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Influence of geometric factors on the punching load resistance of early-age fibre reinforced shotcrete linings
Tunnelling and Underground Space Technology 26 (2011) 541–547
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Influence of geometric factors on the punching load resistance of early-age fibre reinforced shotcrete linings Erik Stefan Bernard ⇑ TSE P/L, PO Box 763 Penrith, NSW 2750, Australia
a r t i c l e
i n f o
Article history: Received 28 September 2010 Received in revised form 1 December 2010 Accepted 15 February 2011 Available online 16 March 2011 Keywords: Ground control Fibre reinforced shotcrete Load resistance Early age Punching shear Testing
a b s t r a c t Understanding the early-age properties of fibre reinforced shotcrete (FRS) is critical to the accurate estimation of the time to safe re-entry under freshly sprayed FRS linings. Previous research in the field has indicated that shear failures dominate early-age load resistance and thereby govern the performance of a lining during the first few hours after spraying. This investigation has examined the influence of several geometric variables on shear resistance in a punching mode of failure. In particular, the research has addressed the influence of the size, shape, eccentricity, and inclination of punching loads on the apparent shear strength of an early-age fibre reinforced shotcrete (FRS) lining. Ó 2011 Elsevier Ltd. All rights reserved.
1. Background In the tunnelling and underground mining industries interest has recently developed into the subject of early-age strength development and its influence on safe re-entry times under freshly sprayed fibre reinforced shotcrete (FRS). This is because cycle times for drive development within mines, and in civil tunnel construction, can strongly depend on the time to safe re-entry and this, in turn, affects progress rates and overall economy. In the present context, the term ‘safe re-entry’ refers to an acceptably low risk of pieces of rock or shotcrete falling onto operators during the first few hours after spraying and resumption of work under a freshly sprayed lining. The majority of research into safe re-entry times has focused on strength development in hardening shotcrete (Golser, 2001; Chang and Stille, 1993) under the implicit assumption that toughness, adhesion to the rock surface, and the ability of the FRS lining to support loose rocks are all related to the strength of the concrete matrix. Evidence to support this assumption has been partially developed through trials conducted at Cliffs, Cannington, Olympic Dam, Argyle, and Cadia mines in Australia (Bernard, 2008). However, these trials have also shown that punching shear is the dominant mode of failure at early ages and that flexural failure mainly occurs at later ages. Compressive failures seldom occur in any FRS linings over hard rock. It is therefore important that factors affecting punching resistance at early ages are well understood. ⇑ Tel.: +61 247255801; fax: +61 247225773. E-mail address: [email protected] 0886-7798/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2011.02.004
Predicting the early-age punching resistance in shear, V, of a FRS lining is presently restricted to the use of simple models such as
V ¼ mpt
ð1Þ
where m is the shear strength of the concrete, p is the critical perimeter, and t is the thickness. This model is based on punching shear behaviour in concrete floors (AS3600, 2010) and the accuracy of the expression has not been rigorously demonstrated for earlyage FRS linings. The present investigation has been developed to extend this simple model of lining capacity and examine the influence of geometric factors on early-age shear resistance. Previous research conducted into early-age shotcrete performance for hard rock applications primarily addressed the rate of strength gain over the first few hours and days after spraying and methods of assessing compressive strength at these ages (Bernard and Geltinger, 2007; Morgan et al., 1999). There has also been a substantial amount of work undertaken addressing strength and stiffness in shotcrete shell linings used in the NATM tunnelling technique through soft ground (British Tunnelling Society, 2010). Data of direct relevance to the estimation of safe early-age re-entry times is presented in Fig. 1 which shows the relation between shear and compressive strengths at early ages. Experiments by Bernard (2008) demonstrated that fall-outs of FRS lining are dominated by the shear mode of failure through the lining thickness. Potvin and Nedin (2004) also showed that early-age fall-outs of shotcrete caused by loose rock are dominated by individual scats and wedges of up to 2 tonnes mass and that larger bodies of mobile rock are rare. This has helped to delineate the 1 MPa compressive strength limit for a 50 mm thick lining as the minimum satisfactory
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shotcrete according to the procedures described by Bernard and Geltinger (2007) who validated these test methods against standard UCS test methods such as cores. The soil penetrometer was 6.0 mm in diameter and could be used to estimate compressive strengths up to about 0.3 MPa. The needle penetrometer comprised a 3.0 mm diameter steel needle at the end of a spring that was forced into the surface of setting concrete. This method is suitable for determining compressive strengths up to 0.8 MPa. The ASTM C116-based beam-end tester (ASTM, 1980; Morgan et al., 1999) was the only early-age strength testing device that involved direct compressive failure of the concrete samples. Beams measuring 75 75 400 mm were produced by spraying shotcrete into an open-ended mould. This device could assess compressive strengths in the range 0.5–8.0 MPa. Unconfined compressive strength tests were conducted at later ages in accordance with AS1012 (1991) using 75 mm diameter cores. 3.2. Shear testing
Fig. 1. Shear strength as a function of compressive strength for FRS (Bernard, 2008).
