# Seismic Behaviour of Cast-In-Situ Phosphogypsum-Reinforced Concrete Grid Frame Composite Walls

Authors: Qin Wu; Huagang Zhang; Hongniao Chen; Xin Zhang; YanHui Wei; Li Li; Kejian Ma
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

This paper mainly studies the effect of cast-in-situ phosphogypsum on seismic behaviour of reinforced concrete grid frame. The mechanical behaviour of three reinforced concrete grid frames and four cast-in-situ phosphogypsum-reinforced concrete grid frame composite walls under low cycle alternating load was designed and tested. The test results show that the reinforced concrete grid frame has less bearing capacity and poor energy consumption. The addition of cast-in-situ phosphogypsum can effectively improve the seismic behaviour of the reinforced concrete grid frame. Compared with the reinforced concrete grid frame, the bearing capacity of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is increased by 2-3 times, the displacement ductility coefficient is increased by 0.95∼1.2 times, and the relative accumulative energy consumption is increased by 86%∼216%. This shows that the composite wall has better bearing capacity, ductility, and energy dissipation capacity.


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## Body

## 1. Introduction

Phosphogypsum is a solid waste discharged from the production of phosphoric acid by wet process. Being rich in P2O5 and fluorides, the dissolution and leakage of this harmful substance during storage cause serious environmental pollution [1]. In China, the accumulative stock of phosphogypsum has reached 300 million tons [2]. Therefore, its pollution should be comprehensively controlled. The provincial government of Guizhou is rich in phosphogypsum resources. Starting in 2018, the government requires phosphorous chemical enterprises to digest not only the phosphogypsum discharged in the current year but also their historical stock year by year.At present, the utilisation of phosphogypsum mainly focuses on the following aspects [3]:(i)
Most of techniques used in the chemical industry require phosphogypsum before treatment, which comes with high investment, high energy consumption, and new emissions.(ii)
Industrial waste phosphogypsum is used as a lime stabilizer for expansive soil to stabilize the soil [4].(iii)
Phosphogypsum and phosphorus slag were used as cementitious materials for cemented paste backfill body to treat goafs in mines [5], but it is unsuitable for open-cast mines.(iv)
Building materials are mainly used for the production of cement retarder [6] and sulfuric acid combined with cement and decoration materials and blocks [7]. These products have low radioactively detection indices [8].(v)
In terms of roadbed materials, phosphogypsum is mainly used as a stabilizer [9] and solidifier [10] to treat sludge, so as to meet the requirements of roadbed materials.All of these approaches to phosphogypsum have shortcomings. Therefore, it is necessary to find ways to use phosphogypsum directly.Based on the characteristics of fast setting time of phosphogypsum (only 3–5 minutes), Ma et al. [11] proposed the idea of pouring phosphogypsum in building, but the fluidity of phosphogypsum slurry is poor, and the free water evaporates slowly after hardening. After hydration of the phosphogypsum provided by WengFu group co. Ltd., Cao et al. [12] observed by JMS-6490LV scanning electron microscope and found that phosphogypsum crystals were parallel-shaped (Figure 1, ruler 100 μm). The gypsum phase composition was analysed by D5000 XRD diffractometer. It was found that gypsum contained not only β-CaSO4·0.5H2O but also a small amount of CaSO4 and SiO2 (Figure 2). Therefore, the interspaces between phosphogypsum crystals can be filled with compatible phosphorus slag powder (Figures 3 and 4), and Ca4Al6SO16 after cement hydration can consume CaSO4. The acidity of phosphogypsum can be integrated with CaO, which can reduce the solubility and dissolution rate of β-CaSO4·0.5H2O, and extend the setting time of phosphogypsum by retarder. The reduction of free water can be achieved by water reducing agent. It is proposed that the quality ratio of raw materials is as follows: 80% phosphogypsum, 17% phosphorus slag powder, 3% CaO, 2% cement, 0.8% water reducer, 0.22%–0.35% retarder, and 0.43–0.46 water-to-cement ratio, which effectively solves the aforementioned problems.Figure 1
SEM photo of phosphogypsum (ruler 100μm).Figure 2
XRD pattern of phosphogypsum.Figure 3
SEM photo of phosphorus slag powder (ruler 10μm).Figure 4
XRD pattern of phosphorus slag powder.On this basis, Wu et al. [13] measured the uniaxial stress-strain curve of phosphogypsum through prismatic specimens and revealed that the elastic modulus of the material was 5300 MPa and Poisson’s ratio was 0.19. Zhang et al. [14] measured the compressive strength of phosphogypsum at 9.6 MPa–10.4 MPa and the partial factor for materials at 1.9 through cube specimens and conducted engineering practice in two rural residences in ZunYi, Guizhou province (Figure 5).Figure 5
Cast-in-situ phosphogypsum residential project example. (a) Formwork. (b) Pouring. (c) Form stripping. (d) Building.
(a)
(b)
(c)
(d)Using phosphogypsum as the filling material of the structure, Ma et al. [15] proposed the cast-in-situ phosphogypsum-reinforced concrete composite box structure. The floor slab adopted the box-shaped floor with precast phosphogypsum mould box, and the load-bearing wall was the cast-in-situ phosphogypsum-reinforced concrete mesh frame composite wall. The stability analysis conducted by Zhang et al. [16, 17] shows that the composite wall has sufficient elastic and stable bearing capacity, and the engineering practice of high-rise housing shown in Figure 6 is carried out in Machangping, Guizhou province. The ratio of concrete and phosphogypsum in the structure is 1 : 0.71, which indicates that a large number of applications of phosphogypsum can be realized in the building structure.Figure 6
Guizhou Machangping high-rise housing. (a) Building elevation. (b) Structural plan. (c) Structural space diagram.
(a)
(b)
(c)According to this project, the construction technology of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall can be summarized as follows. (1) Check the reinforced concrete grid frame and repair construction defects (Figure7(a)). (2) Install the template of cast-in-situ phosphogypsum on both sides of the reinforced concrete grid frame, and seal the gap between the templates by sealing strips (Figure 7(b)). (3) Weigh dry materials such as phosphogypsum, phosphorous slag powder, lime, and cement according to the mass mixing ratio. After mixing uniformly, pour into the aqueous solution prepared by water reducer and retarder, and stir again to obtain the pouring slurry of phosphogypsum (Figure 7(c)). (4) Pumping the slurry into the template, the slurry is self-levelling and basically coagulates in about 30 minutes (Figure 7(d)). (5) Remove the template after about 12 hours (Figure 7(e)).Figure 7
Construction technology of composite wall. (a) Reinforced concrete grid frame. (b) Template installation. (c) Slurry preparation. (d) Phosphogypsum castings. (e) Form stripping.
(a)
(b)
(c)
(d)
(e)The microexpansibility of the cast-in-situ phosphogypsum is closely combined with reinforced concrete grid frame and mutually constrained. After the cracking of phosphogypsum, then the grid frame becomes the main load-bearing framework of the structure [15]. Therefore, cast-in-situ phosphogypsum is the first line of defense against the seismic fortification of structures, and the contribution of its bearing capacity and stiffness in the structure can be considered. However, Lu et al. [18] did not take this effect into account in the study, and the phosphogypsum covered the reinforced concrete grid frame, which is not convenient for the appearance inspection of the grid frame. Jiang et al. [19, 20] proposed closely spaced concrete frame-fibre gypsum board composite wall structure, which is connected with closely spaced columns by setting beams at the height of stories. The structure is similar to the shear wall with vertical joints, and the failure is due to bending failure. The setting of interstorey beams in the skeleton significantly changes the mechanical properties of the composite walls.Modern buildings are mainly high-rise buildings. Based on the above engineering practice and analysis, in order to understand the seismic capacity of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, it is necessary to conduct a comparative test study on the composite wall with pure reinforced concrete grid frame under the action of low cyclic alternating load. In this paper, the seismic performance of reinforced concrete grid frame and cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is compared and tested to understand the structural failure characteristics, bearing capacity, hysteretic curve, skeleton curve, ductility, stiffness, energy dissipation, and other seismic performances.


