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By Andrew Cushing, Joe Carvalho, Jon Hurt

"INTRODUCTIONThe shales of the Greater Toronto Area (GTA) have been known to experience time-dependent deformations (TDD); those initiated by excavation-induced stress relief which progress with time as a function of rock porewater salinity, access to freshwater (or air) of lower salinity, clay and calcite content, and the buildup of swelling pressures within the rock mass. These deformations can induce long-term pressures on shaft walls and tunnel linings, especially if the permanent works are constructed soon after excavation, with very little time delay. This paper presents measurements of time dependent deformation of recent shaft and tunnel projects constructed in the GTA, and draws conclusions regarding the main influences on the TDD. The key input parameters for the numerical predictive model are critically assessed. Projects which are discussed include the Billy Bishop Airport Pedestrian Tunnel, Hydro One Midtown Tunnel and Hanlan Feedermain (Contract 3).MECHANISM OF TIME DEPENDENT DEFORMATIONExplanation of MechanismThe Georgian Bay Shale unit consists of typically moderately weathered to fresh, grey to dark grey, fine to very fine grained fissile shale interbedded with slightly weathered to fresh grey, fine grained calcareous siltstone and limestone interbeds. There are two distinctive features of the shale in the Greater Toronto Area (GTA). One is a high horizontal stress regime, and the second is long-term time dependent swelling behavior which develops when the following factors occur (Lo and Micic, 2010):• Stress relief of the rock mass• Outward salt concentration gradient from pore fluid of the rock to the ambient fluid• Availability of fresh waterThe swelling is a consequence of the reduction in confined stress in the rock which occurs upon excavation in combination with a differential gradient in salinity between the saline rock porewater and freshwater or even humid air. Osmotic and diffusive processes result in a decrease in the salinity of the rock porewater achieved by an overall increase in the water content, resulting in volumetric expansion of the shale rock over time. The development of this time dependent deformation (TDD) relative to the time"

Jan 1, 2016

By F. P. Janse van Rensburg, P. J. Le Roux

"There are numerous factors that affect open stope stability and often result in falls of ground. These falls of ground can be attributed to factors such as beam failure due to a larger than normal roof area (hydraulic radius too large), adverse ground conditions, seismicity, the stress-strain environment, absence of support, and poor drill-and-blast practices. The effect of time on the stability of open stopes is sometimes underestimated and is relatively unknown, especially on Target Mine. Actual data was collected from open stopes at Target and analysed to show the effect of time on open stope stability. The benefits of this analysis will include improved understanding of time-dependent failure, which can assist in reducing dilution and the risk of sterilization of future mining blocks. IntroductionTarget Mine is situated adjacent to the town of Allanridge, some 20 km from Welkom in South Africa’s Free State Province, and is the most northerly mine in the Welkom Goldfields area (Figure 1). The mine consists of a single surface shaft system with a sub-shaft (Target 1C shaft) and a decline. Ownership was attained by Harmony Gold Mining Company Limited in May 2004 (Harmony Gold Mining Company Limited, 2010). Before discussing the selection of open stopes for the back-analyses, a brief explanation of open stoping as practiced at Target Mine will be given. The orebody is some 180 m in thickness and 270 m wide and comprises multiple reefs overlying one another. The 180 m thick reef package is termed the Eldorado Reefs, as shown in Figure 2. The Eldorado Reefs suboutcrop against the Dreyerskuil Reefs, as shown in Figure 3. The dip of the reef varies from as low as 10° in the west to 75° in the east.Compared with most Australian and Canadian open stoping mining operations, Target Mine is unique. In most Australian and Canadian mining operations the hangingwall and footwall of the open stopes comprise waste rock, and the orebody dips relatively steeply. Due to the depth of Target Mine, some 2300 m to 2500 m below surface, a destress slot (Figure 4) is mined to create an artificial, shallow mining environment whereby the field stress is managed and kept at values of around 60 MPa. The destress slot comprises a narrow tabular stope with an average width of 1.5 m, and is mined on the Dreyerskuil Reefs.At Target Mine the hangingwall, sidewalls, and footwall of the open stopes all comprise reef of different grades, except for the EA1, where the EB footwall is waste rock. If a stope, for example, is mined alongside an existing old stope, the western sidewall of this stope will consist of backfill. The general mining direction of open stopes is from the lowest position of the reef on the west, progressing up towards the east as shown in Figure 5."

