BackgroundTime-Domain Reflectormetry (TDR) is a technique commonly used in electrical engineering for detection of faults in transmission lines. It involves sending an electrical pulse along a pair of transmission line / cable and receiving the reflection induced by any discontinuities in the line. By measuring the time for the pulses to travel from the pulse generator to the point of discontinuity, the corresponding distance can be estimated. The working principle is as below:Working PrincipleThe propagation velocity of an electromagnetic wave Vp, travelling along a coaxial cable is as below:

where L = the cable inductance in unit of henries per metre C = the capacitance in unit of farads per metre

The propagation velocity is related to the material properties by the following expression:

Where = the speed of light in vacuum (3 x 108 m/s) = dimensionless property called dielectric constant (air = 1, grout = 10, water = 80)Hence by measuring the pulse traveling time along the soil nail and multiply it with the propagation velocity, we can estimate the length of the soil nail. Remarks: the propagation velocity of electrical pulse in grout is 30% less than that in air. If there is a void along the grouted soil nail, the pulse travel time will be shorter than fully grouted soil nail.Testing Procedure1) Determine the pulse propagation velocity, , from at least 3 nos. of soil nails (namely: calibration nails) of known length. The calibration nails are selected by the RSS. It is suggested that the longest soil nails to be selected for better accuracy.

where = design length of soil nail = pulse travel time in copper wire2) Move line 1 on the display panel of TDR to the starting point of reflected pulse corresponding to the clip

3) Connect the clip to the test nails and move line 2 to the one with largest amplitude. Record the time of travel between line 1 and 2

4) Repeat the step 3 & 4 with different pulse width, one with < 5ns and one > 5ns. Select the most clear and distinct reflection for calculation of pulse traveling time in copper wire, 5) Repeat Step 3-5 for three calibration nails and the average of the measured pulse velocity is called Reference Pulse Propagation Velocity.6) PWL randomly selects soil nails (namely: test nails) for TDR tests. The number of soil nails to be tested is according to the summary table below:

Sample Lot SizeMinimum no. of TDR testsAlert Criterion

2551

26 - 5081

51 - 90131

91 - 150202

151 - 280324

281 - 500506

501 - 12008011

7) The length of tested soil nail, , is determined based on the equation below:

8) If an anomalous TDR results were found, i.e. the deduced length is 15% less than the designed length, RSS shall forward the results to the designer and seek for advice. The designer may review the design / study the site record to consider the follow-up action required.9) If Alert criterion was reached, the RSS and designer should determine if it is warranted to test all the soil nails by TDR method. Other investigation technique such as Electrical Resistance Method, Magnetometry or extraction of soil nail, may also be useful to identify the cause(s) of anomalous.UncertaintiesBy nature, TDR is an indirect way of measuring the length of soil nail in which it is inevitable that uncertainties will be introduced during the course of measurement and interpretation of the results. The uncertainties can be divided into two main group, nail independent uncertainty and nail dependent uncertainty, and are listed below. Nail-independent uncertainty Build-in error of testing instrument Human judgment Nail-dependent uncertainty Wire type Grout annulus aging and integrity Reinforcement diameter Reinforcement length Reinforcement connectors (couplers)A study on the uncertainties was carried out by Dr. Raymond Cheung and Dr. Dominic Lo of GEO and the results are summarized in the table below.Study on Time-Domin Reflectormetry (TDR) Test

Type of UncertaintyUncertaintyDetails of ErrorTest & ResultsJudgment

Nail-independent uncertaintyBuild-in error of testing instrumentAccording to the manufacturer specification, the error is generally less than 1%Calibration on the TDR fault cable detector should be carried out regularly.

Human judgment- Electrical impedance along the soil nail is not constant-Wave dispersion

Human identification of the point of initial reflection from the soil nail end may vary.Test on repeatability was carried out by single operator and multi operator. Variation of measurement by multi-operator is larger than single operator.

Standardizing the test procedure and provide guidelines on results interpretation.

Calibration nails shall be selected on the same site.

Nail-dependent uncertainty

Wire typeDifferent type of wire (diameter and plastic sheaths enclosure) have different dielectric constantTest results on pulse propagation velocity in different type of wire vary from 0.192 to 0.252 m /ns which are significant.

The calibration nails and test nails shall have the same type of wire.

Grout annulus aging and integrityAging of grout may affect the pulse propagation velocity.

If the integrity of grout in calibration nail is significantly vary from test nail, i.e. void in grout annulus. The interpretation of test nail length is affect.Pulse propagation velocity on 1-7d, 42d,128d and 1827d after grouting showed that age of grout has no significant effect on the test results.

No special test on grout characteristics alone.Insignificant effect by the age of grout if test was carried out 1d after completion of grouting.

The error caused by grout annulus integrity is reflected in the overall uncertainty.

Nail-dependent uncertainty

Reinforcement diameterReinforcement diameter may affect the pulse propagation velocity.

Measurement on pulse propagation velocity on 25, 32 and 40mm dia. bar were carried out and no significant difference was found. Insignificant effect by bar diameter

Reinforcement lengthReinforcement length may affect the pulse propagation velocity.

Measurement on pulse propagation velocity on 8,10,12,13,14m bar were carried out and no significant difference was found.Insignificant effect by bar length

Reinforcement couplersCouplers may affect the pulse traveling time.

The presence of coupler may cause a slightly longer travel time.Each coupler may lengthen the deduced length by 10-20mm.The effect is negligible.

Therefore the major causes of error come from: 1) Human judgment and 2) wire types. Here showed different types of discontinuity and the corresponding waveform.

Baic schematic TDR waveforms

My Opinion Even in a small slope feature, the geology may vary greatly. Therefore, the selection of calibration nail to give a representative pulse propagation velocity is important. Otherwise the interpretation of nail length will be adversely affected. For example, slope feature: 3SW-C/C625, which I supervised during the training in LPM3 division, the upper portion of the slope was a filled slope. Based on the visual inspection, drilling record and some core recovery, it was confirmed that it was formed with boulder material with some cement mortar to construct the formation level of the scatter above the slope crest. The lower portion was a cut slope. After trimming of the existing protective hard cover, in-situ material of highly to moderately decomposed granite was found. During the grouting works, the soil nails near the slope crest experienced some excessive grout loss while those near the slope toe did not have this problem. Therefore, in the accuracy point of view, I will suggest the soil nail without grouting problem for determination of Reference Pulse Propagation Velocity. And those nails with excessive grout loss should be selected for testing for confirmation of the grouting quality as well as the length of soil nail. However, I should not make any recommendation to PWL staff due to the procedure requirement. Another important point to note is that, each lot of nails to be tested should be constructed with same batch of steel, wire cable, cement grout material and grout mix such that the possible error caused by variation of material properties can be minimized. Even if an abnormal reading is recorded during the TDR test, we should not conclude that the tested nail is a short nails. This is because TDR test is a non-destructive test which is not a physical measurement on the tested nail and there are different types of uncertainties caused by human, geology and machinery. Therefore, before coming into conclusion, we should carry out more study on the available information such as site diary, grouting records, TDR test results in the whole site, GI logs, etc. If necessary we can extract the concerned nails for detailed study on cause of short interpreted length. DiscussionAs stipulated in Figure A3(b) of Guidelines on Test Procedure using Time Domain Reflectormetry to determine the length of installed soil nail, a negative pulse is reflected from the far end of the soil nail if the wire and reinforcement are short-circuited there. This negative pulse is significantly different from other intermediate fluctuation which may be easier for the operator to identify. I wonder if there is any strong reason to adopt an open circuit instead of a close circuit.