## 2. Materials and Methods

### 2.1. Materials and Mechanical Properties

#### 2.1.1. Cast-In-Situ Phosphogypsum

Phosphogypsum and phosphorus slag powder were obtained from Weng Fu group co. Ltd. The gypsum phase of phosphogypsum was determined, as shown in Table1. The specific surface area of phosphorus slag powder was 380–420 m2/kg, and chemical composition is shown in Table 2. Hydrated lime was bought in the market, and the effective mass fraction of CaO was not lower than 60%. The cement used in this study was P.O. 325 ordinary Portland cement. The water reducer was polycarboxylic acid water reducing agent with a concentration of not less than 10%. The retarder used was citrate sodium.Table 1
Gypsum compositions of phosphogypsum.
Dihydrate gypsum (%)
β-hemihydrate gypsum (%)
Anhydrite (%)
Solubility
Difficult capacitive
0.78
87.61
2.45
2.12Table 2
Chemical compositions of phosphorite slag (%).
SiO2
Fe2O3
Al2O3
CaO
MgO
P2O5
CaF2
42.35
1.67
3.52
45.36
1.73
1.46
1.07The analysis of Zhang et al. [14] shows that the effect of retarder on the compressive strength of cast-in-situ phosphogypsum is great. Therefore, the mix proportion of cast-in-situ phosphogypsum is as follows: 80% phosphogypsum, 17% phosphorus slag powder, 3% hydrated lime, 10% cement, 0.6% water reducer, and 0.3% retarder. The water-to-cement ratio was 0.43. The standard value of the cubic compressive strength of cast-in-situ phosphogypsum was 4.2 MPa, and the modulus of elasticity was 2000 N/mm2.


#### 2.1.2. Steel Bar and Concrete

The concrete used in this study was C20 [21]. The standard value of cubic compressive strength was 20.1 MPa. The modulus of elasticity was 2.55 × 104 MPa. On the basis of similarity analysis, 8# galvanized wire with equal strength was used to substitute steel bars with diameter of less than 6.5 mm. The measured mechanical properties of steel bars are shown in Table 3, where d refers to diameter, fy refers to yield strength, fu refers to tensile strength, and Es refers to the modulus of elasticity.Table 3
Mechanical properties of steel bar.
Model
d (mm)
f
y (MPa)
f
u (MPa)
E
s (MPa)
HPB300
6.5
315
465
2.14 × 105
HRB400
12
448
615
1.98 × 105
Galvanized wire
2.2
416
489
1.49 × 105
Galvanized wire
4
410
480
1.57 × 105


### 2.2. Specimen Design

Four trussets three-storey cast-in-situ phosphogypsum-reinforced concrete grid frame composite walls were made in a 1/5 reduced scale. The serial numbers were ZHQ1–ZHQ4. Cast-in-situ phosphogypsum was filled in the reinforced concrete grid frame (Figure8(a)). At the same time, three trussets three-storey pure reinforced concrete grid frames, numbered KJ1–KJ3 (Figure 8(b)), were made for comparative experiment. The same reinforcement was adopted by all the concrete members of the specimens (Figure 8(c)). The size and reinforcement of specimens are shown in Figure 8.Figure 8
Geometry size and reinforcement of the specimen. (a) Specimen KJ. (b) Specimen ZHQ. (c) Reinforcement of concrete members. (1) Side pillar; (2) center pillar; (3) floor beam; (4) interstorey beams; (5) cast-in-situ phosphogypsum; (6) foundation beam; (7) anchor bolt hole.
(a)
(b)
(c)


### 2.3. Loading Device

After the specimens were installed on the foundation through anchor bolts, the horizontal loading was applied to the end on the top floor beam through a 25 T MTS actuator, and the loading end of the actuator was connected to the specimens through a 25-millimeter-diameter round steel clamp. To avoid the eccentric effect outside the plane during loading, a lateral support with rollers was arranged around the loading end of the actuator and on both sides of the specimen. The vertical load on the top of the specimen was applied and maintained constant by using a 50 T hydraulic jack. A roller was arranged between the jack and the specimen to eliminate the constraint effect on top of the specimen. The test loading device is shown in Figure9.Figure 9
Test loading equipment. (a) Installation diagram. (1) Foundation; (2) sill anchor; (3) test specimen; (4) door type reaction frame; (5) lateral bracing; (6) lateral support at loading end; (7) round steel clamp; (8) vertical force distribution beam; (9) load transducer; (10) jack; (11) the MTS actuators; (12) triangular counter frame. (b) Picture of real products.
(a)
(b)


### 2.4. Loading System

Different vertical loads are applied to each specimen, and the axial compression ratio calculated according to formula (1) is shown in Table 4. After vertical load is constant, horizontal loads were applied through displacement loading, as shown in Figure 10. Under the yield condition of the specimens, the strain of the longitudinal bar at the bottom of the side column reached the yield strain of the steel bar [22]. The specimen was loaded once per stage before cracking. After cracking, three cycles were loaded per stage of displacement. The loading was not stopped until the longitudinal reinforcement yielded and concrete was crushed.where n is the axial compression ratio, N is the vertical load, fc is the measured compressive strength of concrete, fp is the measured compressive strength of the cast-in-situ phosphogypsum, Ac is the cross-sectional area of the column, and Ap is the cross-sectional area of the cast-in-situ phosphogypsum.Table 4
Axial compression ratio of specimen.
Specimen number
KJ1
KJ2
KJ3
ZHQ1
ZHQ2
ZHQ3
ZHQ4
Axial compression ratio
0.072
0.103
0.127
0.107
0.108
0.167
0.154(1)
n
=
N
∑
f
c
A
c
+
∑
f
p
A
p
.Figure 10
Loading cycles.


### 2.5. Layout of Measuring Points

The physical quantities collected in the test were mainly the horizontal displacement of floor beams and foundations and the longitudinal strain of each member. The main measuring points of each specimen were arranged, as shown in Figure11. The layout of the measuring points of reinforced concrete grid frame was the same as that of the reinforced concrete grid frame in the composite walls. In the numbers of measuring points, H refers to the measuring point for displacement, and L and Z refer to the measuring points for the strain of longitudinal bars in the beams and columns, respectively. The computer data acquisition system was used to automatically collect and record the test data and observe and record the crack development and failure process of the specimens manually.Figure 11
Layout of measuring point.


## 2.1. Materials and Mechanical Properties

### 2.1.1. Cast-In-Situ Phosphogypsum

Phosphogypsum and phosphorus slag powder were obtained from Weng Fu group co. Ltd. The gypsum phase of phosphogypsum was determined, as shown in Table1. The specific surface area of phosphorus slag powder was 380–420 m2/kg, and chemical composition is shown in Table 2. Hydrated lime was bought in the market, and the effective mass fraction of CaO was not lower than 60%. The cement used in this study was P.O. 325 ordinary Portland cement. The water reducer was polycarboxylic acid water reducing agent with a concentration of not less than 10%. The retarder used was citrate sodium.Table 1
Gypsum compositions of phosphogypsum.
Dihydrate gypsum (%)
β-hemihydrate gypsum (%)
Anhydrite (%)
Solubility
Difficult capacitive
0.78
87.61
2.45
2.12Table 2
Chemical compositions of phosphorite slag (%).
SiO2
Fe2O3
Al2O3
CaO
MgO
P2O5
CaF2
42.35
1.67
3.52
45.36
1.73
1.46
1.07The analysis of Zhang et al. [14] shows that the effect of retarder on the compressive strength of cast-in-situ phosphogypsum is great. Therefore, the mix proportion of cast-in-situ phosphogypsum is as follows: 80% phosphogypsum, 17% phosphorus slag powder, 3% hydrated lime, 10% cement, 0.6% water reducer, and 0.3% retarder. The water-to-cement ratio was 0.43. The standard value of the cubic compressive strength of cast-in-situ phosphogypsum was 4.2 MPa, and the modulus of elasticity was 2000 N/mm2.