strength of FRS before re-entry can be considered safe. This benchmark compressive strength happens to coincide with the minimum requirement specified by the Austrian Tunnelling Society (2006) for thick-shell shotcrete although this limit was arrived at by different means. However, these conclusions were based on very simple models of lining behaviour at early ages that require development and validation. 2. Objectives of investigation The primary objective of the present investigation was to determine the punching resistance of early-age FRS linings and establish quantitative evidence of the influence on this parameter of geometric factors in the first few hours after spraying. This information will be used to develop a more comprehensive model of factors controlling punching failure of FRS and help to identify the period of curing required before it is safe to re-enter under freshly sprayed excavated ground while including a reasonable margin of safety against fall-outs. The dominant loading case for early-age failures has been taken to be gravity loading associated with loose individual rocks. 3. Experimental program The project was undertaken through four related series of shear trials conducted to examine the influence of the shape and size of the punching zone, as well as the influence of inclined and eccentric loading, on apparent shear strength. Each of the shear trials comprised a set of experiments in which a FRS mix was cast or sprayed to produce panel specimens that were subsequently tested over a 24 h period to determine early-age shear strength in punching under a variety of conditions. A total of 28 trials were conducted involving 630 specimens. Cast FRS specimens were used in many of the trials in the interests of economy. This research was undertaken as part of an industry-funded project administered by AMIRA International and reported by Bernard (2009). The test methods employed in this investigation are described below.
In order to generate punching shear strength data on FRS, laboratory-based punching tests were conducted in a purpose-built apparatus consisting of a thick steel annular base onto which the FRS panel specimens were placed (Bernard and Harkin, 2001). Load was imposed onto the upper surface of each specimen using a servo-controlled hydraulic piston operating under displacement control so as to cause punching failure through the centre. In the majority of tests, load was imposed through a 100 mm diameter spherical seat resting on top of a 200 mm diameter steel plate. The spherical part of the seat was convex, and matched the design used by Bernard and Nyström (2000). This type of seat allowed rotation of the punching cone during failure, thereby simulating the rotational freedom believed possible for rocks that are punched through a FRS lining. All the specimens were cast or sprayed inside thick steel rings that prevented radial dilation during punching. The use of the steel rings has been shown to effectively prevent the specimen edges rotating or translating during a punching test and thereby simulate the lateral confinement associated with a contiguous lining. The annulus under the panel had a diameter that exceeded that of the loading plate by 250 mm for each ;200 mm punching plug as it was driven through the ;580 mm specimens that were used for the majority of trials (Fig. 2). Given that the specimens were 50 mm thick this ensured that the conical failure surface generated during each test was inclined at about u = 65–70° to the loading axis. This is close to the inclination of natural failure surfaces which form at around u 70°. The load was imposed at a controlled rate of displacement equal to 4.0 mm/min up to a total central displacement of 25 mm.