Apr 1, 2019

By Jeongbok Seo

This paper describes successful application of driven tapered-steel-pipe piles for two large-scale projects in the New York metropolitan area: Rego Park Mall, Rego Park, N.Y. and 164 Kent Avenue, Brooklyn, N.Y. The combination of side friction and end bearing resistance produced by tapered-steel-pipe piles has been well-recognized as greater than the side friction and end bearing resistance by pipe piles. Forty-four tapered piles were driven and tested at these two sites. Design pile load for the two sites was 260 kips for Rego Park Mall and 400 kips and 300 kips for 164 Kent Avenue. To measure the pile-drive hammer efficiency, the compressive stress in the pile, and to estimate the ultimate bearing capacity of the pile, dynamic load testing using a Pile Driving Analyzer (PDA) was conducted on index piles at the sites. Subsequent to the field testing, data analysis using the Case Pile Wave Analysis Program (CAPWAP) was conducted. Restrike PDA analysis and full-scale static load tests were performed on the selected test piles. Test piles at the project sites exhibited significant time-dependent increases in bearing capacity caused by the effects of "set-up" or "soil freeze." The dissipation of excess pore-water pressure in the soil, which had been disturbed and remolded by driven pile, was generally considered the primary cause of set-up. The increase at the subject sites ranged from 100 to 300 percent of the capacity measured at the initial driving. This paper discusses the results of various types of load testing on tapered piles and the set-up effects by comparing PDA test results acquired during and after pile driving. Finally, an empirical relationship for the New York metropolitan area has been offered for quantifying set-up.

Jan 1, 2008

By Florian König

It is well known that the bearing capacity and stiffness of displacement piles may increase significantly with time, a phenomenon usually referred to as set-up. In cohesive soils the set-up is commonly explained by consolidation processes in which the dissipation of the excess pore pressures around the pile leads to an increase in effective radial stresses. Recent case histories show that set-up may also occur in sand over a period which exceeds by far the consolidation process. Therefore, other effects apart from the dissipation of excess pore pressures must contribute to this long-term set-up effect. This paper presents the results of a series of multiple pile load tests on prefabricated concrete piles which capture the effect of pile set-up empirically. The main characteristics of the set-up trend are shown with respect to soil type, pile dimensions and distribution over the pile length. Possible reasons for pile set-up like consolidation and stress relaxation after the end of driving are examined using a finite element model which simulates the pile installation process.

Jan 1, 2006

By T. Sugawara, S. Hara, Y. Mitsui

Surfaces of rock slopes in cold regions often become frozen in winter. Therefore, understanding time-dependent behavior of frozen rock, as well as that of unfrozen rock, is important for long-term stability assessment of rock slopes. In this study, a series of uniaxial compression tests and creep tests were carried out on Shikotsu welded tuff under dry and water-saturated conditions at -20 °C to clarify timedependent strength and deformation of the frozen rock. The influence of water content on them also was investigated. It was found that the amount of deformation of the water-saturated specimen was much greater than that of the dry specimen. It also was found that the creep behavior of the water-saturated specimen was similar to that of polycrystalline ice. These show that deformation of the water-saturated specimen is strongly affected by pore ice. The UCS of the water-saturated specimen was approximately equal to that of the dry specimen at a strain rate below 4.2×10-6/s, and its value was about 17 MPa. However, the former increased up to 26 MPa at 4.2×10-4/s with loading rate, whereas there was little increase in the latter. This means that the UCS of the water-saturated specimen was always greater than that of the dry specimen at higher strain rates. The creep life of water-saturated specimens was longer than that of the dry specimens at stress level greater than 15 MPa. These results of UCS and creep life show that inclusion effect due to presence of pore ice plays an important role on strength of the water-saturated specimen. Creep life of the non-failure specimen that was loaded for more than three days was estimated by the relationship between creep life and axial strain rate at 10 s on failure specimens. It was found that creep life of the water-saturated specimens was shorter than that of the dry specimen at stress levels less than 14 MPa. This suggests that estimation of creep life of frozen rock under water-saturated condition is important for the stability assessment of frozen rock slopes. It was clear that the loading-rate dependency of UCS was related to the stress-level dependency of creep life in both dry and wet conditions. This indicates that there are common fracture mechanism in creep and uniaxial compression tests. It also indicates that the creep life can be estimated by the relationship between the UCS and the loading rate. The time dependencies of the water-saturated specimen were in good agreement with those of polycrystalline ice. This confirms that pore ice strongly affects the strength of the water-saturated specimens as, well as the deformation behavior.

