An Ultrasonic Rock Bolt Sensing Technology (I): Methodology and Laboratory Studies

Abstract

Rock bolts play a critical role in ground support in mining, tunneling and construction. Being able to obtain timely information on rock bolt load condition and deformation could help immensely in safeguarding workers’ safety, optimization of ground support system, and ensuring stability and longevity of underground structures. The objective of this work was to develop a practical ultrasonic rock bolt sensing technology for monitoring axial load and deformation of a full-bodied rock bolt in both elastic and plastic deformation regimes. To this end, empirical mathematical models involving simultaneous use of times of flight of longitudinal and shear ultrasonic waves propagating along the axial direction of the rock bolt were developed, sensors were designed and fabricated, and laboratory studies were conducted. The results showed that the technology was able to measure load change, provide early detection of yield, and measure both plastic and total elongations of the rock bolt undergoing a pull test. Additionally, sectional load and elongation information could be obtained by applying the technology to rock bolts divided into sections by drilled holes along their shanks, therefore, providing the capability to assess the condition of grouted bolts at different depths within a rock mass. This work has laid the groundwork for the deployment of the technology in the field.

Highlights

• Empirical models based on simultaneous use of times of flight of longitudinal and shear ultrasonic waves were proposed for condition monitoring of full-bodied rock bolts

• Methods for instrumenting full-bodied rock bolts were developed

• Calibration methods for determining values of parameters used in the empirical models were established

• Pull testing showed that the technology could measure load changes within and beyond the elastic limit, detect yield, and measure plastic and total elongations of the rock bolt

• Sectional load and elongation information could be obtained by applying the technology to rock bolts divided into sections by drilled holes along their shanks

1 Introduction

Rock bolts play a critical role in ground support in mining, tunneling and construction. It is estimated that hundreds of millions of rock bolts are installed annually in mines and tunnels worldwide. It would be extremely beneficial if the integrity and load condition of installed rock bolts could be assessed whenever needed and in a practical, robust, and cost-effective manner. The objective of this research was to develop an ultrasonic rock bolt sensing technology to meet the above need.

Various types of sensors for rock bolt and grout condition monitoring have been reviewed in Song et al. (2017). Some methods are strain gauge based whereby the strain gauges are bonded onto the rock bolt shank and installed in the borehole with the instrumented bolts. For better protection from damage during installation of the instrumented bolt, the strain gauges and signal wires are sealed in grooves engraved along the longitudinal direction of the rock bolt shank, making the bolt instrumentation process labor-consuming and the instrumented bolt less strong compared with non-instrumented ones (Hyett 2013; Li et al. 2012). By bonding the distal end of one or of a plurality of rigid wires of different lengths to different locations along a bolt, together with a plurality of spring-potentiometer assemblies or optical proximity sensors, the deformation profile of the bolt can be determined (Ellasson 2022; Bawden and Hyett 1998). Other methods include a strain gauge-based load cell integrated in the protruded shank of a rock bolt for load measurement (Mitri 2002), an electro-mechanical impedance measurement approach to rock bolt looseness monitoring using a piezoelectric smart washer placed between the bearing plate and the nut of the rock bolt (Wang et al. 2017), and a method for measurement of tension exerted on a fastening element by monitoring stress-induced changes in magnetic susceptibility of the magnetostrictive material that the fastening element is made of (Carlsson et al. 2016).

There have been efforts aiming to inspect rock bolt grouting conditions based either on vibration analysis of a rock bolt upon impact or attenuation/reflection of low frequency ultrasonic waves transmitted into the rock bolt (Fishman 2004, 2005; Zou et al. 2010; Yu et al. 2013; Ivanović and Neilson 2013; Stepinski and Matsson 2016). A major benefit shared by these systems/methods is that they could be used to diagnose rather long tendons/bolts because of low frequency vibrations involved (< 100 kHz). Applications of higher frequency longitudinal ultrasound have been investigated for length measurement and defect detection on grouted bolts (Beard et al. 2002, 2003; Wu et al. 2007).

Commercial products are available for bolt tension measurement within the elastic deformation regime by propagating an ultrasonic wave along the axial direction of the bolt, measuring the time of flight (TOF) of the ultrasound traveling the bolt length, and determining bolt tension from the measured TOF. To minimize the effect of temperature on load measurement, a temperature sensor is used to set the baseline according to the measured bolt temperature. These products would not be suitable for rock bolts because most rock bolts are designed to be able to perform beyond the yield point and of which the temperatures on the bolt section inside a rock mass are most likely be different from the temperature measured outside the rock mass. There have been efforts on using both longitudinal and shear ultrasonic waves for bolt load measurement with a view to either eliminate the bolt length (Chaki et al. 2007; Carlson and Lundin 2015; Johnson et al. 1986), or bolt temperature (Andersson 2000) from load measurement equations in an elastic deformation regime. A theoretical formula was proposed in Pan et al. (2016) for residual stress measurement using both longitudinal and shear ultrasonic waves. This formula could be applicable to plastic deformation regime but it does not deal with situations where load distribution in the sample is not uniform as is the case with most grouted rock bolts.

The objective of this research was to develop a practical ultrasonic technology for condition monitoring of full-bodied rock bolts in real-world conditions where the rock bolts may experience either elastic or plastic deformation and where load and temperature distributions on the bolt may not be uniform as in the case of grouted bolts. Pull testing showed that the technology could measure load changes within and beyond the elastic limit, detect yield, and measure plastic and total elongations of the rock bolt and that the technology is applicable to the rock bolt as a whole or to bolt sections divided by drilled holes. By applying the technology to individual bolt sections, sectional load and elongation information could be obtained. This would allow the bolting condition of grouted bolts at different depths within a rock mass to be assessed, providing valuable insight into rock mass condition and grouting integrity versus depth. The paper is organized as follows. In Sect. 2, empirical mathematic models for rock bolt condition monitoring in elastic and plastic deformation regimes are presented. Section 3 centers around experiments and experimental results. Main conclusions of this research are provided in Sect. 4. A method for improving load measurement accuracy by taking into account the stress-free length of the rock bolt is detailed in Appendix.

2 Methodology

The methodology was detailed in Sun et al. (2018) and recapped in this section. The basis of the methodology is empirical and aims for simplicity in implementation.

2.1 Rock Bolt Condition Monitoring in Elastic Deformation Regime

With reference to Fig. 1, an ultrasonic longitudinal wave transducer (LUT) and an ultrasonic shear wave transducer (SUT) are mounted on the exposed end of a full-bodied rock bolt to propagate longitudinal and shear ultrasonic waves along the rock bolt. These waves will be reflected from the distal end of the bolt and eventually from inside reflectors as well (e.g., drilled holes discussed in Sect. 3.1), and return to the transducers as echo signals. The LUT serves to emit and receive longitudinal waves whereas the SUT does the same for shear waves. The time of flight (TOF) for a particular wave to travel the round-trip distance between the transducer and the distal bolt end or reflectors will depend on the travel distance, the temperature, the stress in the bolt, and the wave type (i.e., longitudinal type for waves of which the wave vibration is along the wave propagation direction, or shear (also called transverse) type for waves of which the wave vibration is perpendicular to the wave propagation direction). Therefore, by measuring TOF of two types of ultrasonic waves simultaneously, it is possible to assess the state of two of the three factors affecting TOF in a bolt, namely length, stress, and temperature, assuming that the state of the remaining one factor is either known or measured otherwise. Oftentimes only changes in a rock bolt condition are of importance and in which case these changes may be determined by utilizing only two or one type(s) of waves if the remaining factor(s) stay unchanged during the process. It is to note that a rock bolt is an acoustic waveguide in which acoustic waves of different frequencies and vibration modes travel at different velocities. When operation frequencies of the LUT are high enough, some modes of the generated acoustic waves will travel at high velocities with relatively low attenuations (Beard et al. 2003). An echo signal of such waves will arrive ahead of others. This is the echo signal that we use and refer to as longitudinal wave echo signal in this work. The center frequency of SUT is selected in such a way that it is high enough to favor better spatial resolution but not too high to avoid excessive attenuation of the acoustic energy by the wave propagation medium. Also, the center frequency of SUT and that of LUT should be distant enough one from the other for the two types of ultrasound signals to be easily separable by applying different digital filters. In this work the echo signal generated by such an SUT is referred to as shear wave echo signal. Detailed information on LUT and SUT is provided in Sect. 3.1.