3.1. Early-age compressive strength A soil penetrometer, needle penetrometer, and beam-end tester were used to assess the early-age compressive strength of
Fig. 2. Punching shear test with confinement ring around side and included angle u.
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The calculated punching shear resistance of a concrete plate represented by Eq. (1) requires an estimate of the critical perimeter. The critical perimeter is the perimeter at which the mid-plane intersects a conical surface subtending 45° from the outline of the loaded plug. Note that the conical failure surface was assumed to always act at an angle of 45° from the loaded surface regardless of what the true angle actually was. This must be considered when the resulting estimates of shear strength are used to calculate the load resistance of a lining. 3.3. Production of specimens Two methods were used to produce the specimens tested in this investigation: either by spraying, or by casting. Both methods of production included the use of precision-milled and surface– ground steel plates as a substrate over which polypropylene sheeting was placed to prevent bond to the newly produced specimen. The surface–ground plates were necessary to produce a very flat underside to the specimens so that flexural stresses were minimised during testing. All the panel specimens were round with a 10 mm thick steel ring acting as both a form and a confining ring to prevent dilation of the specimen during shear testing. Contiguous linings do not dilate around a punching plug as the surrounding lining acts to confine the concrete at the failure zone within the plane of the lining. Dilation during a shear test has been shown to significantly reduce the peak shear strength in laboratory tests of punching in plates (Bernard and Curnow, 1999). 3.3.1. Production by spraying Shear specimens were sprayed in a horizontal position while lying on ground steel plates over pallets (Fig. 3). The shotcrete was a 40 MPa mix with 4–5% bwc SA 160 set accelerator placed using manual spraying. After spraying, the surface was screeded and floated to produce a smooth steel-troweled finish. Companion ASTM C116 beams were produced for UCS determination in the range 1 and 8 MPa. The shear panels themselves were used for early-age soil and needle penetrometer tests up to 1 MPa equivalent UCS.
specimens generally took longer to attain the required compressive strength range deemed suitable for testing each specimen in shear. 3.4. Influence of production method on shear capacity In underground applications all linings are produced by spraying an FRS mixture into place. Many of the specimens produced in this investigation were also sprayed. However, spraying is very expensive in a laboratory environment and thus the majority of specimens were cast in order to limit the cost of the investigation. A preliminary investigation was therefore undertaken to determine whether there is a systematic difference in the relation between shear and compressive strengths for an FRS mix that had been sprayed as opposed to cast. Two trials were undertaken using the 40 MPa nominal shotcrete mix listed in Table 1. One of the sets involved spraying 20 shear specimens and ASTM C116 beam-end specimens followed by testing over a 10–12 h period, and the other involved casting the same nominal mix and testing. The results are shown in Fig. 4. The points do not follow exactly the same trend throughout the entire strength range but given the variability typical of specimens tested in this and earlier investigations there did not appear to be a systematic difference in performance between FRS that is sprayed as compared to cast. For the remainder of this trial it has therefore been assumed that the shear-compressive strength relation does not vary between sprayed and cast specimens for a given FRS mixture.
Table 1 The 40 MPa shotcrete used in all trials. Ingredient
Quantity (kg/m3)
Coarse sand Fine sand 7 mm basalt Cement (GP) Flyash Pozzolith 300Ri (LRWR)
500 455 600 380 90 1200 mL
3.3.2. Production by casting When casting was employed as the method of production the specimens were placed in a horizontal position over the ground steel plates. No set accelerator was used during casting, but internal vibration with a 42 mm poker vibrator was applied to consolidate all the specimens. A screed and float were then used to finish the specimens. The absence of a set accelerator meant that the cast
Fig. 3. Spraying shear specimens.
Fig. 4. Relation between shear and compressive strengths for FRS that has been sprayed versus cast.
