Field Test and Numerical Study of Three Types of Frame Beams Subjected to a 600 kN Anchoring Force

Abstract

Frame beams with anchor cables constitute a crucial method for slope reinforcement projects. With the development of fabricated structures, there has been an increasing focus on precast prestressed frame beams with anchor cables. This paper presents a field test conducted in Yunnan, China and numerical simulations to analyze the structure behavior of three types of frame beams with a 600 kN anchoring force: cast-in-situ frame beams, precast prestressed frame beams, and precast prestressed frame beams with connections. The results showed that: (1) Although all three types of frame beams met the design requirements for a 600 kN anchoring force capacity, the volume of precast prestressed frame beams constituted only 57% of that of the cast-in-situ frame beams. (2) The maximum bending moment for the precast prestressed frame beams with connections was 60 kN·m less than that for the cast-in-situ frame beams. (3) The field test results for bending moments exceeded the values obtained from the numerical simulation. When using a numerical simulation to study the bending moments of the anchor frame beams, it is acceptable to apply appropriate amplifications to the numerical results. (4) Among the three types of frame beams with cables, the precast prestressed frame beams with connections exhibited the best structural performance.

1. Introduction

The anchor frame beam, consisting of frame beams and anchor cables, has been widely used in slope engineering as a new support form [1,2,3,4]. The principle of slope reinforcement using frame beams with anchor cables is to maximize the strength of the anchor cables through tensioning and connect the weak structural plane of the rock mass with the stable rock stratum and the frame beam. This reinforcement method aims to improve the overall stability of the slope.

There have been many studies about anchor frame beams with the anchor cable as the research object [5,6,7,8]. For example, Li et al. [9] advanced a methodology for determining the layout and length of anchor cables based on three-dimensional geological characteristics. Zhang et al. [10] examined the influence of anchoring orientation and position on reinforcement effectiveness using the global method. Because the loss of anchor cable force is a common occurrence that directly impacts the effectiveness of reinforcement, Shi et al. [11] introduced a novel coupled calculation model to accurately predict the behavior and degree of anchor cable force loss.

As the primary component of anchor frame beams, the frame beams have been the subject of numerous studies [12,13,14,15]. For instance, Yuan and Liu [16] established a dynamic simplified model for frame beams with anchor cables to study dynamic response characteristics and the seismic mechanism of the frame beams. Fan et al. [17] devised a new load distribution method intended for calculating internal forces for frame beams. Lian et al. [18] examined the erosion protection provided by frame beams and their impact on stabilization and load-bearing behavior, conducting an analysis of the critical stability conditions of soil particles in a shallow slope under rainfall infiltration. Many studies have also been conducted on the stability of slopes reinforced by anchor frame beams [19,20,21,22].

Although the above studies have contributed to the development of anchor frame beams a lot, it should be noted that the majority of frame beams used were cast-in-situ frame beams. With the development of fabricated structures, there has been an increasing focus on precast frame beams. In construction, precast frame beams give the benefits of simplicity, structural stability, and cost-effectiveness when compared with cast-in-situ frame beams [23]. Based on precast frame beams, the Japan Precast Concrete Frame Association [24,25] proposed a novel type of frame beam called precast prestressed frame beams. These beams utilize either the pre-tensioning or post-tensioning technique to introduce prestresses into the precast frame beams. Precast prestressed frame beams with anchor cables present multiple benefits in reinforcement engineering [26,27], but only limited research has been conducted on these novel frame beams with anchor cables.