Fig. 1

Longitudinal and shear ultrasonic waves are propagated along the rock bolt and time of flights of echoes reflected from discontinuities inside the bolt and the bolt end inside the rock are measured

In the following, we present how to determine a change in a rock bolt condition. Through experiments it was observed that the change of TOF over a bolt or a section of the bolt caused by a temperature change depends rather linearly on the latter when the bolt is stress free. Furthermore, when tested at room temperature and within the elastic deformation limit, the change of TOF over a bolt or a section of the bolt caused by a stress change depends rather linearly on the latter as well. To the first order of approximation, we propose the following relationships to cover both the stress and temperature effects on TOF (Sun et al. 2018):

$$({\tau }_{L}^{e}-{\tau }_{L0}^{e})/{\tau }_{L0}^{e}={C}_{\sigma L}^{e}*\left[\langle {\sigma }^{e}\rangle -\langle {\sigma }_{0}^{e}\rangle \right]+{C}_{TL}*\left[\langle {T}^{e}\rangle -\langle {T}_{0}^{e}\rangle \right]$$

(1)

$$({\tau }_{S}^{e}-{\tau }_{S0}^{e})/{\tau }_{S0}^{e}={C}_{\sigma S}^{e}*\left[\langle {\sigma }^{e}\rangle -\langle {\sigma }_{0}^{e}\rangle \right]+{C}_{TS}*\left[\langle {T}^{e}\rangle -\langle {T}_{0}^{e}\rangle \right]$$

(2)

where superscript e denotes the elastic deformation regime; subscripts L and S denote values or coefficients associated with longitudinal and shear ultrasonic waves, respectively; subscript 0 denotes a value taken in a reference state, $\tau$ denotes TOF over a bolt or over a bolt section of interest (e.g., the section between x₁ and x₂ in Fig. 1); ${C}_{\sigma L}^{e}$ and ${C}_{\sigma S}^{e}$ are stress coefficients for longitudinal and shear waves respectively in the elastic deformation regime; ${C}_{TL}$ and ${C}_{TS}$ are temperature coefficients for longitudinal and shear waves, respectively; 〈σ〉 and 〈T〉 with associated superscript and subscript denote spatial averages of axial stress and temperature, respectively, over the same bolt or bolt section of interest and are defined as follows:

$$\langle \sigma \rangle =\underset{{x}_{1}}{\overset{{x}_{2}}{\int }} \sigma \left(x\right){\text{d}}x/({x}_{2}-{x}_{1})$$

(3)

$$\langle T\rangle =\underset{{x}_{1}}{\overset{{x}_{2}}{\int }}T\left(x\right){\text{d}}x/({x}_{2}-{x}_{1})$$

(4)

where ${x}_{1}$ and ${x}_{2}$ denote coordinates of the starting and end points of a bolt section of interest in the axial direction of the bolt (Fig. 1). The bolt section of interest could be an entire bolt, a section between the transducer and a reflector, between reflectors, or between a reflector and the distal end of the bolt.

It results from Eqs. (1) and (2) that

$$\langle {\sigma }^{e}\rangle -\langle {\sigma }_{0}^{e}\rangle =\left(\frac{{\tau }_{L}^{e}-{\tau }_{L0}^{e}}{{\tau }_{L0}^{e}}-{\beta }_{T} \frac{{\tau }_{S}^{e}-{\tau }_{S0}^{e}}{{\tau }_{S0}^{e}}\right)/({C}_{\sigma L}^{e}-{\beta }_{T}{C}_{\sigma S}^{e})$$

(5)

in which

$${\beta }_{T}={C}_{TL}/{C}_{TS}$$

(6)

and

$$\langle {T}^{e}\rangle -\langle {T}_{0}^{e}\rangle =\left(\frac{{\tau }_{L}-{\tau }_{L0}}{{\tau }_{L0}}-{\beta }_{\sigma }^{e}\frac{{\tau }_{S}-{\tau }_{S0}}{{\tau }_{S0}}\right)/{({C}_{TL}-\beta }_{\sigma }^{e}{C}_{TS})$$

(7)

in which

$${{\beta }_{\sigma }^{e}=C}_{\sigma L}^{e}/{C}_{\sigma S}^{e}$$

(8)

As long as the bolt is stressed within the elastic deformation limit, Eqs. (5) and (7) allow average load change, $\langle {\sigma }^{e}\rangle -\langle {\sigma }_{0}^{e}\rangle$, with respect to a reference state $\langle {\sigma }_{0}^{e}\rangle$, and average temperature change, $\langle {T}^{e}\rangle -\langle {T}_{0}^{e}\rangle$, with respect to a reference state $\langle {T}_{0}^{e}\rangle$ to be determined, by measuring relative change of TOF of longitudinal wave, $({\tau }_{L}^{e}-{\tau }_{L0}^{e})/{\tau }_{L0}^{e}$, and that of shear wave, $({\tau }_{L}^{e}-{\tau }_{L0}^{e})/{\tau }_{L0}^{e}$, with respect to a reference state (denoted by subscript 0). It is to note that all values denoted by a subscript 0 were taken concurrently at a first point in time whereas their counterparts without the subscript 0 are taken concurrently at a second point in time. The reference could be taken when the bolt was stress-free or right after bolt installation. Compared with conventional methods that are based on knowledge of bolt material properties such as longitudinal and shear wave velocities vs temperature, thermal expansion coefficient, Young’s modulus, and acoustoelastic coefficients of longitudinal and shear waves, the approach presented above is much easier to implement as the temperature coefficients ${C}_{TL}$ and ${C}_{TS}$ and the stress coefficients ${C}_{\sigma L}^{e}$ and ${C}_{\sigma S}^{e}$ already include effect of thermal expansion and elastic elongation on TOF; furthermore the approach is able to handle situations where stress and temperature distributions are not uniform along the bolt as is the case in most real-world rock bolt deployments; also there is no need for accurate knowledge of bolt length, which can vary from bolt to bolt.

2.2 Rock Bolt Condition Monitoring in Plastic Deformation Regime

Most rock bolts are designed to support ground deformation beyond the bolt’s elastic deformation limit (yield point). It would be greatly beneficial if a rock bolt sensing technology could provide information on remaining bolt capacity such as whether the bolt has yielded and if yes by how much and the load being experienced by a plastically deformed bolt. To address this need, an empirical approach was proposed (Sun et al. 2018). In the plastic deformation regime, TOF is still affected by the aforementioned three factors, namely, temperature, stress, and bolt length; however, the stress-free bolt length is no longer a constant and therefore cannot be omitted as in the case of elastic deformation. To still be able to use two measurements, i.e., those of TOF of both longitudinal and shear waves, to determine changes in stress and bolt elongation, the temperature effect on TOF needs to be determined with a different means and removed. A temperature-corrected relative change of TOF can be obtained as follows:

$${\Delta }_{Tc}^{rel}{\tau }_{L}=\frac{{\tau }_{L}-{\tau }_{L0}^{e}}{{\tau }_{L0}^{e}}-{C}_{TL}*\left[\langle T\rangle -\langle {T}_{0}^{e}\rangle \right]$$

(9)

$${\Delta }_{Tc}^{rel}{\tau }_{S}=\frac{{\tau }_{S}-{\tau }_{S0}^{e}}{{\tau }_{S0}^{e}}-{C}_{TS}*\left[\langle T\rangle -\langle {T}_{0}^{e}\rangle \right]$$

(10)

where ${\tau }_{L0}^{e}$ and ${\tau }_{S0}^{e}$, also defined in Eqs. (1) and (2), are respective TOF of longitudinal and shear waves over a rock bolt or a rock bolt section of interest and are to be taken when the rock bolt load is within the elastic deformation limit, for example, soon after the bolt was installed; ${\tau }_{L}$ and ${\tau }_{S}$ are respectively TOF of longitudinal and shear waves over the rock bolt or the rock bolt section of interest and may be measured at a second point in time when a user wishes to monitor the rock bolt or when a change in condition of the rock bolt is to be determined, regardless of the deformation regime the rock bolt is in; ${C}_{TL}*\left[\langle T\rangle -\langle {T}_{0}^{e}\rangle \right]$ and ${C}_{TS}*\left[\langle T\rangle -\langle {T}_{0}^{e}\rangle \right]$ represent temperature effect on relative change in TOF of longitudinal waves and that of shear waves, respectively. As can be seen from Eqs. (9) and (10), the effect of temperature on TOF can be removed if the average temperature over the bolt remains constant, i.e., $\langle T\rangle -\langle {T}_{0}^{e}\rangle =0$, or if the average temperature change $\langle T\rangle -\langle {T}_{0}^{e}\rangle$ can be determined, for example, with a temperature sensor.