Jan 1, 2015

By Erik Westman, BEN WESTON, SETAREH GHAYCHI AFROUZ, KATHRYN DEHN

One of the most difficult challenges in underground mining is to forecast significant seismic events prior to their occurrence in order to support the safety of miners and to minimize damage to the underground operation. Passive seismic tomography is a tool to image the seismic velocity changes in a rockmass, which can potentially reveal the rockmass behavior before and after a significant seismic event. In this paper, the changes in seismic velocity of the rockmass before and after three major seismic events are investigated to determine whether there are identifiable precursory velocity changes associated with the major seismic events. Conventional mechanics imply that the induced stress at the hypocenter would continue increasing until failure, in the form of an induced seismic event, occurs. With passive seismic tomography we can image changes to the seismic wave velocity distribution within a rockmass and hence infer the changes to the induced stress near the hypocenter. This paper evaluates the hypothesis that induced stress at the hypocenter (as inferred by the p-wave velocity) increases until the seismic event occurs. In addition to analyzing p-wave velocity changes near the hypocenter, changes to the p-wave velocity at “zone centers” were also analyzed. These “zone centers” are regions within the rockmass that consistently have a p-wave velocity that is much higher than the average p-wave velocity for the rockmass. It is found that the p-wave velocity did not increase at any of the three hypocenters prior to the seismic event occurring, however the p-wave velocity did increase in the closest “zone center” for two of the three events.

Oct 12, 2020

By Erik Westman, BEN WESTON, SETAREH GHAYCHI AFROUZ, KATHRYN DEHN

This study investigates the changes in seismic velocity of rockmass before and after three major seismic events to determine any potential identifiable precursory velocity changes associated with these events. Induced stress measurement is one of the challenging tasks in deep underground mining, with extreme impacts on the safety and stability of the mine. This study used p-wave passive seismic tomography to image the velocity redistribution within a rockmass, which can indicate induced stress level changes in the rockmass and detect the velocity changes that might precede a major seismic event or a rockburst. The ultimate goal of this research focus is to develop another tool for the deep-mining community that will help to increase safety and efficiency. For this purpose, the hypothesis of conventional mechanics, which implies induced stress at the hypocenter (as inferred by the p-wave velocity) increases until the seismic event occurs, is evaluated. It is found that the p-wave velocity did not increase at any of the three hypocenters prior to the seismic event occurring; however, the p-wave velocity did increase in the closest “zone center” for two of the three events. 

By T. Brady, J. Johnson, J. Whyatt, B. Pariseau, M. Stahl

An elastic-viscoplastic material model allows for time-dependent rock mass motion in proportion to excess stress above the elastic limit. The model produces rounded stair-step curves of displacement versus time that are similar to those obtained from recent borehole extensometer measurements made in the central portion of the Ross shaft pillar at the Homestake mine. The work in progress, including two- and three-dimensional finite element analyses using the UTAH2/3 codes, indicates that the model is a step towards more realistic safety and stability analysis, but that inclusion of rock mass damage may be desirable.

Jan 1, 2000

By T. Brady, J. Johnson, J. Whyatt, B. Pariseau, M. Stahl

An elastic-viscoplastic material model allows for time- dependent rock mass motion in proportion to excess stress above the elastic limit. The model produces rounded stair-step curves of displacement vs. time that are similar to those obtained from recent borehole extensometer measurements made in the central portion of the Ross Shaft pillar at the Homestake mine. The work in progress, including two- and three-dimensional finite element analyses using the UTAH2/3 codes, indicates that the model is a step towards more realistic safety and stability analysis, but that inclusion of rock mass damage may be desirable.

Jan 1, 2000

By D. Nyungu

Despite observations of spalling and damage of mine excavation wall rock in the Bushveld Complex (BC) over the passage of time, there have been very few time-dependent or creep tests carried out in South Africa on rock, particularly on BC rock types. The research described in this paper deals with the investigation of stress and strain conditions influencing spalling of wall rock in BC mine excavations, and the influence of time on the tensile strength of several BC rock types. Time-dependent laboratory testing of BC rocks was carried out in indirect tension. The results show that the magnitude of the tensile strength of BC rock types is approximately 5% of their uniaxial compressive strength magnitudes. The average long-term uniaxial compressive strength of the BC rocks, interpreted from the axial stress-volumetric strain graphs, is 56% of the UCS value. The long-term tensile strength is shown to be less than 70% of the normal tensile strength. Extension strains at tensile strength failure ranged between 0.16 and 0.21 millistrain. Values corresponding with the long-term tensile strength are less than 70% of this range, namely, 0.11 to 0.15 millistrain. These results represent new knowledge, since such rock testing and analysis does not appear to have been carried out previously on BC rock types. Elastic numerical modelling was carried out to illustrate the extents of tensile stress zones and extension zones around of typical BC mine excavations. The models showed that large zones of extension strain can occur around BC excavations, and that the magnitudes of the extension strain can substantially exceed the critical values determined from the laboratory testing. The implication of this is that there are substantial zones surrounding BC mine excavations that will be prone to time-dependent spalling conditions and perhaps more significant failure.