In this paper, based on the reinforcement project in the Mengping highway in Yunnan, China, a field test and numerical simulations were conducted to investigate the structural performance of three types of frame beams (cast-in-situ frame beams, precast prestressed frame beams, and precast prestressed frame beams with connections; Figure 1) with a 600 kN anchoring force during loading and the normal service period. Precast prestressed frame beams with connections represent an innovative integrated structure created by interconnecting individual precast prestressed frame beams. The results indicated the following: (1) Although three types of frame beams with anchor cables met the design requirements, precast prestressed frame beams had a volume that was only 57% of that of the cast-in-situ frame beams. (2) Precast prestressed frame beams with connections subjected to a 600 kN anchoring force exhibited a maximum bending moment that was 60 kN·m lower than that of the cast-in-situ frame beams. (3) Field test results of bending moments tended to be higher than the numerical results. This indicates the need to appropriately amplify the numerical results when studying the bending moments of anchor frame beams with a numerical simulation. (4) Precast prestressed frame beams with connections demonstrated superior structural performance because they acted as a unified entity, allowing for the transfer of internal forces.

2. Field Test

2.1. Project View

The experimental project took place on a segment of the Mengping highway from 25 + 580 to 25 + 690, located in Yunnan Province, China. The slope comprises four grades, each with a height of 10 m, and the slope ratios ranged from 1:0.75 to 1:1, as illustrated in Figure 1. For this study, a second-grade slope with a 1:1 ratio was selected as the experimental area; the total length of the experimental section was 110 m. The surface of the slope was silty clay, under which lied heavily weathered fractured rock. The soil parameters were obtained by analogy with engineering projects situated in proximate geological conditions (

Table 1. Material parameters in the field test and numerical simulations.

Parameter	Type	Strength (MPa)	Density (kg/m3)	Young’s Modulus (Pa)	Poisson’s Ratio	Dilatation Coefficient (1/°C)
Steel reinforcement		400	7800	2 × 1011	0.25	—
Prestressed steel strand	φ15.24	1860	7800	2 × 1011	0.25	1.2×10−5
Concrete	C40	40	2643	3 × 1010	0.2	—
Soil	—	—	2000	3 × 107	0.3	—

). The comprehensive friction angle for this structural surface was 33°, while the cohesive strength of the soil–rock interface was determined as 90 kPa. Furthermore, the elastic modulus was specified at 30 MPa.

The experimental slope was reinforced by frame beams with anchor cables. To ensure a safety factor against slope instability exceeding 1.2 and following a rational calculation, an anchoring force of 600 kN was chosen. Appropriate spacing between anchor holes was determined to be 3 m horizontally and 4.25 m vertically. The prestressed anchor cables consisted of four high-strength, low-relaxation steel strands, each with a length of 25 m and a diameter of φ15.24.

2.2. Preparation and Assembly of the Frame Beams

Three types of frame beams were employed in the field test area to reinforce the slope: cast-in-situ frame beams, precast prestressed frame beams with connections, and precast prestressed frame beams. As depicted in Figure 1, each type of frame beam consisted of three columns of beams in the field test. Each frame beam was uniquely identified by its position, where FB-A-X represented the frame beams located in column A, row X, and FB is an abbreviation for the frame beam.

The cast-in-situ frame beams were integral structures comprising three vertical beams and two transverse beams, with specific dimensions as depicted in Figure 2, constructed using conventional building techniques. Conversely, precast prestressed frame beams were manufactured in the fabricated factory and applied prestress with each steel strand pre-tensioned to 15 t. After production completion, these precast prestressed frame beams were transported and hoisted into their respective positions, where prestressed anchor cables were applied. Precast prestressed frame beams and those with connections comprised three columns of beams, each consisting of two cross-shaped beams and one 1-shaped beam, with detailed dimensions illustrated in Figure 3, Figure 4 and Figure 5. The connection method utilized for precast prestressed frame beams involved embedding connecting steel reinforcements at the ends of the frame beams. Once the precast prestressed frame beams were hoisted onto the slope and positioned, concrete was poured at the specified locations where the pre-embedded connecting steel reinforcements were located, effectively joining the three columns of the precast prestressed frame beams into a cohesive structure. This was followed by the application of prestressed anchor cables. The material parameters of frame beams are shown in Table 1.