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4. Results 4.1. The influence of the shape of the punching zone on apparent shear strength in punching
4.2. The influence of the size of the punching zone on apparent shear strength in punching
The first of the shear trials involved an examination of the influence of the shape of the punching zone on the apparent early-age shear strength of FRS in punching. The rationale for this assessment is that loose rocks and wedges in a tunnel crown are very unlikely to be circular in shape like the punching zone imposed in the majority of tests undertaken in this investigation. For this reason both square and triangular punching plugs were used in parallel with round plugs in a series of trials to determine whether shape substantially influences apparent shear strength. Shear testing trials were undertaken in which circular, square, and triangular punching plugs were used to load confined panels. The square and triangular plugs had a critical perimeter that was the same as that of the 200 mm diameter circular plug. All the specimens were 50 mm thick, and the mix designs used included both shotcrete and conventional concrete with 10 mm coarse aggregate, and plain, macro-synthetic, and micro-synthetic FRS shotcrete. The results of this investigation are shown in Fig. 5. The trend lines that have been fitted to each set of shape results show that there appeared to be a statistically insignificant difference in shear strength between punching plugs of different shape. At early ages the variability in shear strength for a given compressive strength displayed by specimens tested for a particular shape of punching plug was much greater than the difference between shapes. This must be qualified by the observation that only 200 mm diameter round plugs and square and triangle plugs of equal critical perimeter were included in the present trials. While it is likely that the lack of a shape effect also applies to larger punching zones, the absence of shape influence on shear resistance in the present tests does not necessarily extend to much larger punching zones. However, in the absence of information to the contrary it has tentatively been concluded that the shape of the punching zone has a negligible influence on apparent shear strength.
The second of the shear trials involved an examination of the influence of the size of the punching zone on the apparent earlyage shear strength of FRS in punching. This trial included a number of tests in which sets of 20–24 shear panels were cast ranging in size from ;400 to ;1200 mm. The punching plugs were round and ranged in diameter from 16 to 700 mm. The diameter of the supporting annulus was always 250 mm greater than the loading plug so the conical failure zone had the same inclination angle. The tests were undertaken over the first 6–24 h after production of the specimens so the testers were faced with the problem that the compressive strength increased relatively rapidly over this period. Since the objective was to isolate the effect of punching zone size from the effect of compressive strength change on shear capacity, each set of 4–5 tests was undertaken within a short period of time so that the UCS was approximately equal within this interval. Compressive strength was monitored and the shear strength results within each set were linearly adjusted relative to the result obtained for the 200 mm diameter specimen. Similarly, the shear strengths obtained for each set of ;16 to ;700 mm specimens were adjusted linearly relative to the strength obtained for the 200 mm diameter specimen. This relative strength has been expressed as a Capacity Ratio (hSE = sR/s100, where sR is the punching shear strength of a plug of radius R, and s100 is the punching resistance of a plug of 100 mm radius) and is plotted as a function of the logarithm of the normalised punching zone radius in Fig. 6. The reason for the reduction in apparent strength as the size of the punching zone increased is due in part to the probability that there is a greater statistical likelihood that a critical flaw will occur within the highly stressed area around the zone of failure as the size of the failure zone increases (Bazˇant and Planas, 1998). The presence of a flaw will typically reduce peak capacity. This phenomenon is known as the size effect and has been well studied in concrete materials. When conventional size effect laws are considered for the range of specimen sizes tested in this investigation the capacity reduction factor hSE can be expressed as
Fig. 5. Effect of punching plug shape on relation between shear and compressive strengths for FRS.
Fig. 6. Size effect on relative shear strength of FRS for present data set.