Jan 1, 2014

By J. D. Bosman

The problems associated with squeezing rock conditions in tunnels are well known and have been extensively investigated in the past. Although squeezing conditions are predominantly found in tunnels developed in weak rock types it has been noted at the No. 6 Shaft of Hartebeestfontein Mine where the host rock consists of hard, brittle quartzites. This paper investigates typical time-dependent deformation mechanisms in the rock at Hartebeestfontein Mine. The paper will focus on observations made in a strike-orientated tunnel that intersected weak quartzite layers, that were sandwiched between two competent quartzite beds. The observed squeezing mechanism is dominated by creep along bedding planes with a soft talcaceous infilling that behaves in a clay-like fashion when saturated in water. Stress-induced deformation processes, some distance into the sidewall of the excavation, force the already fractured periphery of the excavation into the void. A laboratory study of the creep of intact rock and discontinuities collected at this site was conducted to characterize the time-dependent behaviour. The difference in creep rates between the two types of quartzite found at this site is described in the paper. Creep tests performed on the talcaceous infilling material found that its presence allows substantial shear creep along discontinuities. Attempts were also made to simulate the squeezing mechanism observed underground with numerical techniques. Due to the discontinuous nature of the mechanism described above, a viscoplastic displacement discontinuity technique was used as it allowed for the explicit simulation of discontinuity creep. The results of the modelling and how it compared with the observed behaviour are described in the paper. Environmental impact statement The work described in this paper will not cause any new, or contribute to any existing, hazards confronting the environment.

Jan 1, 2000

By Chi-Yuen Wang, Chaw-Long Chu

The time-dependent volumetric constitutive relation for a San Andreas fault gouge and a consolidated kaolinite are experimentally determined at confining pressures to 200 Mpa, under creep condition and at ultrasonic frequency. At any given pressure, the bulk modulus determined at 1 Mhz frequency is identical to the "elastic" modulus determined at a stepwise change of pressure. After the pressure change, there occur a time-dependent change of volume and thus the effective bulk modulus. The constitutive relations may be modeled by a standard linear viscoelastic medium with pressure-dependent moduli and viscosity. For the San Andreas fault gouge, viscosity increases from 2x10 13 poise, at 17 Mpa, and 10 14 poise, at 100 Mpa. For kaolinite sample, the corresponding values are 3x10 12 poise and 10 13 poise. These results imply that both stress and pore pressure in fault zones may show time-dependent variations in response to a change of state of stress, such as that occurring after an earthquake.

Jan 1, 1982

By Ren G. Dong, Jay Kim, Daniel E. Welcome, Won Joon Song, Charles Hayden

Prolonged, extensive exposure to hand-transmitted vibration could cause a series of vibration-induced disorders in the vascular, sensorineural, and musculoskeletal structures of the human hand-arm system, which have been collectively called hand-arm vibration syndrome (HAVS).1 To assess the risk of HAVS the international standard ISO 5349-1 (2001)1 recommends using the root-mean-square (rms) acceleration of the measured vibration with a frequency weighting. While a few epidemiological studies have reported results consistent with the predictions made according to the recommendation, many other studies have reported results with large discrepancies.2 This may be partially attributed to the time-averaging effect involved in calculation of the frequency components, especially for impact type tools. Because the spectral characteristics of impact tools change dramatically with time, a time-frequency (T-F) analysis can provide better characterizations of such highly transient vibrations. The analytic wavelet transform (AWT) is an ideal T-F analysis tool because it possesses the advantages of both the Fourier transform and the wavelet transform.3 The objective of this study was to explore the application of the AWT method for characterizing the impact tool vibrations and assessing their exposure risk. Methods Five tools (two chipping hammers, two riveting hammers, and one concrete cutting saw) were used in this study. The saw vibration was measured when it was used to cut a section of road pavement during a repair. The vibrations on the other tools were measured by the procedure specified in ISO 8662-2 (1992).4 A sampling rate of 16,386 Hz was used in the measurement. The AWT and Fourier analysis were applied to these signals and to identify their characteristics. Results Figure 1 compares the T-F characteristics of the accelerations measured from the relatively steady concrete saw and a riveting hammer. The frequency weighting specified in ISO 5349-11 was applied in the calculations. The comparison clearly shows that the two tools have completely different T-F characteristics.