2.3. Experiment Design

Each column of beams was equipped with three anchor ports, and the prestressed anchor cables consisted of four high-strength, low-relaxation steel strands, each with a length of 25 m and a diameter of φ15.24. The maximum anchoring force applied to frame beams was 600 kN, following a loading sequence: 160 kN–240 kN–320 kN–360 kN–400 kN–600 kN. Vibrating wire anchor load cells were positioned at each anchor port to measure the anchoring forces applied to the frame beams. Additionally, to monitor the forces in the longitudinal steel reinforcement within the frame beams, 180 vibrating wire strain gauges were utilized, with the locations of the measurement points illustrated in Figure 6, and stresses obtained through the sensors could be converted into steel reinforcement forces and section bending moments.

3. Numerical Study

In this study, the performance of three types of frame beams under a 600 kN anchoring force was analyzed using the general finite element analysis software ABAQUS 2020. The frame beams and slope were three-dimensionally modeled at a 1:1 scale to simulate the behavior of longitudinal steel reinforcements within the frame beams during the loading process, and the distribution of section bending moments within the frame beams under a 600 kN anchoring force.

In the numerical simulations, a static general analysis step was employed for the slope. The concrete beams were modelled using eight-node linear hexahedral elements (C3D8R), while steel reinforcements, prestressed steel strands, and anchor cables were represented using two-node linear truss elements (T3D2). The soil used the Mohr–Coulomb model, while the contact method between the soil and the frame beams was set as surface-to-surface contact. Boundary conditions: the x, y, z of the lower surface of the soil were completely constrained. Prestresses were achieved through changes in temperature. The mechanical parameters for the four material types in the model are outlined in Table 1. Figure 7 illustrates the numerical models for the precast prestressed frame beams, precast prestressed frame beams with connections, and the cast-in-situ frame beams.

4. Results and Discussions

4.1. The Analysis of Steel Reinforcement Forces

The study focuses on the experimental beams identified as FB-1-X, FB-4-X, and FB-9-X, representing the precast prestressed frame beams, the precast prestressed frame beams with connections, and the cast-in-situ frame beams, respectively. Figure 8 and Figure 9 depict the force behavior of the longitudinal steel reinforcements in the three types of frame beams during the loading process of prestressed anchoring cables up to 600 kN. These results were obtained from both the field test and numerical simulations. It should be noted that the force was considered positive when it represented pressure and negative when it represented tension.

(1)

As the anchoring force increased, the forces in the upper layer of the longitudinal steel reinforcements in all three types of frame beams increased linearly. Additionally, the forces in the lower layer of the longitudinal steel reinforcements decreased linearly. This observation implies that the three types of frame beams remained within the elastic deformation range under a 600 kN anchoring force, meeting the design load capacity requirements. It is worth noting that the volume of precast prestressed frame beams was only 57% of that of the cast-in-situ frame beams. Under the anchoring force, the upper layer steel reinforcements experienced pressure, while the lower layer steel reinforcements underwent tension.

(2)

In the absence of an anchoring force, the longitudinal steel reinforcement in the precast frame beams experienced pressure due to the presence of prestresses. The forces in the longitudinal steel reinforcements for the precast prestressed frame beams with connections were slightly lower than those of the precast prestressed frame beams. This phenomenon could be attributed to the precast prestressed frame beams with connections acting as a unified whole, which facilitated pressure transmission.

(3)

The discrepancy between the measured steel reinforcement forces and the numerical simulation values could be attributed to the fact that the numerical simulation did not account for prestress loss in the anchor cables during the calculation. To improve the accuracy of the numerical simulation, it would be appropriate to apply a suitable reduction factor to the anchoring force when studying the steel reinforcement forces of the frame beams with an anchoring force.

(4)

The steel reinforcement forces obtained from the field test and numerical simulations closely matched, mutually validating the accuracy of the data.

