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The prestress level is a key factor of prestressed concrete (PSC) beams, affecting their long-term serviceability and safety. Existing monitoring methods, however, are not effective in obtaining the force or stress of embedded tendons. This paper investigates the feasibility of elastomagnetic (EM) sensors, which have been used for external tendons, in monitoring the long-term prestress loss of bonded tendons. The influence of ambient temperature, water, eccentricity ratio, plastic duct, and cement grouts on the test results of EM sensors is experimentally examined. Based on the calibrated EM sensors, prestress loss of a group of PSC beams was monitored for one year. In order to further consider the high randomness in material, environment, and construction, probabilistic analysis of prestress loss is conducted. Finally, the variation range of prestress loss with a certain confidence level is obtained and is compared with the monitored data, which provides a basis for the determination of prestress level in the design of PSC beams.

Prestressed concrete (PSC) beams have been widely used in highway and railway bridges, in which the effective prestress is one key factor influencing the bridge serviceability and safety. However, it is well known that the time-dependent prestress loss is a very complex process, influenced by inherent material properties, external loads or environmental effects, and construction details. [

In order to learn the authentic status of prestress loss in existing PSC beams, various long-term monitoring measures have been investigated. The vibrating wire strain gauges (VWSGs) can obtain the prestress loss due to shrinkage and creep of concrete [

EM sensors used for the stress monitoring of external cables. (a) For stayed cables. (b) For suspenders. (c) For external tendons.

In this paper, the feasibility of elastomagnetic (EM) sensors in monitoring the long-term prestress loss in bonded tendons is experimentally investigated, and the influence of ambient temperature, water, eccentricity ratio, plastic duct, and cement grouts on the test results is discussed. Based on the calibrated EM sensors, prestress loss of two PSC beams was monitored for one year. In order to further consider the high randomness in material, environment, and construction, probabilistic analysis of prestress loss is conducted based on the prediction model that can take into account the influence of nonprestressed steels and interaction among concrete creep, shrinkage, and steel relaxation. Finally, the variation range of prestress loss with a certain confidence level is obtained and is compared with the monitored data, which provides a basis for rational determination of prestress level in the design of PSC beams.

The EM sensor is a nondestructive and noncontact test method, based on the inherent magnetic-elastic effect in the ferromagnetic material. The change in tension force can be obtained by measuring variations in magnetic permeability of prestressed tendons. As shown in Figure

Configuration of an EM sensor.

Measuring principle.

The increment of magnetic permeability of the test specimen with respect to its zero stress state is expressed as follows:

A group of tests were designed to investigate the factors that may influence the performance of EM sensors. First, the influence of ambient temperature on the tests is experimentally investigated. It is known that the permeability of steel specimens changes with the temperature, while the slope of the relationship between the permeability and stress of steel specimens does not change within −30°C to 60°C [

Temperature vs. permeability relationship.

Secondly, the influence of ambient media on the test results was analyzed, where there were four tests. In the test No. 1, the EM sensor was put in air while in the test No. 2, the EM sensor was immerged in water. No specimens were put inside the sensor in the test Nos. 1 and 2. In the test Nos. 3 and 4, the EM sensors were put in air and immerged in water, respectively, with a steel tendon inside the sensor. In each test, the integral voltages were measured for six times, and the ambient temperature was 16°C. According to the test results in Table

Integral voltages of specimen with various ambient media (unit: voltage).

Test | Serial number of measurement | Mean | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

1 | 526.7 | 526.3 | 526.7 | 527.0 | 526.9 | 527.0 | 526.8 |

2 | 526.6 | 526.7 | 526.3 | 526.7 | 526.9 | 526.5 | 526.6 |

3 | 641.0 | 640.7 | 640.8 | 640.6 | 641.2 | 640.6 | 640.8 |

4 | 640.9 | 640.4 | 641.1 | 640.5 | 640.7 | 640.8 | 640.7 |

In addition, the inner diameter of EM sensor is usually significantly larger than the specimen; therefore, in some cases the specimen is difficult to be completely located in the centroid of EM sensor. To investigate the influence of eccentricity, another three tests were conducted, as shown in Figure

Positions of tendon in the sensor.

Integral voltages of specimen with various eccentricities (unit: voltage).

Test | Serial number of measurement | Mean | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

5 | 640.9 | 641.2 | 640.5 | 640.4 | 640.8 | 640.5 | 640.7 |

6 | 637.6 | 637.4 | 637.4 | 637.1 | 637.2 | 636.9 | 637.3 |

7 | 640.4 | 640.6 | 640.8 | 640.1 | 640.5 | 639.9 | 640.4 |

In practice, the steel tendons are usually embedded in corrugated ducts with or without grouts. In order to study the influence of tendon ducts and grouts, the test No. 8 and test No. 9 were conducted, where in the test No. 8, there is a corrugated plastic duct outside the tendon and in the test No. 9, the duct was grouted. As compared with the results in the test No. 3, the two tests in Table

Integral voltages of specimens with duct and grout (unit: voltage).