### 2.1.2. Steel Bar and Concrete

The concrete used in this study was C20 [21]. The standard value of cubic compressive strength was 20.1 MPa. The modulus of elasticity was 2.55 × 104 MPa. On the basis of similarity analysis, 8# galvanized wire with equal strength was used to substitute steel bars with diameter of less than 6.5 mm. The measured mechanical properties of steel bars are shown in Table 3, where d refers to diameter, fy refers to yield strength, fu refers to tensile strength, and Es refers to the modulus of elasticity.Table 3
Mechanical properties of steel bar.
Model
d (mm)
f
y (MPa)
f
u (MPa)
E
s (MPa)
HPB300
6.5
315
465
2.14 × 105
HRB400
12
448
615
1.98 × 105
Galvanized wire
2.2
416
489
1.49 × 105
Galvanized wire
4
410
480
1.57 × 105


## 2.1.1. Cast-In-Situ Phosphogypsum

Phosphogypsum and phosphorus slag powder were obtained from Weng Fu group co. Ltd. The gypsum phase of phosphogypsum was determined, as shown in Table1. The specific surface area of phosphorus slag powder was 380–420 m2/kg, and chemical composition is shown in Table 2. Hydrated lime was bought in the market, and the effective mass fraction of CaO was not lower than 60%. The cement used in this study was P.O. 325 ordinary Portland cement. The water reducer was polycarboxylic acid water reducing agent with a concentration of not less than 10%. The retarder used was citrate sodium.Table 1
Gypsum compositions of phosphogypsum.
Dihydrate gypsum (%)
β-hemihydrate gypsum (%)
Anhydrite (%)
Solubility
Difficult capacitive
0.78
87.61
2.45
2.12Table 2
Chemical compositions of phosphorite slag (%).
SiO2
Fe2O3
Al2O3
CaO
MgO
P2O5
CaF2
42.35
1.67
3.52
45.36
1.73
1.46
1.07The analysis of Zhang et al. [14] shows that the effect of retarder on the compressive strength of cast-in-situ phosphogypsum is great. Therefore, the mix proportion of cast-in-situ phosphogypsum is as follows: 80% phosphogypsum, 17% phosphorus slag powder, 3% hydrated lime, 10% cement, 0.6% water reducer, and 0.3% retarder. The water-to-cement ratio was 0.43. The standard value of the cubic compressive strength of cast-in-situ phosphogypsum was 4.2 MPa, and the modulus of elasticity was 2000 N/mm2.


## 2.1.2. Steel Bar and Concrete

The concrete used in this study was C20 [21]. The standard value of cubic compressive strength was 20.1 MPa. The modulus of elasticity was 2.55 × 104 MPa. On the basis of similarity analysis, 8# galvanized wire with equal strength was used to substitute steel bars with diameter of less than 6.5 mm. The measured mechanical properties of steel bars are shown in Table 3, where d refers to diameter, fy refers to yield strength, fu refers to tensile strength, and Es refers to the modulus of elasticity.Table 3
Mechanical properties of steel bar.
Model
d (mm)
f
y (MPa)
f
u (MPa)
E
s (MPa)
HPB300
6.5
315
465
2.14 × 105
HRB400
12
448
615
1.98 × 105
Galvanized wire
2.2
416
489
1.49 × 105
Galvanized wire
4
410
480
1.57 × 105


## 2.2. Specimen Design

Four trussets three-storey cast-in-situ phosphogypsum-reinforced concrete grid frame composite walls were made in a 1/5 reduced scale. The serial numbers were ZHQ1–ZHQ4. Cast-in-situ phosphogypsum was filled in the reinforced concrete grid frame (Figure8(a)). At the same time, three trussets three-storey pure reinforced concrete grid frames, numbered KJ1–KJ3 (Figure 8(b)), were made for comparative experiment. The same reinforcement was adopted by all the concrete members of the specimens (Figure 8(c)). The size and reinforcement of specimens are shown in Figure 8.Figure 8
Geometry size and reinforcement of the specimen. (a) Specimen KJ. (b) Specimen ZHQ. (c) Reinforcement of concrete members. (1) Side pillar; (2) center pillar; (3) floor beam; (4) interstorey beams; (5) cast-in-situ phosphogypsum; (6) foundation beam; (7) anchor bolt hole.
(a)
(b)
(c)


## 2.3. Loading Device

After the specimens were installed on the foundation through anchor bolts, the horizontal loading was applied to the end on the top floor beam through a 25 T MTS actuator, and the loading end of the actuator was connected to the specimens through a 25-millimeter-diameter round steel clamp. To avoid the eccentric effect outside the plane during loading, a lateral support with rollers was arranged around the loading end of the actuator and on both sides of the specimen. The vertical load on the top of the specimen was applied and maintained constant by using a 50 T hydraulic jack. A roller was arranged between the jack and the specimen to eliminate the constraint effect on top of the specimen. The test loading device is shown in Figure9.Figure 9
Test loading equipment. (a) Installation diagram. (1) Foundation; (2) sill anchor; (3) test specimen; (4) door type reaction frame; (5) lateral bracing; (6) lateral support at loading end; (7) round steel clamp; (8) vertical force distribution beam; (9) load transducer; (10) jack; (11) the MTS actuators; (12) triangular counter frame. (b) Picture of real products.
(a)
(b)


## 2.4. Loading System

Different vertical loads are applied to each specimen, and the axial compression ratio calculated according to formula (1) is shown in Table 4. After vertical load is constant, horizontal loads were applied through displacement loading, as shown in Figure 10. Under the yield condition of the specimens, the strain of the longitudinal bar at the bottom of the side column reached the yield strain of the steel bar [22]. The specimen was loaded once per stage before cracking. After cracking, three cycles were loaded per stage of displacement. The loading was not stopped until the longitudinal reinforcement yielded and concrete was crushed.where n is the axial compression ratio, N is the vertical load, fc is the measured compressive strength of concrete, fp is the measured compressive strength of the cast-in-situ phosphogypsum, Ac is the cross-sectional area of the column, and Ap is the cross-sectional area of the cast-in-situ phosphogypsum.Table 4
Axial compression ratio of specimen.
Specimen number
KJ1
KJ2
KJ3
ZHQ1
ZHQ2
ZHQ3
ZHQ4
Axial compression ratio
0.072
0.103
0.127
0.107
0.108
0.167
0.154(1)
n
=
N
∑
f
c
A
c
+
∑
f
p
A
p
.Figure 10
Loading cycles.


## 2.5. Layout of Measuring Points

The physical quantities collected in the test were mainly the horizontal displacement of floor beams and foundations and the longitudinal strain of each member. The main measuring points of each specimen were arranged, as shown in Figure11. The layout of the measuring points of reinforced concrete grid frame was the same as that of the reinforced concrete grid frame in the composite walls. In the numbers of measuring points, H refers to the measuring point for displacement, and L and Z refer to the measuring points for the strain of longitudinal bars in the beams and columns, respectively. The computer data acquisition system was used to automatically collect and record the test data and observe and record the crack development and failure process of the specimens manually.Figure 11
Layout of measuring point.


## 3. Test Result and Discussion

### 3.1. Test Phenomena and Failure Characteristics

#### 3.1.1. Reinforced Concrete Grid Frame

When the vertical load of reinforced concrete grid frame is completed, there is no cracking on the surface of specimens. When the horizontal loading displacement is 12 mm, vertical cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column; cracks develop in the joint area between the storey beam and side column; and oblique cracks appear. When the horizontal loading displacement is 25 mm, cross cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column, and lateral cracks appear on the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, oblique cracks appear in the foot area of side columns, and local failure of concrete occurs in the cross cracks of beam-column joints, with increasing transverse cracks of side columns. When the horizontal displacement is loaded to the failure displacement, original cracks increase gradually, the concrete is crushed, the steel bar buckles and the specimens are damaged. The failure of specimens is shown in Figure12.Figure 12
Failure modes of each specimen. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4. (h) Details of the damage.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


#### 3.1.2. Cast-In-Situ Phosphogypsum-Reinforced Concrete Grid Frame Composite Wall

When the vertical load of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is completed, there is no cracking on the surface of specimens. At the early stage of horizontal displacement loading, slip cracks appear at the joint of cast-in-situ phosphogypsum and concrete. When the horizontal loading displacement is loaded to about 30% of the failure displacement, vertical cracks appear in the joint area between the storey beam and side column, oblique cracks appear in the joint area between the interstorey beam and middle column, and lateral cracks appear in the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, the corner of cast-in-situ phosphogypsum of ZHQ1 and ZHQ2 is broken, oblique cracks appear in the joint area between the storey beam and side column, and many oblique cracks appear in cast-in-situ phosphogypsum, with increasing transverse cracks of side columns. The corner of the cast-in-situ phosphogypsum of ZHQ3 and ZHQ4 is broken, vertical cracks appear in the middle of the lower part of the interstorey beam, and transverse cracks appear at the bottom of the middle column. Many oblique cross cracks appear in the beam-column joint area, and vertical fracture cracks appear at the bottom of the interstorey beam. When the horizontal displacement is loaded to the failure displacement, original cracks on ZHQ1 and ZHQ2 continue to develop, cast-in-situ phosphogypsum crushes and falls off, the concrete in the beam-column joint area is broken, steel bars are exposed and buckled, and the specimen is damaged. On the lower part of ZHQ3 and ZHQ4, splitting failure occurs on phosphogypsum, the transverse crack width of the side columns increases gradually, the concrete at the root of the side columns is broken, the steel bars are exposed and buckled, and the specimens are damaged. The failure of specimens is shown in Figure12.