4.2. The Analysis of Section Bending Moments

The study focuses on the experimental beams designated as FB-1-X, FB-4-X, and FB-9-X, representing the precast prestressed frame beams, the precast prestressed frame beams with connections, and the cast-in-situ frame beams, respectively. Regarding the time when the anchoring force was loaded up to 600 kN, Figure 10 presents a comparative chart of section bending moments for the three types of frame beams obtained from the field test and numerical simulations, and Figure 11 displays a comparative chart of section bending moments obtained from numerical simulations for three types of frame beams. In terms of bending moments, the upper portion of the beam experiencing tension and the lower portion experiencing pressure were considered positive bending moments, while the reverse was considered negative bending moments.

(1)

In Figure 10, the bending moments obtained from the field test and numerical simulations were in substantial agreement, validating the accuracy of the data. Notably, most measured section bending moments were generally higher than the numerical values. This discrepancy could be attributed to the numerical simulations not accounting for the loss of prestresses in the anchor cables and other unavoidable interfering factors in the field test, such as uneven soil distribution, frame beam disturbance, temperature, etc.

(2)

Figure 10 indicates that the bending moment range for precast prestressed frame beams was −110 to −30 kN·m; for precast prestressed frame beams with connections, the range was from −70 to −20 kN·m; and for cast-in-situ frame beams, it fell within the range of −140 to −20 kN·m. This suggests that precast prestressed frame beams exhibited better load-bearing performance. This improvement could be attributed to the presence of prestresses in the precast frame beams, which could offset some bending moments generated by the anchoring force. Additionally, connecting all precast prestressed frames optimized their load-bearing performance.

(3)

In Figure 11, it is evident that the maximum bending moment for all three types of frame beams occurred at the anchor point. Notably, the maximum bending moment for precast prestressed frame beams with connections was 60 kN·m smaller than that for cast-in-situ frame beams. This reduction was attributed to the bending moment generated by prestresses in the precast prestressed frame beams, countering a portion of the bending moment caused by the anchoring force.

(4)

The maximum bending moment in the precast prestressed frame beams with connections was significantly lower than that in the precast prestressed frame beams. This phenomenon could be attributed to the precast prestressed frame beams with connections functioning as an integrated entity, facilitating the distribution and sharing of bending moments among the components. Consequently, the bending moment distribution in the precast prestressed frame beams with connections was more uniform.

5. Conclusions

This study, conducted through a field test in Yunnan, China and numerical simulations, investigated the load-bearing performance of three types of frame beams subjected to a 600 kN anchoring force during both loading and the normal service period. These frame beams included cast-in-situ frame beams, precast prestressed frame beams with connections, and precast prestressed frame beams. The following conclusions were drawn:

(1)

The field test results closely aligned with the numerical values, affirming the reliability of the simulation approach employed in this study. This method can be extended to exploring diverse properties and characteristics of frame beams with anchor cables, thereby paving the way for further research in this field.

(2)

Throughout the anchoring force loading process, all three types of frame beams remained within the elastic range; it was shown that three types of frame beams met the design requirements. However, it is crucial to emphasize that the volume of the precast frame beams was merely 57% of that of the cast-in-situ frame beams. Furthermore, the precast prestressed frame beams exhibited superior load-bearing performance. This improvement was primarily attributed to prestresses in the precast prestressed frame beams.

(3)

When the anchoring force reached 600 kN, the maximum bending moment in the precast prestressed frame beams with connections was 60 kN·m less than that in the cast-in-situ frame beams. The reduction could be attributed to the bending moment generated by the prestresses in the precast prestressed frame beams, which counteracted a portion of the bending moment caused by the anchoring force.

(4)

The precast prestressed frame beams with connections outperformed precast frame beams in terms of steel reinforcement forces and section bending moments. This improvement could be attributed to the precast prestressed frame beams with connections functioning as an integrated entity, allowing for the transfer of forces and bending moments at the connection points, resulting in a more even distribution of forces and moments.

(5)

The numerical results of section bending moments were generally lower than the field test values. When using numerical simulation methods to study the bending moments of anchor frame beams, applying a suitable amplification factor to the numerical values may be appropriate.