Jan 6, 2006

By Douglas A. Anderson

We have instrumented well-controlled free-face blasts with six- component borehole strain gages, in order to determine the complete strain tensor as a function of time due to explosive loading. The strain tensors have been diagonalized to determine the principal strain time-histories, and further processed to determine the octahedral shear strains as a function of time. Principal strain time-histories, when compared with a computer model, indicate the arrival of various direct and reflected phases. Strong shear strains coincide with the expected arrival time of shear waves. These shear waves are probably instrumental in the fragmentation of confined rock due to explosive loading, and should be incorporated in models of the fragmentation process.

Jan 1, 1984

By D Wallace, H Guo, B Shen

Appropriate management of the ground subsidence induced by coal mining activities is essential. To assess the effectiveness of grout injection for mining subsidence control, time-lapse ground penetrating radar (GPR) imaging data were collected before and after grouting. The pregouting subsurface responses were interpreted to have changed after grout injection. The changes were caused by injecting the grout materials (flyash and water) into the delaminated strata and permeable fracture zones. The largest distance of the observed GPR event changes at the right end of the main profile is 132 m away from the injection borehole. Although the GPR images could not easily tell if the image changes were caused by the injected ashes or the water, it does suggest that the injection materials had been pushed at least 130 m away from the injection borehole. This is consistent with the borehole scan monitoring, which confirmed that the grout has travelled more than 90 m from the injection borehole.

Jan 1, 2006

By Kray Luxbacher

Three-dimensional time-lapse velocity tomograms were generated to image stress redistribution around a longwall panel to produce a better understanding of the mechanisms that lead to ground failure. Mining-induced microseismic events provided passive sources for the three-dimensional velocity tomography. Surface-mounted geophones monitored microseismic activity for 18 days. Most similar studies have utilized active sources including longwall shearers, controlled explosions, and hammer blows. These active sources generally require a person to initiate and measure the location and time of the source, and are not conducive to continuous monitoring. This method utilizes mining induced microseismic events as passive sources and lends itself well to continuous monitoring. Two event location methods were compared in order to move toward quantification of tomographic results in terms of ground conditions. Additionally, LAMODEL was utilized to determine the expected stress distribution around the longwall panel and compare these images to the velocity tomograms. Eighteen tomograms were generated, one per day, and high velocity regions in the set of tomograms generated from the initial location algorithm correlated with abutment stress redistribution predicted by numerical modeling. This research is significant as it has the potential to improve safety in underground mines and is the only example of long term passive velocity tomography implementation for the purpose of inferring stress redistribution around an area of active mining. Though still immature, this technology has the potential to allow mine personnel to image areas of active mining on a regular basis and detect areas with anomalous velocity distributions indicating potential safety hazards.

Jan 1, 2007

By Kray Luxbacher, Erik Westman, Peter Swanson

Three-dimensional time-lapse velocity tomograms were generated to image stress redistribution around a longwall panel to produce a better understanding of the mechanisms that lead to ground failure. Mining-induced microseismic events provided passive sources for the three-dimensional velocity tomography. Surface-mounted geophones monitored microseismic activity for 18 days. Most similar studies have utilized active sources including longwall shearers, controlled explosions, and hammer blows. These active sources generally require a person to initiate and measure the location and time of the source, and are not conducive to continuous monitoring. This method utilizes mining induced microseismic events as passive sources and lends itself well to continuous monitoring. Two event location methods were compared in order to move toward quantification of tomographic results in terms of ground conditions. Additionally, LAMODEL was utilized to determine the expected stress distribution around the longwall panel and compare these images to the velocity tomograms. Eighteen tomograms were generated, one per day, and high velocity regions in the set of tomograms generated from the initial location algorithm correlated with abutment stress redistribution predicted by numerical modeling. This research is significant as it has the potential to improve safety in underground mines and is the only example of long term passive velocity tomography implementation for the purpose of inferring stress redistribution around an area of active mining. Though still immature, this technology has the potential to allow mine personnel to image areas of active mining on a regular basis and detect areas with anomalous velocity distributions indicating potential safety hazards.