Test | Serial number of measurement | Mean | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

8 | 640.4 | 640.9 | 640.7 | 640.5 | 640.2 | 640.1 | 640.5 |

9 | 640.2 | 640.4 | 640.5 | 640.0 | 640.4 | 640.0 | 640.3 |

Finally, the relative magnetic permeability of the EM sensor was measured under various levels of loads, as illustrated in Figure

Relative magnetic permeability vs. tension force relationship.

Based on the feasibility of EM sensors in monitoring the long-term prestress loss in bonded tendons, as depicted in Section

Structural dimensions and sensor layout of beams PC1 and PC4. (a) Profile. (b) Cross section (at midspan).

Figure

Long-term prestress losses of beams PC1 and PC4.

Based on the method of age-adjusted effective modulus [

In order to consider the uncertainties in creep model and shrinkage model, two coefficients,

The coefficients

The mechanism and influence factors of concrete shrinkage and creep are very complicated, and there are usually large deviations between the predicted and measured values of effects of concrete creep and shrinkage. There are many reasons leading to this phenomenon, and one of the main reasons is that the selected prediction model of shrinkage and creep itself is not perfect. At present, most of the shrinkage and creep models are the empirical formulas obtained through statistical regression based on experimental data, and the models themselves have the fitting errors; therefore, model uncertainty factors are used to describe the deviation. Some scholars have conducted extensive research on uncertainty of shrinkage and creep models [

Statistical properties of random variables.

Random variables | Unit | Mean | COV | Distribution | Sources |
---|---|---|---|---|---|

Uncertainty factor for creep model, |
— | 1 | 0.339 | Normal | [ |

Uncertainty factor for shrinkage model, |
— | 1 | 0.451 | Normal | [ |

Concrete strength, |
MPa | 63.9 | 0.089 | Normal | [ |

Density of concrete, |
kN/m^{3} |
25.5 | 0.046 | Normal | [ |

Initial stress in steel, |
MPa | 723 (PC1) | 0.020 | Normal | [ |

977 (PC4) | |||||

Annual relative humidity, |
% | 75.0 | 0.161 | Normal | Observed |

Initial loading age, |
d | 30 | 0.110 | Uniform | Assumed |

Elastic modulus of prestressing steel, |
MPa | 1.95 × 10^{5} |
0.060 | Normal | [ |

Area of nonprestressed steel, |
mm^{2} |
565.5 | 0.035 | Normal | [ |

Area of prestressed steel, |
mm^{2} |
140 | 0.0125 | Normal | [ |

Meanwhile, it is necessary to consider the randomness of parameters in the prediction model during the analysis of long-term loss of prestress, where the concrete compressive strength, ambient relative humidity, and loading age are treated as random variables. According to [

According to the probabilistic model in Section

Time-varying PDFs of long-term loss. (a) PC1. (b) PC4.

Time-varying SDs of long-term loss.

As shown in Figure

Comparison of probability results of long-term loss with measured values. (a) PC1. (b) PC4.

This paper provides a preliminary investigation on the feasibility of EM sensors in monitoring the long-term prestress loss of bonded tendons. According to the presented study, conclusions are drawn as follows:

The performance tests of EM sensor show that the external media such as water, cement grouting, and plastic duct have no influence on the measurement results, showing that the EM sensor can be well used in steel members bonded in concrete. The temperature has certain influence on the magnetic permeability of the tested specimens, and the correction coefficient can be obtained through temperature calibration at the zero stress state. The eccentricity of the steel specimens relative to the EM sensor has some impact on the test results, and therefore, the steel specimens should be located in the centroid of the EM sensor when it is installed.

The long-term prestress loss due to shrinkage, creep of concrete, and stress relaxation is complicated, and there are significant uncertainties. Therefore, the uncertainty analysis of long-term loss should be carried out in order to make the design of bridges more safe and realistic. Based on the probabilistic analysis model adapted in this study, the probability analyses were conducted, which indicate that the long-term loss of prestress does not reject the normal distribution at each time, and its discreteness gradually become larger with the extension of time. The bandwidth surrounded by the upper and lower bound of 95% confidence interval also gradually increase with time. In addition, the predicted prestress loss in bridge design from deterministic analysis may be significantly different from the authentic monitored values. Therefore, to conduct a safe design, it is suggested that some suitable confidence limits such as 95% should be adopted instead of the mean value.

For the internal prestressed tendons of widespread PSC box girder bridges, the EM sensors installed in the construction stage can be used for the real-time monitoring of effective prestress force in the service process of bridges, which would provide the basis for the long-term performance assessment of the structures. These will be done in the next study.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The support from the Open Foundation of National Engineering Laboratory for High Speed Railway Construction under the Grant No. HSR2013029, the Education Department of Jiangsu under Grant No. JHB2012-1, and the Priority Academic Program Development of Jiangsu Higher Education Institutions under the Grant No. CE02-1-38 is gratefully acknowledged.