Figure 2 shows a typical relationship between the temperature-corrected relative changes of the times of flight of longitudinal and shear ultrasonic waves during a pull test covering an elastic deformation phase and a plastic deformation phase. The elastic deformation phase features a steep linear slope of ${\beta }_{\sigma }^{e}$ whereas the plastic deformation phase is characterized by a much less steep slope of ${\beta }_{\sigma }^{p}$. Thus, based on the relationship between the temperature-corrected relative change in the TOFs of the longitudinal and shear ultrasonic waves it may be possible to determine whether the rock bolt is in the elastic or plastic deformation regime.

Fig. 2

Plot of a typical relationship between the temperature-corrected relative changes of the times of flight of longitudinal and shear ultrasonic waves during a pull test

It may also be possible to determine the permanent elongation that the rock bolt has experienced. Refer to Fig. 2. Let P be the current state point of a rock bolt section of interest and O an earlier state point chosen as reference of the rock bolt. For the same rock bolt section, let ${\tau }_{L}$(·) and ${\tau }_{S}$(·) be respectively the corresponding temperature-corrected TOFs of longitudinal and shear ultrasonic waves at a state point, $\langle \sigma (\cdot )\rangle$ the corresponding spatial average of stress being experienced by the rock bolt, and $l(\bullet )$ the corresponding length of this rock bolt section. If the stress being experienced by the rock bolt at state P were to be released, the rock bolt would transition from the state point P to another state point along an elastic deformation path of slope ${\beta }_{\sigma }^{e}$ (downward dashed line from the state point P), under the assumption that the elastic deformation slope remains unchanged after a plastic deformation According to an experimental study presented in Sect. 3.4, the above assumption holds relatively well. Let P′ be a conceptual state point on the above elastic deformation path and at which the rock bolt has the same spatial average stress as the state point O, i.e.,

$$\langle \sigma ({P}{^\prime})\rangle =\langle \sigma (O)\rangle$$

(11)

Let $\delta {\tau }_{S1}$ and $\delta {\tau }_{L1}$ be the relative changes of temperature-corrected TOFs of longitudinal and shear ultrasonic waves at the state point P′ with respective to state point O, $l\left(O\right)$ the length of the bolt section of interest at the state point O, and $l\left(P{^\prime}\right)$ the conceptual length of the bolt section at the state point P′ and at the same average temperature as the state point O. Since state points O and P′ have the same spatial average stress and that the temperature effect has already been excluded from $\delta {\tau }_{S1}$ and $\delta {\tau }_{L1}$, $\delta {\tau }_{S1}$ and $\delta {\tau }_{L1}$ are solely attributable to a permanent change in bolt length, i.e., a plastic elongation from the state point O to the state point P′. Mathematically this translates to $\delta {\tau }_{S1}=\left(l\left({P}{^\prime}\right)-l(O)\right)/l(O)$ and $\delta {\tau }_{L1}=\left(l\left({P}{^\prime}\right)-l(O)\right)/l(O)$. In other words, the state point P′ lies on the dashed line with a slope of 1 in the figure. Therefore, the plastic elongation can be determined through measurement of either $\delta {\tau }_{S1}$ or $\delta {\tau }_{L1}$ as follows:

$$\frac{l\left(P{^\prime}\right)-l(O)}{l(O)}=\delta {\tau }_{S1} =\delta {\tau }_{L1}$$

(12)

where $l\left(O\right)$ is the length of the bolt section of interest at the state point O, and $l\left(P{^\prime}\right)$ the conceptual length of the bolt section at the state point P′ and at the same average temperature as the state point O.

Let $\delta {\tau }_{S2}$ and $\delta {\tau }_{L2}$ be the relative changes of temperature-corrected TOFs of longitudinal and shear ultrasonic waves at the state point P with respective to the state point P′. The dash line connecting state points P′ and P represents an elastic deformation path with a slope given by

$$\delta {\tau }_{L2}/\delta {\tau }_{S2}={\beta }_{\sigma }^{e}$$

(13)

Since points P′ and P are on an elastic deformation path, according to Eqs. (1) and (2), the following equations holds:

$$\langle \sigma \left(P\right)\rangle -\langle \sigma \left({P}{^\prime}\right)\rangle =\delta {\tau }_{L2}/{C}_{\sigma L}^{e}=\delta {\tau }_{S2}/{C}_{\sigma S}^{e}$$

(14)

and an elastic elongation of the bolt section of interest transitioning from the state point P′ to the state point P can be obtained as:

$$\frac{l\left(P\right)-l(P{^\prime})}{l(P{^\prime})}=\frac{\langle \sigma \left(P\right)\rangle -\langle \sigma \left({P}{^\prime}\right)\rangle }{E}$$

(15)

in which $E$ is the Young’s modulus of the bolt material. In practice the value of $l(P\mathrm{^{^\prime}})$ is very close to that of $l(O)$ and the elastic elongation can be obtained using the following approximation:

$$\frac{l\left(P\right)-l(P{^\prime})}{l(O)}\approx \frac{\langle \sigma \left(P\right)\rangle -\langle \sigma \left({P}{^\prime}\right)\rangle }{E}$$

(16)

According to Fig. 2, the following equations exist:

$$\delta {\tau }_{L1}+\delta {\tau }_{L2}=\frac{{\tau }_{L}(P)-{\tau }_{L}(O)}{{\tau }_{L}(O)}$$

(17)

$$\delta {\tau }_{S1} +\delta {\tau }_{S2} =\frac{{\tau }_{S}(P)-{\tau }_{S}(O)}{{\tau }_{S}(O)}$$

(18)

From Eq. (8) and (11) to (18) the following equations can be obtained:

• (i)(i) Load change from the state point O to the state point P

  $$\langle \sigma (P)\rangle -\langle \sigma \left(O\right)\rangle =\frac{\left[ \frac{{\tau }_{L}\left(P\right)-{\tau }_{L}\left(O\right)}{{\tau }_{L}\left(O\right)} - \frac{{\tau }_{S}\left(P\right)-{\tau }_{S}\left(O\right)}{{\tau }_{S}\left(O\right)} \right]}{{C}_{\sigma L}^{e}-{C}_{\sigma S}^{e}}$$

  (19)

• (ii)(ii) Plastic deformation from the state point O to the state point P′

  $$l\left(P{^\prime}\right)-l(O)=l(O)\frac{{\beta }_{\sigma }^{e}\frac{{\tau }_{S}\left(P\right)-{\tau }_{S}\left(O\right)}{{\tau }_{S}\left(O\right)} - \frac{{\tau }_{L}\left(P\right)-{\tau }_{L}\left(O\right)}{{\tau }_{L}\left(O\right)}}{{\beta }_{\sigma }^{e}-1}$$

  (20)

• (iii)(iii) Elastic elongation from the state point P′ to the state point P

  $$l\left(P\right)-l(P{^\prime})\approx \frac{l(O)}{E}\frac{\left[ \frac{{\tau }_{L}\left(P\right)-{\tau }_{L}\left(O\right)}{{\tau }_{L}\left(O\right)} - \frac{{\tau }_{S}\left(P\right)-{\tau }_{S}\left(O\right)}{{\tau }_{S}\left(O\right)} \right]}{{C}_{\sigma L}^{e}-{C}_{\sigma S}^{e}}$$

  (21)

• (iv)(iv) Total elongation from the state point O to the state point P

  $$l\left(P\right)-l\left(O\right)\approx l\left(O\right)\frac{{\beta }_{\sigma }^{e}\frac{{\tau }_{S}\left(P\right)-{\tau }_{S}\left(O\right)}{{\tau }_{S}\left(O\right)} - \frac{{\tau }_{L}\left(P\right)-{\tau }_{L}\left(O\right)}{{\tau }_{L}\left(O\right)}}{{\beta }_{\sigma }^{e}-1}+\frac{l(O)}{E}\frac{\left[ \frac{{\tau }_{L}\left(P\right)-{\tau }_{L}\left(O\right)}{{\tau }_{L}\left(O\right)} - \frac{{\tau }_{S}\left(P\right)-{\tau }_{S}\left(O\right)}{{\tau }_{S}\left(O\right)} \right]}{{C}_{\sigma L}^{e}-{C}_{\sigma S}^{e}}$$

  (22)

It is worth pointing out that the state point P′ is virtual and auxiliary for determination of load change and deformation with respect to a reference state after the bolt has entered the plastic deformation regime. Since there is no elastic deformation from the state point O to the state point P′ and no plastic deformation from the state point P′ to the state point O, Eq. (20) represents the total plastic elongation from the state point O to the state point P and Eq. (21) represents the total elastic elongation from the state point O to the state point P. Equation (20) would be particularly useful for detecting whether a rock bolt has passed the yield point.

