Msx(t) represents a bending moment of the xth cross-section at the time t,
Msx
⁡
(
t
)
=
(
1
-
D
s
,
x
(
ε
s
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
s
,
x
(
t
)
)
⁢
A
s
(
d
-
h
+
y
0
,
x
(
t
)
)
+
(
1
-
D
s
,
x
(
ε
sc
,
x
(
t
)
)
)
⁢
σ
s
,
x
(
ε
sc
,
x
(
t
)
)
⁢
A
s
′
(
h
-
d
′
-
y
0
,
x
(
t
)
)
;
Msx(t)=; and
a curve plotting subunit configured to plot the bending moment-curvature curve based on the bending moment and the curvature.