### 3.2. Hysteretic Curve

Figure13 shows the load-displacement hysteretic curve of each specimen at the horizontal loading point, where F refers to the horizontal load of the specimens, and δ refers to the horizontal displacement of the specimens. The following information can be derived from Figure 13:(1)
At the early stage of loading, the hysteretic curves of all specimens are basically fusiform, and residual deformation is small. Under the horizontal displacement loading, the hysteretic curve inclines to the displacement axis. The area around the curve and the energy dissipation capacity increase. However, under the same loading level, the hysteretic loop area of the second loading is smaller than that of the first loading.(2)
For reinforced concrete grid frame, the hysteretic curve of KJ2 is fuller than that of the two other specimens. Before reaching the peak load, the hysteretic curves of the specimens become similar in shape with kneading phenomenon. After reaching the peak load, the kneading phenomena of KJ1 and KJ3 hysteretic curves are more serious than that of KJ2, and their enclosed areas are smaller. When the loading displacement was 12 mm, local damage occurred to specimen KJ3, resulting in a gap in the hysteretic curve, and the area enclosed by the hysteretic loop became smaller.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the curves of ZHQ1 and ZHQ2 are roughly the same with obvious kneading phenomenon, and the hysteretic curves of ZHQ3 and ZHQ4 are slightly full. Compared with ZHQ1 and ZHQ3, when the axial compression ratio is relatively large, the hysteresis curve is fuller and the bearing capacity is increased.(4)
It can be seen that the hysteresis curve of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is fuller than the reinforced concrete grid frame, and the enclosed area is larger and the energy consumption is higher.Figure 13
Hysteretic curves. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4.
(a)
(b)
(c)
(d)
(e)
(f)
(g)


### 3.3. Skeleton Curve

The skeleton curve is the envelope curve formed by connecting the peak points of the first cycle of each loading stage of the hysteretic curve. The skeleton curves of the specimens are shown in Figure14.Figure 14
Skeleton curve.The following information can be derived from Figure14:(1)
At the early stage of loading, the skeleton curve is basically linear. As the horizontal displacement increases gradually, the skeleton curve begins to bend and rise. After reaching the peak, the skeleton curve gradually decreases until the specimen is destroyed.(2)
For reinforced concrete grid frame, the skeleton curves are similar before yielding under different axial compression ratios. After the specimen yields, a certain difference is observed in the skeleton curve. The skeleton curves tend to be gentle. This finding indicates that the concrete grid frame has strong deformation capacity.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the skeleton curves of ZHQ1 and ZHQ2 have obvious ascending and descending sections, respectively. The skeleton curves of ZHQ3 and ZHQ4 have obvious ascending sections but no obvious descending sections. In the case of the same displacement, the load of ZHQ4 is the largest, the load of ZHQ3 is the second, and the load of the other two specimens is the smallest. This finding indicates that the peak load increases with the axial compression ratio. The descending section of the skeleton curve is relatively abrupt. The stiffness of the specimen degenerates rapidly, and the deformation ability is low.(4)
The skeleton curves of KJ2 and ZHQ1 have obvious ascending and descending sections, respectively, with strong deformation capacity. The bearing capacity of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is higher than the reinforced concrete grid frame. This finding shows that the addition of cast-in-situ phosphogypsum can evidently improve the bearing capacity of composite walls.


### 3.4. Bearing Capacity

The load and displacement at the measured characteristic points of the specimens are listed in Table5. The following information can be derived from Table 5:(1)
For reinforced concrete grid frame, the comparison of KJ1 and KJ2 indicates that the load of the specimens increases with the axial compression ratio. Among them, the cracking loading increases more obviously. Given the increase of horizontal displacement, the specimens enter the yielding stage too early due to the high axial compression ratio of KJ3. Then, the bearing capacity of specimens obviously decreases. Finally, the bearing capacity of the specimens becomes smooth.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the comparison of ZHQ1 and ZHQ2 shows that the axial compression ratios are approximately the same; thus, the load and displacement of specimens are also roughly the same. Meanwhile, the comparison of ZHQ1 and ZHQ3 shows that when the axial compression ratios are different, the load and displacement of specimens also vary considerably. When the axial compression ratio is large, the corresponding cracking displacement occurs earlier and the cracking load is also large. In addition, the characteristic displacements of ZHQ3 appear earlier than those of ZHQ1. However, the peak and limit loads of ZHQ3 are larger than those of ZHQ1.(3)
In comparison with KJ2,Fcr, Fy, Fm, and Fu of ZHQ1 increase by 33.6%, 151.81%, 158.21%, and 134.39%, respectively, under the same axial compression ratio. This finding shows that the addition of cast-in-situ phosphogypsum can effectively improve the bearing capacity of composite wall.Table 5
Test results of characteristic points.
Specimen number (axial compression ratio)
Loading direction
Cracking point
Yield point
Peak point
Ultimate point
μ
θ
u
F
cr (kN)
δ
cr (mm)
F
y (kN)
δ
y (mm)
F
m (kN)
δ
m (mm)
F
u (kN)
δ
u (mm)
KJ1
Reverse
8.810
9.353
14.587
24.056
18.110
57.364
15.829
85.668
3.566
1/21
(0.072)
Forward
8.334
6.874
14.274
21.104
16.817
52.303
14.611
78.478
3.488
1/23
KJ2
Reverse
11.776
9.190
15.609
18.463
18.677
38.074
16.278
63.580
3.444
1/28
(0.103)
Forward
11.402
8.311
12.319
17.567
13.774
36.075
9.996
61.419
3.496
1/29
KJ3
Reverse
11.854
8.691
13.642
17.334
13.968
35.160
13.580
61.029
3.521
1/29
(0.127)
Forward
11.810
7.532
10.249
16.921
13.106
33.869
12.937
55.147
3.259
1/33
ZHQ1
Reverse
16.385
8.084
36.293
22.725
43.054
33.296
31.254
85.784
3.775
1/21
(0.107)
Forward
14.581
8.058
34.032
21.537
40.738
35.534
30.330
73.619
3.418
1/24
ZHQ2
Reverse
16.385
7.662
36.293
22.130
43.054
32.472
31.254
84.4522
3.816
1/21
(0.108)
Forward
14.581
8.381
34.032
22.001
40.739
37.160
30.330
76.704
3.486
1/23
ZHQ3
Reverse
20.626
6.022
27.701
11.869
46.333
35.064
37.755
44.522
3.751
1/40
(0.167)
Forward
13.100
5.094
26.944
9.975
39.216
32.596
37.798
41.763
4.186
1/43
ZHQ4
Reverse
19.112
5.129
30.837
10.518
46.828
34.178
46.828
34.178
3.249
1/53
(0.154)
Forward
18.215
4.298
29.913
9.159
50.961
29.275
50.961
29.275
3.196
1/61


### 3.5. Ductility Coefficient and Limit Displacement Angle

The ductility coefficient of the structure refers to the capability of the structure to continue increasing its deformation after yielding. It is measured by the displacement ductility coefficientμ=δu/δy. The limit displacement angle at specimen failure is θu=δu/H, where H refers to the total wall height. The displacement ductility coefficient μ and limit displacement angle θu of specimens are shown in Table 5.The following information can be derived from Table5:(1)
For reinforced concrete grid frame, the positive displacement ductility coefficients of specimens are in the range of 3.4–3.6, with a mean value of 3.510. The reverse displacement ductility coefficients of specimens are in the range of 3.2–3.5, with a mean value of 3.414. The limit displacement angleθu decreases with the increase of the axial compression ratio, between 1/21 and 1/33, and the average value of 1/27.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the positive displacement ductility coefficients of specimens are in the range of 3.2–3.9, with a mean value of 3.648. The reverse displacement ductility coefficients of specimens are in the range of 3.1–4.2, with a mean value of 3.572. The limit displacement angle decreases with the increase of axial compression ratio, and the limit displacement angle of ZHQ4 is the smallest, while the limit displacement angle of ZHQ3 is the second. Among ZHQ1–ZHQ4, ZHQ3 has the largest ductility coefficient, followed by ZHQ1 and ZHQ2, and ZHQ4 has the smallest ductility coefficient. ZHQ1 and ZHQ2 have a large limit displacement angle.(3)
It can be seen that the ductility coefficient of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is slightly larger than the reinforced concrete grid frame, and the limit displacement angle of ZHQ1 and ZHQ2 in the composite wall is slightly larger than the reinforced concrete grid frame.