As indicated earlier in this section, of the two equations available for measurement of stress change. Equation (5) is applicable when bolt deformation is in an elastic deformation regime and as such this equation is referred to as the elastic model. This model is immune to temperature variation. Equation (19) is applicable regardless whether the bolt deformation is in an elastic or a plastic deformation regime and therefore this equation is referred to as the general model. When using the general model, the temperature effect on TOF needs to be removed. When temperature is constant, the difference of stress estimates provided by the two models can be derived from Eqs. (5), (8), (19) and (20) and determined as

$${\langle \Delta \sigma \rangle }_{{\text{elastic}}}-{\langle \Delta \sigma \rangle }_{{\text{general}}}=\frac{\left(P{^\prime}\right)-l\left(O\right)}{l\left(O\right)}\frac{({\beta }_{\sigma }^{e}-1)(1-{\beta }_{T})}{\left({\beta }_{\sigma }^{e}-{\beta }_{T}\right)({C}_{\sigma L}^{e}-{C}_{\sigma S}^{e})}$$

(23)

In other words, when temperature remains unchanged, the difference in stress estimates provided by the two models will be proportional to the plastic elongation of the bolt. When plastic elongation is zero with respect to a reference state, the two models will provide the same measurement of stress change in comparison with the reference state.

3 Experiments and Discussions

3.1 Sensor and Instrumented Bolts

Rock bolt sensor (RBS) is composed of one LUT, one SUT and a sensor head. Both LUT and SUT are made of piezo-electric PZT plates fully covered with thin film electrodes on both sides. They are glued side-by-side on the end face of the rebar bolt. Preferably, the polarization direction of the SUT is to be aligned with the ridge line of the bolt for a stronger shear wave echo signal reflected from the distal end of the bolt. A sensor arrangement is depicted in Fig. 3. The bottom electrodes of LUT and SUT are in electrical contact with the bolt end face and the top electrodes are electrically connected to the center conductor of the sensor head. The sensor head allows the bottom and top electrodes of the transducers to be electrically connected to an ultrasonic wave generation and data acquisition system via a coaxial cable (Fig. 4). Before gluing the transducers, the front end and the distal end of the bolt were rectified using a lathe. For best signal quality, sizes, locations and operation frequencies of SUT and LUT are to be adjusted according to bolt type, length and material. As will be elucidated in later sections, for calibration purpose or in situations where sectional information on stress distribution and deformation is needed, one or more hole(s) may be drilled perpendicularly to the rock bolt shank. The diameter and depth of the holes may be customized to provide required echo signal quality from the hole. For rebar bolts, the holes are to be drilled through the ridge lines as illustrated in Fig. 5 for better signal quality. Figure 6 shows an ultrasound signal generated in a 1777-mm long and 19.5-mm nominal bar diameter rock bolt with two holes and grouted in a resin. A 6.5 mm × 4.0 mm 7.5 MHz LUT and a 7.5 mm × 7.5 mm 2.5 MHz SUT were used. Both holes were 1-mm diameter through holes passing two ridge lines. The locations of the 1st and 2nd holes were determined in such a way that all longitudinal and shear wave echoes returned from these holes and the distal end of the bolt were well separated in time. In the figure, L₁, L₂ and L_End denote longitudinal wave echoes from the 1st and 2nd holes and the distal bolt end respectively whereas S₁, S₂ and S_End denote respective shear wave echoes. In the raw signal (Fig. 6a), echo L₂ is not discernible. Application of a 5.0–8.0 MHz and a 2.5–3.5 MHz bandpass digital filters improves remarkably the signal-to-noise ratio for the longitudinal (Fig. 6b) and shear (Fig. 6c) wave echoes respectively. It is to note that all rebar bolts tested in this work were of ASTM A615 Grade 60.

Fig. 3

Layout of ultrasound transducers on the front end of a rebar bolt

Fig. 4

A sensor head mounted on the threaded end of a rock bolt

Fig. 5

Drill hole(s) perpendicularly to the axial direction of the bolt and through the ridge lines

Fig. 6

Ultrasound signal generated in a rock bolt with two holes. a Raw signal; b Signal after applying a 5.0–8.0 MHz bandpass digital filter; c Signal after applying a 2.5 to 3.5 MHz bandpass digital filter

3.2 Temperature Calibration

Temperature calibration is needed for determining the values of temperature coefficients ${C}_{TL}$ and ${C}_{TS}$ introduced in Eqs. (1) and (2). The temperature calibration consists of the following steps: (1) Cut a rock bolt to a length that fits in a temperature-regulated chamber to be used; (2) Instrument the cut piece of rock bolt with an LUT and an SUT; (3) Heat or cool the instrumented piece of rock bolt in the temperature chamber to a few set temperatures that cover the intended operation temperature range for the rock bolt and record ultrasound echo signals reflected from the extremity opposite to the transducer; (4) Measure relative change of TOF vs temperature. Figure 7 shows temperature calibration results on a #6 rebar bolt (nominal bar diameter 19.5 mm) over a temperature range of -30 to 80 °C. The state at 20 °C was chosen to be the reference against which the relative change of TOF was measured. As can be seen in the figure, TOF of shear waves is more sensitive to temperature than that of longitudinal waves. For both waves, the relative change of TOF vs temperature variation is very linear in the temperature range of interest with an ${R}^{2}$ value larger than 0.999 for the linear fit in both cases. The temperature coefficients ${C}_{TL}$ and ${C}_{TS}$ are given by the slope of the respective linear fit, i.e., ${C}_{TL}$=1.044 × 10^–4/°C and ${C}_{TS}$=1.378 × 10^–4/°C.