E.S. Bernard / Tunnelling and Underground Space Technology 26 (2011) 541–547
hSE ¼
1n R 100
ð2Þ
in which n lies in the range 2–3 (Bazˇant and Planas, 1998). The data presented in Fig. 6 indicates that n = 3 offers a good fit to the present results for R > 50 mm. Below this, the capacity of the shotcrete in shear is lower than predicted by this generalised size-effect relationship, but this is not of major concern since this region involves shear failures of insignificant size. A secondary size-dependent effect on the present results may have been associated with the roughness of the surface of the specimens. The loading plates were 20–40 mm thick and made of steel so these rigid plates did not bend and thereby cause flexural stress in the specimens during testing. However, detritus and small bumps on the surface of each specimen possibly gave rise to a combination of flexural and shear stress through the thickness of some specimens and this influence is likely to have been more prominent for the larger specimens due to the larger lever arm between each bump and the edge of the punching zone. Bumps may approximate the effect of loose rubble giving rise to a combination of flexural and shear stresses in a large failure zone compared to a smaller failure zone. 4.3. The influence of eccentric loading on apparent shear strength in punching The third of the shear trials involved an examination of the influence of eccentric loading on the apparent early-age shear strength of FRS in punching. The reason why eccentricity was examined is that the centre of gravity for a loose rock or wedge is unlikely to exactly coincide with the centre of load resistance provided by the FRS lining (Fig. 7). When an eccentricity between load and resistance occurs there arises a couple between the two forces that increases the shear stress on one side of the conical failure zone through the FRS lining compared to the other. The result is likely to be a reduction in the peak load resistance exhibited by the lining. The magnitude of this reduction in capacity, and the relationship between eccentricity and the reduction in capacity, are of interest to designers of FRS linings. In the current investigation the eccentricity has been expressed as a ratio x/R where x is the offset between the centre of loading and resistance and R is the radius of the round plates used to load the specimens. Two sizes of punching plug were used: 300 mm and 400 mm in diameter. The supporting annulus was 250 mm greater in diameter than the punching plug in all the tests. A 150 mm high concrete block was placed between the spherical seat and plate to approximate
Fig. 7. Eccentricity between load and resistance in tests undertaken to examine the relative shear strength of FRS.
545
a solid mass of rock so that the rotation characteristics during failure resembled a real wedge or scat. The results of the investigation of the effects of eccentricity are shown in Fig. 8. This graph indicates that peak load resistance during punching shear tests diminishes as the eccentricity in loading increases. The relation between the relative load capacity hecc and the eccentricity x/R was found to be well represented by
hecc ¼ e1:5ðx=RÞ
1:5
ð3Þ
for which 0 < x/R < 0.5. This expression has been plotted as the curve in Fig. 8. The large scatter in results in this figure is possibly due to variations in strength between panel specimens because each point represents the relative load resistance of an eccentrically loaded panel compared to another symmetrically loaded specimen tested at approximately the same age after production. The reduction in punching load resistance for x/R = 0.5 compared to x/R = 0.0 was about 41%. 4.4. The influence of inclined loading on apparent shear strength in punching The last of the shear trials involved an examination of the influence of inclined loading on the apparent early-age shear strength of FRS in punching. This part of the investigation was prompted by the observation that FRS linings normally span the entire arc of a tunnel invert, and often include the walls, and thus gravity loading may be imposed on the inclined side of a lining as well as the horizontal crown. Ground stresses may also induce intrusion of rocks at an angle to the plane of a lining. The angle of inclination between the plane of the lining and the gravity load associated with loose scats and wedges will typically range from 0–45°. In the present investigation a series of shear trials were executed in which an inclined test bed was used to mount the supporting annulus under each test specimen. The test bed had the capacity to be inclined at between 0–45°. Four sets of 24 50 mm thick panels measuring ;580 mm were tested in the device using the ;200 mm punching plug and a ;450 mm support annulus. The concrete used in each batch was the standard 40 MPa mix (Table 1) with
Fig. 8. Effect of eccentricity x/R of the punching zone on the relative shear strength of FRS.