### 3.6. Attenuation of Bearing Capacity

The reduction factor of bearing capacityϕ [23] is adopted to characterise the attenuation law of the bearing capacity of specimens. The reduction factor of the bearing capacity of specimens ϕ refers to the ratio of peak load of cycle 2 to that of cycle 1 under the same stage of loading. The relationship between ϕ and the horizontal displacement at the loading point is shown in Figure 15.Figure 15
Bearing capacity degradation. (a) Concrete gird frame wall. (b) Cast-in-place phosphogypsum-reinforced concrete grid frame composite wall.
(a)
(b)The following information can be derived from Figure15:(1)
For reinforced concrete grid frame, the reduction factor of the bearing capacityϕ of specimens remains in the range of 0.827–0.955. This finding shows that all the specimens do not show serious bearing capacity attenuation.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the reduction factor of the bearing capacityϕ of specimens remains in the range of 0.626–1.0. The attenuation of ZHQ1 and ZHQ2 is nearly the same, whereas that of ZHQ3 and ZHQ4 is relatively serious. When the displacement is less than the peak displacement, the bearing capacity reduction coefficient of ZHQ3 and ZHQ4 is greater than that of the other two specimens. When the displacement exceeds the peak displacement, the bearing capacity of ZHQ3 and ZHQ4 declines seriously.Hence, the attenuation of specimens increases with the axial compression ratio. After loading to the peak, the reduction factor of bearing capacity evidently decreases. Moreover, the attenuation degree of the composite wall is slightly greater than the reinforced concrete grid frame.


### 3.7. Energy Dissipation

The energy dissipation of specimens is measured by the area surrounded by the hysteretic curve of the load-displacement curve. The equivalent viscous damping coefficients of all specimens under peak load and failurehe [24] are shown in Table 6.(2)he=S12πS2+S3,where S1 refers to the energy dissipated by the components in a reverse and forward cycle, and S2 and S3 are the energy absorbed by an ideal elastic structure at the same displacement, as shown in Figure 16 [25].Table 6
Equivalent viscous damping coefficienthe.
Specimen number
KJ1
KJ2
KJ3
ZHQ1
ZHQ2
ZHQ3
ZHQ4
Peak point
0.092
0.129
0.088
0.083
0.084
0.132
0.129
Ultimate point
0.103
0.164
0.104
0.091
0.094
0.137
0.129Figure 16
Calculation of equivalent viscous damping coefficient.The accumulated energy consumptionE refers to the sum of areas surrounded by hysteretic loops. The accumulated energy consumption by all specimens is normalised on the basis of the accumulated energy consumption by KJ1. The relative accumulated energy consumption Er is obtained, as shown in Figure 17.Figure 17
Relative accumulated energy consumption.From Table6 and Figure 17, the following information can be derived:(1)
For reinforced concrete grid frame, the equivalent viscous damping coefficienthe of KJ2 is obviously higher than those of KJ1 and KJ3. The relative accumulated energy consumption of KJ2 and KJ3 is lower than that of KJ1. With the increase of axial compression ratio, the equivalent viscous damping coefficient he of KJ1 and KJ2 increases gradually, and the relative accumulated energy consumed decreases accordingly.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the equivalent viscous damping coefficienthe of ZHQ3 and ZHQ4 is obviously higher than those of two specimens. With the increase of axial compression ratio, the equivalent viscous damping of specimens increases gradually, and the relative accumulated energy consumption decreases accordingly.(3)
The relative accumulated energy consumption by KJ2, KJ3, and ZHQ1–ZHQ4 is approximately 0.84, 0.55, 2.13, 2.16, 1.31, and 0.86 times of that of base contrast specimen KJ1, respectively.This finding shows that the addition of cast-in-place phosphogypsum can effectively increase the energy consuming capacity of the reinforced concrete grid frame.


### 3.8. Stiffness Degradation

According to JGJ/T-2015 specification of testing methods for earthquake resistant buildings [22], the degree of stiffness degradation is measured by the slope of the connection between the peak points of positive load in the first hysteresis loop of each stage cycle. The calculation formula is as follows [26]:(3)Ki=+Fi+−Fi+δi+−δi,where +Fi and −Fi refer to the positive and negative maximum loads of the first hysteresis loop under i stage cycle loading, respectively, and +δi and −δi refer to the positive and negative maximum displacements of the first hysteresis loop under i stage cycle loading, respectively. The stiffness degradation curves of all specimens are shown in Figure 18.Figure 18
Stiffness degradation curve.From the comparison of curves in Figure18, the following information can be derived:(1)
The stiffness degradation laws in the loading process of specimens are consistent. The faster the stiffness attenuation is in the early stage of loading, the slower it is in the middle and late stages of loading, which gradually tends to be horizontal.(2)
For reinforced concrete grid frame, the initial stiffness of KJ3 is larger than those of KJ1 and KJ2. As the horizontal displacement increases, the stiffness of specimens decreases gradually. Among them, the stiffness degradation of KJ3 is rapid. When the horizontal displacement is approximately 18 mm, the late stiffness of specimens is roughly the same and tends to be smooth.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the initial stiffness of ZHQ4 is the highest, followed by that of ZHQ3. The stiffness of ZHQ1 and ZHQ2 is roughly the same. As the horizontal displacement increases, the stiffness degradation of ZHQ3 and ZHQ4 is fast. The stiffness of specimens decreases gradually. When the horizontal displacement is approximately 36 mm, the late stiffness of specimens is roughly the same and tends to be smooth.Hence, the stiffness of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is higher than that of reinforced concrete grid frame. This finding shows that the addition of cast-in-situ phosphogypsum can significantly improve the stiffness of composite wall.


### 3.9. Strain of Longitudinal Reinforcement

The measuring points of strain shown in Figure11 are measured. Figure 18 shows the strain distribution of each specimen with the increase of loading displacement. The following information can be derived from Figures 11 and 19:(1)
For reinforced concrete grid frame, steel strain increases gradually with the displacement. In the strain of column longitudinal reinforcement,Z13 has the largest strain at the base of column, and L1 has the largest in the strain of beam longitudinal reinforcement. However, steel strain does not gradually reduce with the increase of the specimen height. Hence, the lower strain of the specimens is large, although the stress of the specimens is complex.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, steel strain increases gradually with the displacement. In the strain of column longitudinal reinforcement,Z13 has the largest strain at the base of column, and L1 has the largest in the strain of beam longitudinal reinforcement. Steel strain decreases with the increase of specimen height. Thus, the addition of cast-in-situ phosphogypsum can properly change the stress performance of specimens. The lower strain of the specimens is large, and the upper strain is small.Figure 19
Steel strain curve. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4.
(a)
(b)
(c)
(d)
(e)
(f)
(g)It can be seen that the addition of cast-in-situ phosphogypsum changes the stress of the reinforced concrete grid frame, which results in the difference between the steel strain of the composite wall and the steel strain of reinforced concrete grid frame.