Fig. 7

Temperature calibration results on a #6 rebar bolt

3.3 Load Calibration

Load calibration is needed for determining the values of stress coefficients ${C}_{\sigma L}^{e}$ and ${C}_{\sigma S}^{e}$ introduced in Eqs. (1) and (2). Figure 8 shows a typical setup for rock bolt calibration on a tensile tester. The toe section of the bolt was held by the upper grips whereas the other end section of the bolt was blocked by a bearing plate. A rock bolt sensor (RBS) head was screwed onto the threaded end of the bolt and connected to an ultrasound signal generation and acquisition system. Two thru-holes were drilled in the bolt according to Fig. 5 of which the hole closer to RBS had a diameter of 1 mm whereas the farther one had a diameter of 1.5 mm for larger reflectivity compared with the 1-mm hole. An optional extensometer was attached to the bolt in between the two holes. By measuring arrival times of echoes reflected off the two holes, TOFs for longitudinal and shear waves to travel between the two holes during the tensile test were determined. Then the values of stress coefficients ${C}_{\sigma L}^{e}$ and ${C}_{\sigma S}^{e}$ were obtained from relationships between changes in TOF and changes in the applied load, assuming that the applied load was fully transferred along the bolt shank. It is to note that the above assumption is only required for bolt calibration purpose and is achievable in a laboratory setting. The values of stress coefficients obtained through the calibration test are applicable to rock bolts deployed in a real-world environment. Figure 9 shows variations of load and corresponding changes of TOF of longitudinal and shear waves between two holes in a load calibration experiment. The rebar was 1880 mm long after rectification of both extremities and had a nominal bar diameter of 19.5 mm. The two holes were drilled at approximately 490 mm and 1180 mm from the sensor end, respectively. Tensile load was applied at increments of 15 kN from 0 to 75 kN and then down to 0 by steps of 15 kN. At each multiple of 15 kN, the load was held for 15–30 s and then transitioned to the next level. Load and ultrasound data were collected every one second. The nominal minimum yield strength of the bolt was 89 kN (for the threaded section), therefore the bolt was in the elastic deformation regime during the entire calibration process. As can be seen in the figure, TOFs of both longitudinal and shear waves follow well the load variations. Figure 10 shows relative changes of TOF of longitudinal and shear waves as a function of load change. The data points taken into consideration were those indicated with dots in Fig. 9 when the load reached stability at a set point. For both waves the relative change of TOF vs load variation is remarkably linear in the tested load range with an ${R}^{2}$ value larger than 0.999 for the linear fit in both cases. The stress coefficients ${C}_{\sigma L}^{e}$ and ${C}_{\sigma S}^{e}$ are given by the slope of the respective linear fit, i.e., ${C}_{\sigma L}^{e}$=5.961 × 10^–5/kN and ${C}_{\sigma S}^{e}$=2.135 × 10^–5/kN. Considering the nominal bar diameter of 19.5 mm of the bolt, the stress coefficients translate to ${C}_{\sigma L}^{e}$=1.780 × 10^–5/MPa and ${C}_{\sigma S}^{e}$=6.376 × 10^–6/MPa. As a consequence, ${{\beta }_{\sigma }^{e}=C}_{\sigma L}^{e}/{C}_{\sigma S}^{e}=2.792$, i.e., TOF of longitudinal waves is about 3 times more sensitive than TOF of shear waves to load change.

Fig. 8

A typical setup for rock bolt load calibration

Fig. 9

Load calibration results on a rebar bolt with 19.5 mm nominal bar diameter

Fig. 10

Relative change of TOF vs load change

3.4 Pull Testing

To obtain Eqs. (19) to (22), it was assumed that after a plastic deformation in the axial direction of a rock bolt, the slope of a pure elastic deformation path would remain unchanged in a Cartesian plane formed by the intersection of two perpendicular axes of which one being the relative change of TOF of longitudinal waves and the other that of shear waves. In other words, we assume that the effect of a plastic deformation on the acoustic and acoustoelastic properties of the rock bolt is negligible for the purpose of producing meaningful rock bolt condition monitoring results. To assess this assumption, a pull test was conducted on a 1777-mm long rebar bolt with 19.5 mm nominal bar size. The bolt was fully grouted in a steel tube up to 1352 mm. The remaining 425-mm section extended out to accommodate a single-cylinder hydraulic ram (Figs. 11, 12). A steel wire was affixed to the front plate of the hydraulic ram and hooked to the spring-loaded drum of a rotary potentiometer (AMETEK Rayelco™ model P-20A) for displacement measurement. Another steel wire was affixed to the toe of the rock bolt and hooked to a displacement potentiometer at the other end. A safety guard was welded to the rig base to catch ejected debris in case the rock bolt was to be pulled beyond the ultimate tensile stress. The safety guard was a hollow steel cylinder with a closed end. The closed end of the cylinder had a circular hole in the center, which allowed the aforementioned steel wire to pass through the cylinder. The load was controlled manually by visually checking the measured hydraulic load value (white line) displayed on a computer screen (Fig. 13). In some tests, a desired load profile was also displayed on the screen (red line) for the operator to follow. J-Lok resin cartridges (32 mm × 40 cm) were used. During the pull test, the tension load exerted on the bolt through the hydraulic ram was measured with a hydraulic pressure sensor. From potentiometer displacement measurements, the bolt elongation during the pull test was determined. The test bolt underwent 4 load and unload cycles displayed in Fig. 14 with maximum load of each cycle exceeding that of the preceding one. A 6.5 mm × 4.0 mm 7.5 MHz LUT and a 7.5 mm × 7.5 mm 2.5 MHz SUT were used. Relative changes of TOF of longitudinal and shear waves reflected off the toe of the test bolt were measured and displayed in Fig. 14 as well. The fourth cycle went on until the bolt ruptured at the threaded section. Photos of the ruptured bolt are shown in Fig. 15. According to Fig. 14, on two occasions the relative changes of TOF experienced abrupt increases versus a step load increase—one in cycle 3 after the load reached 122 kN, and the other one in cycle 4 when the load was exceeding the maximum load (135 kN) of cycle 3. These abrupt increases of TOF versus load are an indication of plastic deformation of the bolt.

Fig. 11

Schematic of a pull test setup

Fig. 12

A pull test rig

Fig. 13

Manual load control

Fig. 14

Variation of applied load to a test rock bolt and resulting relative changes of longitudinal and shear waves

Fig. 15

Photos of a ruptured test bolt

Figure 16 shows the relative changes of TOF of longitudinal waves versus those of shear waves during the pull test presented in Fig. 14. A more detailed view of the result is provided in Fig. 17 where four cycles are color coded. In the figures, two sets of elastic deformation paths were identified, one with a slope of ${\beta }_{\sigma }^{e}=2.64$ and an R-squared value of 0.9985 for linear fitting, and the other with a slope of ${\beta }_{\sigma }^{e}=2.65$ and an R-squared value of 0.9982. For the first elastic deformation path, the slope value was determined by taking into consideration all measurements of which relative change of TOF of shear waves was less than 0.0005. For the second elastic deformation path, the slope value was determined by taking into consideration all measurements in the unload phase of the third cycle and the load phase of the fourth cycle until the maximum load of the third cycle was reached, i.e., all samples between points P’ and Q (Fig. 17). The closeness of the slopes of the two elastic deformation paths, i.e., $2.64$ vs 2.65, supports the assumption made in the establishment of Eqs. (19) to (22) that following a plastic deformation in the axial direction of a rock bolt, the slope of a pure elastic deformation path would remain unchanged comparing to that before the plastic deformation. However, as will be discussed later, this assumption may not hold well if the rock bolt is bent. It is also to point out that at the end of the unload phase of the third cycle, the state point P' in Fig. 17 was anticipated to lie on the dashed line with a slope of 1, but in the test, it deviated slightly from the expected position. This discrepancy is believed to be caused by bolt bending during the pull test.

Fig. 16

Relative changes of TOF of longitudinal waves versus those of shear waves during the pull test presented in Fig. 14

Fig. 17

Relative changes of TOF of longitudinal waves versus those of shear waves during the pull test presented in Fig. 14 (detailed view)

Knowing the slope value, ${\beta }_{\sigma }^{e}$, of the elastic deformation path in the above pull test, the plastic deformation during the test was determined using Eq. (20) and shown in Fig. 18. The measured plastic elongation showed clearly that the bolt yielded on two occasions, one in Cycle 3 between 122 and 135 kN, and one in Cycle 4 after the load exceeded the previous high of 135 kN and that the plastic elongation remained close to zero before the first yielding event and at a constant level around 3 mm between the first and second yielding events. Elongation measurements with potentiometers were noisy and showed uncharacteristic negative elongation values before the first yield point was reached. This means that the spring-loaded rotary potentiometers in conjunction with the way they were connected to the test bolt were not responsive and accurate enough for small elongation/contraction measurements.

Fig. 18

Comparison of applied hydraulic load, bolt elongation measured with potentiometers and plastic elongation measured by RBS

To assess the capability of the RBS technology for determining sectional load and deformation on a rock bolt under a tensile load, an 1810-mm long rebar rock bolt with 22.2 mm nominal bar size was tested. A schematic of the test rock bolt and the test rig is shown in Fig. 19. Two 1-mm diameter thru-holes were drilled at 635 mm and 1470 mm from the sensor (RBS) end. The bolt, partially covered with a plastic sleeve, was grouted in a steel tube. The plastic sleeve extended to about 710 mm from the sensor end (Fig. 20) and prevented the covered bolt section from being grouted. The drilled holes divided the rock bolt in three sections, namely, L1, L2 and L3. Section L1 was completely isolated from the resin and hence not grouted whereas section L2 was partially grouted and section L3 fully grouted. It is to note that section L1 can be further divided into an equivalent stress-free section of length ${l}_{ESF}$ and an equivalent fully loaded section of length ${l}_{1}{^\prime}$. The values of ${l}_{ESF}$ and ${l}_{1}{^\prime}$ were estimated to be 66 mm and 569 mm respectively for the test rock bolt. The methods for determining equivalent stress-free length and using it for more accurate load measurement are detailed in Appendix.