By Michael Wieland

Work-principle computations for explosions underwater or in rock reveal the way the thermodynamic characteristics of surrounding material influence the resulting shock and heave. To reach total thermodynamic equilibrium under such transitory dynamic circumstances, reactions must quickly readjust to changing circumstances, which works for molecular (military) explosives where the fuel and oxidizer type atoms are originally in close proximity. For non-molecular mixtures with their dispersed zones of oxidizer or fuel, in particle or droplet form, there are numerous unproductive collisions, increasing the wait time required to reach chemical equilibrium. Underwater test data for molecular explosives compare rather well with the shock and heave resolved from the work-principal model, while the non-molecular explosives normally used in mining tend to yield a noticeable discrepancy. Years ago, it was recognized that the underwater shock was lower than expected and the heave was higher than expected for ammonium nitrate fuel oil (ANFO), though their resultant sum for the total work was roughly what was expected. When the readjustment of thermodynamic equilibrium warrants quicker chemistry than occurs in underwater or rock shooting, the time-retarded chemistry reduces the shock and raises the heave within the surrounding material without reducing the total work, unless the reaction retardation is quite severe. This technical complication in reality is a nonequilibrium issue that is difficult to resolve with just thermodynamics, though a rational set of transformation factors is formulated herein to represent those circumstances.

Jan 1, 2008

By W. Zhu

ABSTRACT: This paper presents further developments of the principle of Construction Process Mechanics of rockmasses, The principle of loading variations analyses in space-time is systematically described. To demonstrate the applicability of the theory and method, the effect of the construction process of two practical engineering cases are analysed. ZUSAMMENFASSUNG: Das Mechaniksprinzip vom Konstruktionsprozess des Massenfels wird in diesem Aufsatz weiter Entwickelt.. Das Prinzip von Variationsladungsanalyse mit dem Zeit-Raumseffekt wird systematisch erklaert. Um die Anwendungsmoeglichkeit der Theorie und der Methode zu anschaulich darstellen, das Mechanikseffekt des Konstruktionsprozess wird fuer zwei praktische Anwendungsbeispielen zergliedert. : RESUME: Dans ce papier le development se fait pour principles de la mechanique de process de construction . Le principle de variable analyse considerant effet de temps et de Space est present ´e . Pour demonstrer l´appilicabilite de le theorie et la methode , l´èffect de processe de construction pour ce deax examples sont analysés .

Jan 1, 2003

By L. D. Jaffe, J. H. Hollomon

THE effect of tempering temperature and time upon the properties of quenched steel is clearly a subject of great practical importance, as well as of considerable theoretical interest. It would be very desirable to be able to predict the properties of a quenched steel when given any selected tempering cycle, with a minimum of experimental work upon that heat or even type of steel. Two problems are involved: one consists of relating the structure obtained to the physical properties, and will not be discussed here; the other, with which this paper deals, involves the relations of time, temperature and composition with the structure obtained on tempering. Indentation hardness is perhaps the most convenient quantitative measure of the tempered structure, or of what might be called the "degree of tempering." Undoubtedly, it is not an exact measure, and in some cases (as when temper-brittleness occurs) pieces of the same quenched and tempered steel may have widely differing properties at the same hardness. However, hardness has the advantage of being simple to determine and is certainly the most widely used indication of the degree of tempering. Moreover, for fully quenched steels that are not temper-brittle and do not contain retained austenite when quenched, it appears that, in general, if the hardness of the steel is the same, the tensile and impact properties will also be identical, whether a high or a low tempering temperature is used. The tempering charts available in the metallurgical literature usually give the hardness as a function of tempering temperature for only one tempering time. However, in practice, tempering times frequently vary, and a method of converting tempering curves for one time to tempering curves for some other time would be very valuable. It is also advantageous, in determining the tempering treatment necessary for a given part, not to have to temper samples at several temperatures for the time used for the commercial tempering operation. A more satisfactory procedure would be to employ times of the order of 10 to 30 min., rather than 5 or 10 hr., and if possible to use only one temperature. Furthermore, it is frequently desirable, for reasons such as temper-brittleness,* to obtain a given hardness with short times at relatively high temperatures, and it would be convenient to be able to compute without tests the time required to produce this hardness. Remarkably few quantitative studies of the hardness of quenched steel tempered over wide ranges of temperature and time

Jan 1, 1945