### 3.10. Analysis of Failure Mechanism

The addition of cast-in-situ phosphogypsum not only can improve the stress of reinforced concrete grid frame and its bearing capacity and stiffness but can also restrain the deformation of concrete and change the stress mechanism of specimens. Under horizontal load, cast-in-situ phosphogypsum and reinforced concrete grid frame works together. Cast-in-situ phosphogypsum is constrained by reinforced concrete grid frame. Meanwhile, the deformation of reinforced concrete grid frame is constrained by cast-in-situ phosphogypsum. Both conditions interact with each other, exert force together, and give full play to their respective performance. At the same time, cast-in-situ phosphogypsum has the property of microexpansion and can fully be in contact with the reinforced concrete grid frame. Hence, the deformation of both tends to coordinate and work together. When the horizontal load is small, the horizontal load is borne by the concrete grid frame. As the loading displacement increases, the deformation of reinforced concrete grid frame increases and cast-in-situ phosphogypsum is extruded to bear the horizontal load together. The horizontal load continues to increase with the displacement.This finding shows that the collaborative work of cast-in-situ phosphogypsum and reinforced concrete grid frame can effectively restrain each other and improve the bearing capacity and stiffness of the specimens. Then, cast-in-situ phosphogypsum is damaged with penetrated cracks, broken base of column, and buckling steel bar. The cast-in-situ phosphogypsum in grids is broken, and the specimen is destroyed finally.


## 3.1. Test Phenomena and Failure Characteristics

### 3.1.1. Reinforced Concrete Grid Frame

When the vertical load of reinforced concrete grid frame is completed, there is no cracking on the surface of specimens. When the horizontal loading displacement is 12 mm, vertical cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column; cracks develop in the joint area between the storey beam and side column; and oblique cracks appear. When the horizontal loading displacement is 25 mm, cross cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column, and lateral cracks appear on the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, oblique cracks appear in the foot area of side columns, and local failure of concrete occurs in the cross cracks of beam-column joints, with increasing transverse cracks of side columns. When the horizontal displacement is loaded to the failure displacement, original cracks increase gradually, the concrete is crushed, the steel bar buckles and the specimens are damaged. The failure of specimens is shown in Figure12.Figure 12
Failure modes of each specimen. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4. (h) Details of the damage.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


### 3.1.2. Cast-In-Situ Phosphogypsum-Reinforced Concrete Grid Frame Composite Wall

When the vertical load of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is completed, there is no cracking on the surface of specimens. At the early stage of horizontal displacement loading, slip cracks appear at the joint of cast-in-situ phosphogypsum and concrete. When the horizontal loading displacement is loaded to about 30% of the failure displacement, vertical cracks appear in the joint area between the storey beam and side column, oblique cracks appear in the joint area between the interstorey beam and middle column, and lateral cracks appear in the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, the corner of cast-in-situ phosphogypsum of ZHQ1 and ZHQ2 is broken, oblique cracks appear in the joint area between the storey beam and side column, and many oblique cracks appear in cast-in-situ phosphogypsum, with increasing transverse cracks of side columns. The corner of the cast-in-situ phosphogypsum of ZHQ3 and ZHQ4 is broken, vertical cracks appear in the middle of the lower part of the interstorey beam, and transverse cracks appear at the bottom of the middle column. Many oblique cross cracks appear in the beam-column joint area, and vertical fracture cracks appear at the bottom of the interstorey beam. When the horizontal displacement is loaded to the failure displacement, original cracks on ZHQ1 and ZHQ2 continue to develop, cast-in-situ phosphogypsum crushes and falls off, the concrete in the beam-column joint area is broken, steel bars are exposed and buckled, and the specimen is damaged. On the lower part of ZHQ3 and ZHQ4, splitting failure occurs on phosphogypsum, the transverse crack width of the side columns increases gradually, the concrete at the root of the side columns is broken, the steel bars are exposed and buckled, and the specimens are damaged. The failure of specimens is shown in Figure12.


## 3.1.1. Reinforced Concrete Grid Frame

When the vertical load of reinforced concrete grid frame is completed, there is no cracking on the surface of specimens. When the horizontal loading displacement is 12 mm, vertical cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column; cracks develop in the joint area between the storey beam and side column; and oblique cracks appear. When the horizontal loading displacement is 25 mm, cross cracks appear in the joint area between the storey beam and side column and between the interstorey beam and middle column, and lateral cracks appear on the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, oblique cracks appear in the foot area of side columns, and local failure of concrete occurs in the cross cracks of beam-column joints, with increasing transverse cracks of side columns. When the horizontal displacement is loaded to the failure displacement, original cracks increase gradually, the concrete is crushed, the steel bar buckles and the specimens are damaged. The failure of specimens is shown in Figure12.Figure 12
Failure modes of each specimen. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4. (h) Details of the damage.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


## 3.1.2. Cast-In-Situ Phosphogypsum-Reinforced Concrete Grid Frame Composite Wall

When the vertical load of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is completed, there is no cracking on the surface of specimens. At the early stage of horizontal displacement loading, slip cracks appear at the joint of cast-in-situ phosphogypsum and concrete. When the horizontal loading displacement is loaded to about 30% of the failure displacement, vertical cracks appear in the joint area between the storey beam and side column, oblique cracks appear in the joint area between the interstorey beam and middle column, and lateral cracks appear in the side of the side column. When the horizontal displacement is loaded to 75% of the failure displacement, the corner of cast-in-situ phosphogypsum of ZHQ1 and ZHQ2 is broken, oblique cracks appear in the joint area between the storey beam and side column, and many oblique cracks appear in cast-in-situ phosphogypsum, with increasing transverse cracks of side columns. The corner of the cast-in-situ phosphogypsum of ZHQ3 and ZHQ4 is broken, vertical cracks appear in the middle of the lower part of the interstorey beam, and transverse cracks appear at the bottom of the middle column. Many oblique cross cracks appear in the beam-column joint area, and vertical fracture cracks appear at the bottom of the interstorey beam. When the horizontal displacement is loaded to the failure displacement, original cracks on ZHQ1 and ZHQ2 continue to develop, cast-in-situ phosphogypsum crushes and falls off, the concrete in the beam-column joint area is broken, steel bars are exposed and buckled, and the specimen is damaged. On the lower part of ZHQ3 and ZHQ4, splitting failure occurs on phosphogypsum, the transverse crack width of the side columns increases gradually, the concrete at the root of the side columns is broken, the steel bars are exposed and buckled, and the specimens are damaged. The failure of specimens is shown in Figure12.


## 3.2. Hysteretic Curve

Figure13 shows the load-displacement hysteretic curve of each specimen at the horizontal loading point, where F refers to the horizontal load of the specimens, and δ refers to the horizontal displacement of the specimens. The following information can be derived from Figure 13:(1)
At the early stage of loading, the hysteretic curves of all specimens are basically fusiform, and residual deformation is small. Under the horizontal displacement loading, the hysteretic curve inclines to the displacement axis. The area around the curve and the energy dissipation capacity increase. However, under the same loading level, the hysteretic loop area of the second loading is smaller than that of the first loading.(2)
For reinforced concrete grid frame, the hysteretic curve of KJ2 is fuller than that of the two other specimens. Before reaching the peak load, the hysteretic curves of the specimens become similar in shape with kneading phenomenon. After reaching the peak load, the kneading phenomena of KJ1 and KJ3 hysteretic curves are more serious than that of KJ2, and their enclosed areas are smaller. When the loading displacement was 12 mm, local damage occurred to specimen KJ3, resulting in a gap in the hysteretic curve, and the area enclosed by the hysteretic loop became smaller.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the curves of ZHQ1 and ZHQ2 are roughly the same with obvious kneading phenomenon, and the hysteretic curves of ZHQ3 and ZHQ4 are slightly full. Compared with ZHQ1 and ZHQ3, when the axial compression ratio is relatively large, the hysteresis curve is fuller and the bearing capacity is increased.(4)
It can be seen that the hysteresis curve of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is fuller than the reinforced concrete grid frame, and the enclosed area is larger and the energy consumption is higher.Figure 13
Hysteretic curves. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4.
(a)
(b)
(c)
(d)
(e)
(f)
(g)