Fig. 19

Schematic of a test rock bolt and test rig

Fig. 20

A plastic sleeve was used to prevent the covered bolt section from being grouted

Photos of the pull test rig are shown in Fig. 21. The test rock bolt was grouted in a steel tube firmly affixed to an immobile base. The rock bolt sensor was mounted on the exposed end of the rock bolt. A steel wire was affixed to the sensor end of the rock bolt and hooked to a displacement potentiometer. The toe of the rock bolt was hooked to another displacement potentiometer via a steel wire. A dual-cylinder hydraulic ram was used to exert a pull force on the rock bolt. An exposed section of the partially grouted bolt is shown in Fig. 22.

Fig. 21

Rig for pull testing

Fig. 22

A partially grouted bolt

Refer to Fig. 23 for RBS results over section ${l}_{1}{^\prime}$ obtained using Eqs. (19), (20), and (22). The pull test started with preloading the rock bolt at three torque values, i.e., 81.6, 136 and 204 Nm (60, 100 and 150 lbf-ft), and recording corresponding load values (18.3, 32.2, 46.5 kN) with the load cell. Then load cell and displacement readings were reset to zero and RBS signal acquisition started. From this point on, both the load cell and RBS system read load change with reference to the bolt load of 46.5 kN at the moment of reset. Next, two load and unload cycles were performed. In the first cycle, load increased in 20 kN increments until 100 kN, then in 10 kN increments until 2 mm elongation was achieved. In the second cycle, load increased in 20 kN increments until 120 kN, then in 10 kN increments until 5 mm elongation was achieved. Both cycles had symmetrical unload phases. The load was held for approximately 20 s at a desired level before proceeding with the next increment or decrement. As can be seen in the figure, the load change over section ${l}_{1}{^\prime}$ measured by RBS was quite close to the change of the applied load measured by the load cell. This is reasonable because ${l}_{1}{^\prime}$ was not grouted and as a consequence the applied load was expected to be fully transferred along this section of the bolt. At the end of the first load cycle (around 19 min), i.e., when the hydraulic load came down to zero, the load changes measured by the load cell and RBS dropped to about − 46.2 and − 40.6 kN, respectively. Taking into account the reference load of 46.5 kN, these negative load changes would mean 0.3 kN and 4.9 kN actual load on the bolt measured by the two means respectively. Plastic and total elongations measured by RBS are displayed in the lower panel of Fig. 23. The bolt started to show obvious plastic deformation at about 180 kN applied load (time line t_a). After the peak load of 200 kN in the first cycle was over (time line t_b) and before the same peak load of 200 kN was reached again in the second load cycle (time line t_c), the measured plastic elongation was almost constant. The plastic elongation started to increase rapidly once the previous load height was reached (time line t_c), then flattened after the peak loading period was over (time line t_d). At the end of the two unload phases, the total elongations were smaller than the plastic elongations. This is because the bolt section was contracted compared with the preloaded reference state.

Fig. 23

Comparison of load change over section ${l}_{1}{^\prime}$ measured by RBS, applied load change measured by the load cell, and the applied hydraulic load, upper panel; and comparison of plastic and total elongations over section ${l}_{1}{^\prime}$ measured by RBS, lower panel

Discrepancies were seen between the load cell and RBS load readings, particularly in the second cycle following a plastic deformation. Furthermore, while plastic elongations were expected to remain constant between time lines t_b and t_c and after time line t_d, due to the fact that only elastic deformation was involved during the corresponding periods, the actual measurement results were not quite so. These anomalies were also observed in some other experiments and are mainly attributable to the bending of the test rock bolt occurred during the pull test as evidenced in a picture taken at about 13–14 min. into the test (Fig. 24) and in another picture taken after the test (Fig. 25). The bending of a rock bolt can be partially recoverable (elastic) and partially permanent (plastic). The decreasing trend of the measured plastic elongations with decreasing load after the time line t_b and the time line t_d is an indication that the rock bolt was recovering from the bending taking place prior to these time lines. In this regard, measurement of plastic elongation of a rock bolt using the RBS technology can also serve as a means to assess whether the bolt has bent. For instance, if a decrease of measured load is accompanied by a decrease of measured plastic elongation, bolt bending may have happened.

Fig. 24

Instance of apparent bend of the bolt end with respect to the axial direction of the steel tube

Fig. 25

Misalignment of the bolt with the steel tube

Figure 26 shows a comparison of load over section ${l}_{1}{^\prime}$ measured by RBS, applied load measured by load cell, and applied hydraulic load. The load over section ${l}_{1}{^\prime}$ measured by RBS and the applied load measured by load cell are obtained by adding the preload of 46.5 kN to respective load changes shown in Fig. 23. In the loading phases, the applied hydraulic load was consistently higher than the load measured by the load cell, suggesting that the applied load was not fully transferred to the axial direction of the load cell, probably as a result of the previously mentioned misalignment between the rock bolt and the steel tube.

Fig. 26

Comparison of load over section ${l}_{1}{^\prime}$ measured by RBS, applied load measured by load cell, and applied hydraulic load

Figure 27 displays average load changes over sections L1, L2, and L3 and over full length measured by RBS. Compared with section L1, section L2 of the bolt took much less load due to the fact that this section was mostly grouted and most of the load was dissipated into the surrounding steel tube through the resin. Section L3 was fully grouted and did not experience any noticeable load change. Average load change over full length was smaller than that over section L1 but larger than that over section L2.

Fig. 27

Comparison of average load changes over sections L1, L2, L3 and over full length measured by RBS

Figure 28 shows plastic elongations measured by RBS over sections L1, L2, and L3. While the onset of plastic elongation over section L1 was clearly detectable in both cycles, this was not the case with section L2 in the first cycle. According to Fig. 24 and Fig. 25, a threaded portion of section L1 was stressed. This threaded portion had thinner cross-sections than that of the shank of the bolt and as a consequence yielded first and was the major contributor to the plastic elongation in the first cycle. When this threaded portion continued to deform plastically under increasing load, it gradually hardened, and then the shank of the rock bolt started to yield, resulting in noticeable plastic elongation of section L2 in the second cycle. Section L3 never yielded.

Fig. 28

Comparison of plastic elongations over sections L1, L2, and L3 measured by RBS

Field trial results, to be published in a subsequent paper, showed that applying the technology to individual bolt sections of a grouted rock bolt allowed the load on the bolt at different depths to be monitored and that the load distribution and its evolution were closely correlated with rock mass integrity vs depth from the rock face. In other words, the capability of applying the RBS technology to bolt sections would allow ground control engineers to gain extra insight into the integrity of both rock mass and the bolting system.

Figure 29 shows elongations of the entire rock bolt measured by displacement potentiometers and RBS during the pull test. In the test, the potentiometer connected to the toe did not show any displacement, therefore, the displacement measured by the potentiometer connected to the protruded section of the rock bolt (Fig. 21) provided a measure of bolt elongation. TOFs of echoes from the distal end of the rock bolt were used in RBS measurements. Plastic elongations measured by RBS are also displayed in the figure. There is a good agreement between the potentiometer and RBS results in the loading phases of the test. However, except a few spikes in the potentiometer data caused by glitches of the measurement system, there are notable discrepancies in the unload phase of the first load cycle. This is because the spring-loaded rotary potentiometer was unable to recoil responsively when displacement was small. Inaptitude of this type of potentiometer for small displacement measurement was also observed in Fig. 18. Another period during which the RBS results were noticeably different from the potentiometer data was roughly between 27 and 29 min into the test where the bolt elongation reached a plateau. In this period the differences between the two types of measurements are believed to be caused mainly by the effect of bolt bending on TOF measurements. At the end of each of the two unload phases, total bolt elongations measured by RBS were smaller than the plastic elongations. This is because the bolt tension was released in comparison with the pretensioned reference state, resulting in a reduction in the measured bolt elongation compared with the reference.