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6 kg/m3 of Barchip Shogun fibre. The tests were carried out for a compressive strength range of 0.2–4.0 MPa, and the results are plotted in Fig. 9. This data shows that inclination angle appears to have very little effect on the relation between shear and compressive strength of FRS at early ages, at least for angles in the range 0–30°. Tests could not be done at larger inclination angles because the loading plate slid down the face of the specimen rather than punch through the concrete. While there appeared to be some local differentiation between test results for different angles of inclination there was no consistent trend across all strengths up to 3–4 MPa compressive strength. It has therefore been concluded that inclination angle has a negligible influence on punching shear resistance for angles of inclination in the range 0–30°. 4.5. Combined influence of all geometric factors When all of the results presented in Sections 4.1–4.4 are considered together it is apparent that a single expression can be developed and used to predict the punching shear resistance of early-age FRS. In doing so it has been assumed that the influence of each variable is independent of the influence of all other variables but the effect of each is also multiplicative. In order to prevent collapse the shear resistance V of a lining must exceed the imposed shear load P by a suitable margin u such that
V
u
PP
ð4Þ
in which
V ¼ hSE hecc mpt
ð5Þ
where, for shotcrete reinforced with normal dosage rates of macrofibre and no micro-synthetic fibre, we have
m ¼ 0:28fc0:60 0:11
ð6Þ
in which fc is the mean compressive strength of the shotcrete (in MPa). The size effect correction factor hSE was given in Eq. (2) in which n = 3, and the eccentric loading correction factor hecc was given by Eq. (3).
The radius of the expected punching zone R must be normalised to a 100 mm radius zone because all of the data obtained and presented in Fig. 1, for example, was obtained in tests conducted using punching plugs of this radius. The critical perimeter p and thickness t have been defined earlier. The capacity reduction factor u can assume a value somewhere in the range 1.1–1.5, but typically for short-term construction requirements would equal about 1.3. A more rational choice for the magnitude of u must await a formal risk analysis. Note that the angle of inclination is taken to have no effect on punching shear resistance for angles of inclination up to 30°. The shape of the punching zone is similarly taken to have no influence on the punching resistance of the lining in shear as long as the critical perimeter is used in Eq. (5). It must be noted that the distributed loading case was not considered at present because it has been assumed that loose clumps of fragmented rock capable of imposing a distributed load on a lining are removed by scaling prior to spraying of a lining. It has therefore been assumed in all of the calculations listed above that induced flexural stresses are low compared to shear stresses. This is a reasonable assumption given that observed early-age failures in the field have primarily comprised individual intact rocks rather than fragmented material (Potvin and Nedin, 2004). 5. Design calculations In the process of FRS lining ‘design’ for early-age re-entry under freshly sprayed ground, it must first be determined whether potentially loose ground acts under the influence of gravity alone or ground stresses. The estimation of localised forces acting on a lining as a result of ground stress is beyond the scope of the present investigation. However, if gravity is assumed to be solely responsible for ground mobility then it will only be necessary to take into account the loose rock that presents the potential of collapse, its perimeter, and the possibility of eccentric load imposition onto the FRS lining. As an example of the process by which the minimum compressive strength of FRS required before re-entry is safe can be calculated, consider the following. For simplicity, take the mass of a loose rock to assume the shape of a hemisphere and the direction of gravity to be acting at less than 30° inclination to the plane of the lining. The shape of the punching zone will be round, and with the area estimated to be 1.0 m2 the radius will be R 564 mm. The magnitude of u is taken to be 1.3, n is 3, and the eccentricity of loading is assumed be no worse than 0.2. Thus the size effect factor is hSE = 0.562 and hecc = 0.8744. The critical perimeter is 3700 mm and the mean minimum thickness of the lining is taken to be 50 mm. The density of the rock is assumed to be 2800 kg/m3 and that of the shotcrete lining 2350 kg/m3. It is necessary to solve the following expression to obtain the minimum shear strength required before entry is possible, thus
P6
1
u
hSE hecc mpt
ð7Þ
in which the force acting on the lining, P, is found as volume multiplied by density for both the rock and lining, that is P = 4pR3qRock/6 + pR2tqFRS = 11,461 N. We take V P uP and thus
mP
uP ¼ 0:164MPa hSE hecc pt
ð8Þ
Referring to Eq. (6) for the relation between shear and compressive strength for the FRS, we find that the minimum required compressive strength is Fig. 9. Effect of load inclination on the relation between shear and compressive strength of FRS.