## 3.3. Skeleton Curve

The skeleton curve is the envelope curve formed by connecting the peak points of the first cycle of each loading stage of the hysteretic curve. The skeleton curves of the specimens are shown in Figure14.Figure 14
Skeleton curve.The following information can be derived from Figure14:(1)
At the early stage of loading, the skeleton curve is basically linear. As the horizontal displacement increases gradually, the skeleton curve begins to bend and rise. After reaching the peak, the skeleton curve gradually decreases until the specimen is destroyed.(2)
For reinforced concrete grid frame, the skeleton curves are similar before yielding under different axial compression ratios. After the specimen yields, a certain difference is observed in the skeleton curve. The skeleton curves tend to be gentle. This finding indicates that the concrete grid frame has strong deformation capacity.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the skeleton curves of ZHQ1 and ZHQ2 have obvious ascending and descending sections, respectively. The skeleton curves of ZHQ3 and ZHQ4 have obvious ascending sections but no obvious descending sections. In the case of the same displacement, the load of ZHQ4 is the largest, the load of ZHQ3 is the second, and the load of the other two specimens is the smallest. This finding indicates that the peak load increases with the axial compression ratio. The descending section of the skeleton curve is relatively abrupt. The stiffness of the specimen degenerates rapidly, and the deformation ability is low.(4)
The skeleton curves of KJ2 and ZHQ1 have obvious ascending and descending sections, respectively, with strong deformation capacity. The bearing capacity of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is higher than the reinforced concrete grid frame. This finding shows that the addition of cast-in-situ phosphogypsum can evidently improve the bearing capacity of composite walls.


## 3.4. Bearing Capacity

The load and displacement at the measured characteristic points of the specimens are listed in Table5. The following information can be derived from Table 5:(1)
For reinforced concrete grid frame, the comparison of KJ1 and KJ2 indicates that the load of the specimens increases with the axial compression ratio. Among them, the cracking loading increases more obviously. Given the increase of horizontal displacement, the specimens enter the yielding stage too early due to the high axial compression ratio of KJ3. Then, the bearing capacity of specimens obviously decreases. Finally, the bearing capacity of the specimens becomes smooth.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the comparison of ZHQ1 and ZHQ2 shows that the axial compression ratios are approximately the same; thus, the load and displacement of specimens are also roughly the same. Meanwhile, the comparison of ZHQ1 and ZHQ3 shows that when the axial compression ratios are different, the load and displacement of specimens also vary considerably. When the axial compression ratio is large, the corresponding cracking displacement occurs earlier and the cracking load is also large. In addition, the characteristic displacements of ZHQ3 appear earlier than those of ZHQ1. However, the peak and limit loads of ZHQ3 are larger than those of ZHQ1.(3)
In comparison with KJ2,Fcr, Fy, Fm, and Fu of ZHQ1 increase by 33.6%, 151.81%, 158.21%, and 134.39%, respectively, under the same axial compression ratio. This finding shows that the addition of cast-in-situ phosphogypsum can effectively improve the bearing capacity of composite wall.Table 5
Test results of characteristic points.
Specimen number (axial compression ratio)
Loading direction
Cracking point
Yield point
Peak point
Ultimate point
μ
θ
u
F
cr (kN)
δ
cr (mm)
F
y (kN)
δ
y (mm)
F
m (kN)
δ
m (mm)
F
u (kN)
δ
u (mm)
KJ1
Reverse
8.810
9.353
14.587
24.056
18.110
57.364
15.829
85.668
3.566
1/21
(0.072)
Forward
8.334
6.874
14.274
21.104
16.817
52.303
14.611
78.478
3.488
1/23
KJ2
Reverse
11.776
9.190
15.609
18.463
18.677
38.074
16.278
63.580
3.444
1/28
(0.103)
Forward
11.402
8.311
12.319
17.567
13.774
36.075
9.996
61.419
3.496
1/29
KJ3
Reverse
11.854
8.691
13.642
17.334
13.968
35.160
13.580
61.029
3.521
1/29
(0.127)
Forward
11.810
7.532
10.249
16.921
13.106
33.869
12.937
55.147
3.259
1/33
ZHQ1
Reverse
16.385
8.084
36.293
22.725
43.054
33.296
31.254
85.784
3.775
1/21
(0.107)
Forward
14.581
8.058
34.032
21.537
40.738
35.534
30.330
73.619
3.418
1/24
ZHQ2
Reverse
16.385
7.662
36.293
22.130
43.054
32.472
31.254
84.4522
3.816
1/21
(0.108)
Forward
14.581
8.381
34.032
22.001
40.739
37.160
30.330
76.704
3.486
1/23
ZHQ3
Reverse
20.626
6.022
27.701
11.869
46.333
35.064
37.755
44.522
3.751
1/40
(0.167)
Forward
13.100
5.094
26.944
9.975
39.216
32.596
37.798
41.763
4.186
1/43
ZHQ4
Reverse
19.112
5.129
30.837
10.518
46.828
34.178
46.828
34.178
3.249
1/53
(0.154)
Forward
18.215
4.298
29.913
9.159
50.961
29.275
50.961
29.275
3.196
1/61


## 3.5. Ductility Coefficient and Limit Displacement Angle

The ductility coefficient of the structure refers to the capability of the structure to continue increasing its deformation after yielding. It is measured by the displacement ductility coefficientμ=δu/δy. The limit displacement angle at specimen failure is θu=δu/H, where H refers to the total wall height. The displacement ductility coefficient μ and limit displacement angle θu of specimens are shown in Table 5.The following information can be derived from Table5:(1)
For reinforced concrete grid frame, the positive displacement ductility coefficients of specimens are in the range of 3.4–3.6, with a mean value of 3.510. The reverse displacement ductility coefficients of specimens are in the range of 3.2–3.5, with a mean value of 3.414. The limit displacement angleθu decreases with the increase of the axial compression ratio, between 1/21 and 1/33, and the average value of 1/27.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the positive displacement ductility coefficients of specimens are in the range of 3.2–3.9, with a mean value of 3.648. The reverse displacement ductility coefficients of specimens are in the range of 3.1–4.2, with a mean value of 3.572. The limit displacement angle decreases with the increase of axial compression ratio, and the limit displacement angle of ZHQ4 is the smallest, while the limit displacement angle of ZHQ3 is the second. Among ZHQ1–ZHQ4, ZHQ3 has the largest ductility coefficient, followed by ZHQ1 and ZHQ2, and ZHQ4 has the smallest ductility coefficient. ZHQ1 and ZHQ2 have a large limit displacement angle.(3)
It can be seen that the ductility coefficient of the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is slightly larger than the reinforced concrete grid frame, and the limit displacement angle of ZHQ1 and ZHQ2 in the composite wall is slightly larger than the reinforced concrete grid frame.


## 3.6. Attenuation of Bearing Capacity

The reduction factor of bearing capacityϕ [23] is adopted to characterise the attenuation law of the bearing capacity of specimens. The reduction factor of the bearing capacity of specimens ϕ refers to the ratio of peak load of cycle 2 to that of cycle 1 under the same stage of loading. The relationship between ϕ and the horizontal displacement at the loading point is shown in Figure 15.Figure 15
Bearing capacity degradation. (a) Concrete gird frame wall. (b) Cast-in-place phosphogypsum-reinforced concrete grid frame composite wall.
(a)
(b)The following information can be derived from Figure15:(1)
For reinforced concrete grid frame, the reduction factor of the bearing capacityϕ of specimens remains in the range of 0.827–0.955. This finding shows that all the specimens do not show serious bearing capacity attenuation.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the reduction factor of the bearing capacityϕ of specimens remains in the range of 0.626–1.0. The attenuation of ZHQ1 and ZHQ2 is nearly the same, whereas that of ZHQ3 and ZHQ4 is relatively serious. When the displacement is less than the peak displacement, the bearing capacity reduction coefficient of ZHQ3 and ZHQ4 is greater than that of the other two specimens. When the displacement exceeds the peak displacement, the bearing capacity of ZHQ3 and ZHQ4 declines seriously.Hence, the attenuation of specimens increases with the axial compression ratio. After loading to the peak, the reduction factor of bearing capacity evidently decreases. Moreover, the attenuation degree of the composite wall is slightly greater than the reinforced concrete grid frame.