Fig. 29

Comparison of bolt elongations measured by displacement potentiometers and RBS

It is worth pointing out that for a grouted rock bolt, the bolt may yield at a locally highly stressed location even when the average load being experienced by the entire bolt is much less than the designed yield load of the bolt or when the bolt elongation is still much less than the designed elongation limit. An interesting benefit of the RBS technology is that even under the above conditions, the yield of the rock bolt and the extent of the yield can be detected and measured through the measurement of plastic deformation by RBS.

As presented in Sect. 2, two equations are available for measurement of load change. Equation (5) is applicable when bolt deformation is in an elastic deformation regime and as such this equation is referred to as the elastic model. This model is immune to temperature variation. Equation (19) is applicable regardless whether the bolt deformation is in an elastic or a plastic deformation regime and therefore, this equation is referred to as the general model. When using the general model, the effect of temperature on TOF needs to be removed unless its effect is negligible. Figure 30 shows a comparison of load changes over section ${l}_{1}{^\prime}$ measured with the RBS general and elastic models, and changes of the applied load measured by load cell, all with respect to the reference load of 46.5 kN taken at about 3 min into the test. Plastic elongation of the same section and measured by RBS is also displayed. In the first load cycle, the general and elastic models produced almost identical results until the onset of yield. From that point on, the elastic model produced higher estimates of load changes than the general model. According to Eq. (30), when temperature remains unchanged during a pull test, the difference in the estimates of load changes produced by the two models is proportional to the plastic elongation of the bolt. This relationship is shown in Fig. 31. Data points (red dots) in the figure were produced from the results shown in Fig. 30. According to the figure, when plastic elongation is less than 1 mm, the measurement error produced by the elastic model would be less than 15 kN. This measurement error might be acceptable for some field applications. In practice, when no plastic elongation is expected or detected, the elastic model is to be used because this model does not need temperature measurement. If plastic elongation, for example, larger than 1 mm, is detected, the general model should be used to produce more meaningful load measurements. When using the plastic model, the effect of temperature on TOF measurements should be taken into account. Example on how to deal with this temperature effect in field applications will be presented in a subsequent article.

Fig. 30

Comparison of load changes over section ${l}_{1}{^\prime}$ measured with RBS general and elastic models, changes of the applied load measured by load cell, and corresponding plastic elongation

Fig. 31

Difference of estimates of load changes over section ${l}_{1}{^\prime}$ produced by two models vs plastic elongation

It was discussed that bending can affect RBS load and plastic elongation measurements. This also means that bending can be sensed through these measurements. For example, if a load reading is excessive or a descending trend is seen in measured plastic elongation, there is a good chance that the bolt has bent. At the present time how to use the RBS technology to quantify rock bolt bending is still a subject for exploration. In practical applications, rock bolt bending can happen to the protruded bolt section during bolt installation. After the installation, the protruded section will remain stress free and can be treated the same way as section ${l}_{ESF}$ shown in Fig. 19. Although the bending of the protruded section can result in offsets of initial load and elongation measurements in comparison with a straight installation, these offsets can be minimized in or removed from subsequent measurements by taking an RBS signal right after the bolt installation and using this signal as reference. From this point on the RBS technology will measure load change and bolt elongation with respect to this reference state. The load at the above reference state may be estimated using the load data for a standard installation established by the operator or bolt supplier.

3.5 Evaluation of Mechanical Strength of Drilled Rock Bolts

RBS technology is applicable to rock bolts regardless whether or not they have drilled holes through their shanks. In situations where drilled rock bolts are to be used for obtaining sectional information on load distribution inside a rock mass or for rock bolt load calibration, it is good to know how drilled holes on rock bolts may compromise the rock bolt integrity. To acquire this knowledge, destructive tensile tests were conducted on rebar bolts with or without a drilled hole. All test bolts were of ASTM A615 Grade 60, 608 to 609 mm long, with nominal bar size of either 19.5- or 22.2-mm diameter. For bolts with a hole, the hole was drilled thru a center line according to Fig. 5 at the midpoint from bolt extremities, with a diameter of either 1.0 mm, 1.59 mm, or 2.0 mm. A Tinius Olsen Super L-120 Tensile Tester was used. Figure 32 shows the test setup and photos of bolts with and without a drilled hole after rupture. Necking before rupture was obvious on the bolt without a drilled hole. After the tensile test, the broken pieces were put together and the total length was measured (Fig. 33). Figure 34 shows load vs displacement charts on 19.5-mm nominal bar size bolt samples (#6 rebar) and 22.2-mm nominal bar size bolt samples (#7 rebar). In the tests, one end of the test bolt was held immobile while the other end was stretched by a pair of mobile grips. The displacement in the charts refers to the displacement of the mobile grips. Some results are outlined in Table 1. From Fig. 34 and Table 1, several observations can be made for the bolts tested: (i) The presence of a drilled hole didn’t change the yield load; (ii) The presence of a 1.0 mm diameter hole did not change the maximum load; (iii) For the 22.2-mm rebar bolt tested, the presence of a 1.59 mm hole had a negligible effect on the load-vs-displacement relationship until close to bolt rupture; (iv) For the 19.5-mm rebar bolt tested, the presence of a 1.59 mm hole had some minor effects on the on the load-vs-displacement relationship until close to bolt rupture; (v) The presence of a 2-mm hole had noticeable effects on the load-vs-displacement relationship, and therefore, its use should be avoided; (vi) The presence of a drilled hole led to a reduced elongation limit and the larger the hole was the earlier the bolt ruptured; (vii) Even before the yield load was reached, a drilled bolt tended to deform more elastically than a bolt without a drilled hole under the same load due to a higher stress in the area around the hole. Based on the above observations, it is recommended to limit hole diameter to 1.0 mm when dealing with #6 rebar bolts and to 1.5 mm when dealing with #7 rebar bolts. For other bolt types and sizes, appropriate hole sizes need to be determined by experiments. When implementing instrumented drilled rock bolts, it should be kept in mind that even the bolts may sustain the same ultimate tensile strength as non-drilled bolts, they will fail earlier than non-drilled bolts once the ultimate tensile strength has been reached.

Fig. 32

Destructive tensile test on a rebar bolt with a drilled hole at the midpoint (left) and a rebar bolt without a drilled hole (right)

Fig. 33

After the tensile test, the broken pieces were put together and the total length was measured

Fig. 34

Load vs displacement charts on 19.5-mm nominal bar size bolt samples (left) and 22.2-mm nominal bar size bolt samples (right)

Table 1 Summary of destructive tensile tests results

4 Conclusions

In this work, we have established the foundation of an ultrasonic technology for monitoring changes in axial load and elongation of full-bodied rock bolts. The technology is based on two sets of practical empirical models that relate changes of times of flight (TOF) of longitudinal and shear ultrasonic waves propagating along the axial direction of a rock bolt to changes in load, length and temperature being experienced by the rock bolt. Of the two sets of models, one is applicable to elastic deformation regime regardless of bolt temperature and the other to both elastic and plastic deformation regimes as long as the effect of temperature on TOF is negligible or can be determined by other means. Rock bolt calibration and pulling tests were conducted and following conclusions were drawn:

• (1) The RBS technology was able to produce good load measurements within and beyond the elastic deformation limit.

• (2) The RBS technology was able to detect plastic yield and measure both plastic and total elongations.

• (3) The RBS technology is applicable to bolt sections divided by drilled holes for sectional load and elongation measurements. The capability of applying the RBS technology to bolt sections would allow ground control engineers to gain extra insight into the integrity of both rock mass and the bolting system.

• (4) The presence of a 1-mm thru hole on the shank of a #6 rebar bolt would not change the yield and the ultimate tensile strengths of the bolt, and the presence of a 1.59-mm thru hole on the shank of a #7 rebar bolt would not change the yield and the ultimate tensile strengths of the bolt either. Therefore 1-mm thru hole is recommended for #6 rebar bolts and a diameter between 1 and 1.5 mm is recommended for #7 rebar bolts when sectional information is sought after.

• (5) The accuracy of the RBS technology on rock bolt axial load and elongation measurements can be biased by bolt bending. To ensure highest accuracy of axial load and elongation measurements, instrumented rock bolts need to be installed as straight as possible. The effect of the bending of the protruded section of a rock bolt incurred during bolt installation on subsequent measurements can be minimized or removed by taking an RBS signal right after the bolt installation and using this signal as reference. From this point on the RBS technology will measure load change and bolt elongation with respect to this reference state. Using the RBS technology for assessing the degree of bolt bending remains a subject for future exploration.

Owing to its ability to detect yield and to measure rock bolt elongation and load in both elastic and plastic regimes, the technology holds great promise for being a practical tool for determining remaining capacity of instrumented bolts.

At the time of this writing the technology has been deployed in several production mines. Key outcomes of these deployments will be presented in a subsequent paper.

Appendix: improving load measurement accuracy by taking into account stress-free length

The RBS technology measures average load and deformation changes over a rock bolt or a section of the rock bolt. Depending on how the bolt is anchored, part of the bolt may be stress-free, for example, the threaded end of which the length is denoted by ${l}_{1}$ in Fig. 35, or part of the distal end beyond the anchor shown in Fig. 36. The axial stress distribution on the bolt section covered by the nut is not uniform and can vary depending on thread geometry, length of thread engagement and friction on thread surface (Lu et al. 2019). The above-mentioned factors affect overall TOF of ultrasonic waves reflected off the distal end of the bolt but do not carry information on what happens on the bolt section in between the anchors. In other words, they reduce the accuracy on load measurement over the bolt section of most interest. To tackle this issue, a two-state stress model is proposed. According to this model, the bolt section to the left of the bearing plate shown in Fig. 35 is conceptually divided into an equivalent stress-free section of length ${l}_{ESF}$ and an equivalent stressed-section of length ${l}_{ES}$. Let $F$ be the total axial load applied to the bolt shank through tightening the nut, $A$ the equivalent radial cross-sectional area of the threaded section of the bolt, $\sigma \left(x\right)$ the axial stress distribution along the bolt section between points ${x}_{a}$ and ${x}_{c}$ as a result of the applied load $F$, ${\tau }_{0}$ and $\tau$ the TOF for an ultrasonic wave, longitudinal or shear, to travel the distance between these two points before and after applying the axial load $F$, and ${C}_{\sigma }$ the stress coefficient for the type of ultrasonic wave under consideration. For the bolt section between points ${x}_{a}$ and ${x}_{c}$, we further define an equivalent stress distribution as follows:

$${\sigma _E}\left( x \right) = \left\{ {\begin{array}{*{20}{l}} {0,}&{{\mkern 1mu} {x_a} \leqslant x < {x_b}} \\ {F/A,}&{{x_b} \leqslant x \leqslant {x_c}} \end{array}} \right.$$

(24)

Since the bolt section for $0\le x<{ x}_{a}$ is stress free, the value of $\sigma \left(x\right)$ is zero for $0\le x<{ x}_{a}$.

Based on Eqs. (1) to (4) and in terms of TOF, the equivalent stressed length of the threaded portion of the bolt covered by the nut is defined in such a way that the following equation holds:

$$\tau -{\tau }_{0}={\tau }_{0}{C}_{\sigma }{\int }_{{x}_{a}}^{{x}_{c}}\sigma \left(x\right)dx/\left({x}_{c}-{x}_{a}\right)={\tau }_{0}{C}_{\sigma }{\int }_{{x}_{a}}^{{x}_{c}}{\sigma }_{E}(x)dx/\left({x}_{c}-{x}_{a}\right)$$

(25)

From Eqs. (24) and (25) and the fact that ${l}_{ES}={x}_{c}-{x}_{b}$, the equivalent stressed length can be determined as

$${l}_{ES}=A{\int }_{{x}_{a}}^{{x}_{c}}\sigma \left(x\right)dx/F$$

(26)

In practice the stress distribution $\sigma \left(x\right)$ is not easy to determine and each thread will take a different percentage of the total load, for example, the 1st to 6th threads may take 34%, 23%, 16%, 11%, 9% and 7% of the total load respectively (https://engineerdog.com/2015/01/11/10-tricks-engineers-need-to-know-about-fasteners/); however, the cumulative load of all threads amounts to the total load. Taking this into consideration and letting $p$ be the thread pitch, $\sigma \left(i\right)$ and ${F}_{i}$ respectively the average axial stress and load on the i^th thread, $N$ the total number of threads, Eq. (26) translates to

$${l}_{ES}\approx \sum_{i=1}^{N}A\sigma \left(i\right)\mathrm{ p}/F=p\sum_{i=1}^{N}{F}_{i}/F=p$$

(27)

Therefore, the anchored end of a rock bolt outside the bearing plate can be modeled as being the combination of a stress-free segment of length ${l}_{ESF}$, which is the distance from the sensor end of the bolt to the bearing plate minus one thread pitch, and a fully loaded segment of which the length is one thread pitch. By the same token, if the rock bolt is anchored at the distal end with a threaded anchor, the distal end of the rock bolt after the threaded anchor can be conceptually divided into an equivalent stress-free section after the first thread of the anchor and an equivalent fully stressed 1st thread (Fig. 36).

Fig. 35

The bolt section to the left of the bearing plate is conceptually divided into an equivalent stress-free section of length ${l}_{ESF}$ and an equivalent fully loaded section of length ${l}_{ES}$

Fig. 36

The distal end of the rock bolt after the threaded anchor is conceptually divided into an equivalent stress-free section after the first thread of the anchor (length ${l}_{ESF})$ and an equivalent fully loaded 1st thread of which the length is the thread pitch (${l}_{ES}$)

Refer to Fig. 37. For illustration of how to remove the effect of equivalent stress-free length on load measurement, a rock bolt is divided into three sections of length${l}_{1}$,${l}_{2}$, and ${l}_{3}$ respectively with a total length of$l$. Two stress-free sections, of length ${l}_{ESF1}$ and ${l}_{ESF2}$ respectively, are present, one on the RBS side and the other at the distal end. Let ${\langle \Delta \sigma \rangle }_{l}$,${\langle \Delta \sigma \rangle }_{{l}_{1}}$, ${\langle \Delta \sigma \rangle }_{{l}_{3}}$ be average load change over sections $l$, ${l}_{1}$ and ${l}_{3}$ respectively, and${\langle \Delta \sigma \rangle }_{{l}{^\prime}}$, ${\langle \Delta \sigma \rangle }_{{l}_{1}{^\prime}}$ and ${\langle \Delta \sigma \rangle }_{{l}_{3}{^\prime}}$ be average load change over sections ${l}{^\prime}$, ${l}_{1}{^\prime}$ and${l}_{3}{^\prime}$, respectively. The value of ${\langle \Delta \sigma \rangle }_{l}$,${\langle \Delta \sigma \rangle }_{{l}_{1}}$, ${\langle \Delta \sigma \rangle }_{{l}_{3}}$ is obtained from TOF over sections $l$, ${l}_{1}$ and${l}_{3}$, respectively. The value of${\langle \Delta \sigma \rangle }_{{l}{^\prime}}$, ${\langle \Delta \sigma \rangle }_{{l}_{1}{^\prime}}$ and${\langle \Delta \sigma \rangle }_{{l}_{3}{^\prime}}$, which excludes the effect of equivalent stress-free sections, can be obtained as follows:

$${\langle \Delta \sigma \rangle }_{{l}{^\prime}}=l{*\langle \Delta \sigma \rangle }_{l}/\left(l-{l}_{ESF1}-{l}_{ESF2}\right)$$

(28)

$${\langle \Delta \sigma \rangle }_{{l}_{1}{^\prime}} ={l}_{1}{*\langle \Delta \sigma \rangle }_{{l}_{1}}/\left({l}_{1}-{l}_{ESF1}\right)$$

(29)

$${\langle \Delta \sigma \rangle }_{{l}_{3}{^\prime}} ={l}_{3}{*\langle \Delta \sigma \rangle }_{{l}_{3}}/\left({l}_{3}-{l}_{ESF2}\right)$$

(30)

Fig. 37

Partition of a rock bolt for sectional load information