## 3.7. Energy Dissipation

The energy dissipation of specimens is measured by the area surrounded by the hysteretic curve of the load-displacement curve. The equivalent viscous damping coefficients of all specimens under peak load and failurehe [24] are shown in Table 6.(2)he=S12πS2+S3,where S1 refers to the energy dissipated by the components in a reverse and forward cycle, and S2 and S3 are the energy absorbed by an ideal elastic structure at the same displacement, as shown in Figure 16 [25].Table 6
Equivalent viscous damping coefficienthe.
Specimen number
KJ1
KJ2
KJ3
ZHQ1
ZHQ2
ZHQ3
ZHQ4
Peak point
0.092
0.129
0.088
0.083
0.084
0.132
0.129
Ultimate point
0.103
0.164
0.104
0.091
0.094
0.137
0.129Figure 16
Calculation of equivalent viscous damping coefficient.The accumulated energy consumptionE refers to the sum of areas surrounded by hysteretic loops. The accumulated energy consumption by all specimens is normalised on the basis of the accumulated energy consumption by KJ1. The relative accumulated energy consumption Er is obtained, as shown in Figure 17.Figure 17
Relative accumulated energy consumption.From Table6 and Figure 17, the following information can be derived:(1)
For reinforced concrete grid frame, the equivalent viscous damping coefficienthe of KJ2 is obviously higher than those of KJ1 and KJ3. The relative accumulated energy consumption of KJ2 and KJ3 is lower than that of KJ1. With the increase of axial compression ratio, the equivalent viscous damping coefficient he of KJ1 and KJ2 increases gradually, and the relative accumulated energy consumed decreases accordingly.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the equivalent viscous damping coefficienthe of ZHQ3 and ZHQ4 is obviously higher than those of two specimens. With the increase of axial compression ratio, the equivalent viscous damping of specimens increases gradually, and the relative accumulated energy consumption decreases accordingly.(3)
The relative accumulated energy consumption by KJ2, KJ3, and ZHQ1–ZHQ4 is approximately 0.84, 0.55, 2.13, 2.16, 1.31, and 0.86 times of that of base contrast specimen KJ1, respectively.This finding shows that the addition of cast-in-place phosphogypsum can effectively increase the energy consuming capacity of the reinforced concrete grid frame.


## 3.8. Stiffness Degradation

According to JGJ/T-2015 specification of testing methods for earthquake resistant buildings [22], the degree of stiffness degradation is measured by the slope of the connection between the peak points of positive load in the first hysteresis loop of each stage cycle. The calculation formula is as follows [26]:(3)Ki=+Fi+−Fi+δi+−δi,where +Fi and −Fi refer to the positive and negative maximum loads of the first hysteresis loop under i stage cycle loading, respectively, and +δi and −δi refer to the positive and negative maximum displacements of the first hysteresis loop under i stage cycle loading, respectively. The stiffness degradation curves of all specimens are shown in Figure 18.Figure 18
Stiffness degradation curve.From the comparison of curves in Figure18, the following information can be derived:(1)
The stiffness degradation laws in the loading process of specimens are consistent. The faster the stiffness attenuation is in the early stage of loading, the slower it is in the middle and late stages of loading, which gradually tends to be horizontal.(2)
For reinforced concrete grid frame, the initial stiffness of KJ3 is larger than those of KJ1 and KJ2. As the horizontal displacement increases, the stiffness of specimens decreases gradually. Among them, the stiffness degradation of KJ3 is rapid. When the horizontal displacement is approximately 18 mm, the late stiffness of specimens is roughly the same and tends to be smooth.(3)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, the initial stiffness of ZHQ4 is the highest, followed by that of ZHQ3. The stiffness of ZHQ1 and ZHQ2 is roughly the same. As the horizontal displacement increases, the stiffness degradation of ZHQ3 and ZHQ4 is fast. The stiffness of specimens decreases gradually. When the horizontal displacement is approximately 36 mm, the late stiffness of specimens is roughly the same and tends to be smooth.Hence, the stiffness of cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall is higher than that of reinforced concrete grid frame. This finding shows that the addition of cast-in-situ phosphogypsum can significantly improve the stiffness of composite wall.


## 3.9. Strain of Longitudinal Reinforcement

The measuring points of strain shown in Figure11 are measured. Figure 18 shows the strain distribution of each specimen with the increase of loading displacement. The following information can be derived from Figures 11 and 19:(1)
For reinforced concrete grid frame, steel strain increases gradually with the displacement. In the strain of column longitudinal reinforcement,Z13 has the largest strain at the base of column, and L1 has the largest in the strain of beam longitudinal reinforcement. However, steel strain does not gradually reduce with the increase of the specimen height. Hence, the lower strain of the specimens is large, although the stress of the specimens is complex.(2)
For cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, steel strain increases gradually with the displacement. In the strain of column longitudinal reinforcement,Z13 has the largest strain at the base of column, and L1 has the largest in the strain of beam longitudinal reinforcement. Steel strain decreases with the increase of specimen height. Thus, the addition of cast-in-situ phosphogypsum can properly change the stress performance of specimens. The lower strain of the specimens is large, and the upper strain is small.Figure 19
Steel strain curve. (a) Specimen KJ1. (b) Specimen KJ2. (c) Specimen KJ3. (d) Specimen ZHQ1. (e) Specimen ZHQ2. (f) Specimen ZHQ3. (g) Specimen ZHQ4.
(a)
(b)
(c)
(d)
(e)
(f)
(g)It can be seen that the addition of cast-in-situ phosphogypsum changes the stress of the reinforced concrete grid frame, which results in the difference between the steel strain of the composite wall and the steel strain of reinforced concrete grid frame.


## 3.10. Analysis of Failure Mechanism

The addition of cast-in-situ phosphogypsum not only can improve the stress of reinforced concrete grid frame and its bearing capacity and stiffness but can also restrain the deformation of concrete and change the stress mechanism of specimens. Under horizontal load, cast-in-situ phosphogypsum and reinforced concrete grid frame works together. Cast-in-situ phosphogypsum is constrained by reinforced concrete grid frame. Meanwhile, the deformation of reinforced concrete grid frame is constrained by cast-in-situ phosphogypsum. Both conditions interact with each other, exert force together, and give full play to their respective performance. At the same time, cast-in-situ phosphogypsum has the property of microexpansion and can fully be in contact with the reinforced concrete grid frame. Hence, the deformation of both tends to coordinate and work together. When the horizontal load is small, the horizontal load is borne by the concrete grid frame. As the loading displacement increases, the deformation of reinforced concrete grid frame increases and cast-in-situ phosphogypsum is extruded to bear the horizontal load together. The horizontal load continues to increase with the displacement.This finding shows that the collaborative work of cast-in-situ phosphogypsum and reinforced concrete grid frame can effectively restrain each other and improve the bearing capacity and stiffness of the specimens. Then, cast-in-situ phosphogypsum is damaged with penetrated cracks, broken base of column, and buckling steel bar. The cast-in-situ phosphogypsum in grids is broken, and the specimen is destroyed finally.


## 4. Conclusions

The main conclusions are summarized on the basis of cyclic pseudostatic seismic testing of the reinforced concrete grid frame and the cast-in-situ phosphogypsum-reinforced concrete grid frame composite wall, as follows:(1)
The failure mode of the reinforced concrete grid frame is mainly the concrete fracture at the beam-column joints, the buckling of the steel bars. The failure mode of the composite wall is mainly the cracks appearing in the beam-column joint region, the cracking of the phosphogypsum, and finally the concrete breaking at the beam-column joint, the buckling of the steel bar.(2)
Compared with the reinforced concrete grid frame, the hysteretic performance of the composite wall is significantly improved, and the enclosed area is larger and the energy consumption is higher.(3)
The addition of cast-in-situ phosphogypsum in the reinforced concrete grid frame can significantly improve the bearing capacity of the composite wall. Compared with the reinforced concrete grid frame, the ultimate bearing capacity of the composite wall is increased by at least 134.39%, which means that the plastic deformation capacity of the reinforced concrete grid frame is effectively improved.(4)
The axial compression ratio has a great influence on the displacement ductility coefficient, limit displacement angle, and relative cumulative energy consumption of the composite wall.(5)
Compared with the reinforced concrete grid frame, the strength of the composite wall is relatively large. At the initial stage of loading, the stiffness decay speed is faster, but the destruction stiffness of the composite wall is still larger than the reinforced concrete grid frame.



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*Source: 1529137-2019-11-04.xml*