fc P
1 0:164 þ 0:11 0:60 ¼ 0:96MPa 0:28
ð9Þ
E.S. Bernard / Tunnelling and Underground Space Technology 26 (2011) 541–547
A similar process can be used to develop general estimates of the minimum mean compressive strength of concrete fc required before re-entry is safe. For a cone or pyramid the volume of mobile ground to use can be based on the model proposed by Barrett and McCreath (1995) in which the subtended angle between rock bolt and inclined surface of the failure zone is taken to be 30°. Hence the height (or depth) h of the unstable rock mass is h = R tan(60°) = 1.732R and Vcone = pR2h/3, or Vpyramid = 4R2h/3. Calculations indicate that most failure zones comprising a loose rock under gravity loading (with competent adhesion and no other ground stresses acting) of up to 500 mm equivalent radius can essentially be supported in the short term using a 50 mm thick FRS lining of 1.0 MPa compressive strength even with u = 1.3 and x/R = 0.2. 6. Conclusions An experimental investigation of the influence of geometric factors on the punching shear resistance of FRS at early ages was undertaken to assist in the development of a rational approach to the estimation of safe re-entry times under freshly sprayed shotcrete. The work has identified a number of factors that appear to strongly influence punching shear capacity at early ages, and several factors that have a negligible influence. A relatively simple expression has also been developed to quantify the influence of the significant geometric factors on punching shear resistance at early ages. Among geometric factors of possible influence on punching capacity, the shape of the punching zone did not appear to influence shear strength at least for punching zones of around 200 mm span. The angle of inclination between the lining and imposed force also appeared to have an insignificant influence on capacity for angles in the range 0–30°. In contrast, the size of the punching zone and eccentricity of loading both had a substantial influence on capacity. Punching resistance was found to be significantly reduced as the size of the loaded zone increased and as eccentricity between the imposed load and centre of resistance increased.
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References Australian Standard AS1012 Testing Concrete, 1991. Standards Australia, Sydney. Australian Standard AS3600 Concrete Structures, 2010. Standards Australia, Sydney. ASTM C 116-68 (Reapproved 1980). Standard Test Method for Compressive Strength of Concrete Using Portions of Beams Broken in Flexure. American Society for Testing and Materials. Austrian Tunnelling Society, Guideline on Inner Shell Concrete, Österreichischen Vereinigung für Beton-und Bautechik, August 2006. Barrett, S., McCreath, D.R., 1995. Shotcrete support design in blocky ground – towards a deterministic approach. Tunnels and Deep Space 10 (1), 79–88. Bazˇant, Z.P., Planas, J., 1998. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boca Raton. Bernard, E.S., 2008. Early-age load resistance of fibre reinforced shotcrete linings. Tunnelling and Underground Space Technology 23, 451–460. Bernard, E.S., 2009. Load Capacity of Early-Age Fibre Reinforced Shotcrete Linings, TSE Report 197, TSE Pty Ltd, Sydney, p. 54. Bernard, E.S., & Curnow, M.C.P., 1999. Experimental factors affecting punching resistance in fibre reinforced concrete panels. In: Third International Symposium on Shotcrete for Ground Support, Gol, Norway, September 26–28, pp. 47–57. Bernard, E.S., Geltinger, C., 2007. Early-Age Determination of Compressive Strength in Shotcrete. Shotcrete, vol. 94. American Shotcrete Association, pp. 22–27. Bernard, E.S., Harkin, S., 2001. Punching and rock bolt assembly through a fibre reinforced concrete panel. In: Bernard (Ed.), Shotcrete: Engineering Developments. Swets & Zeitlinger, Lisse, pp. 65–70. Bernard, E.S., Nyström, E.M.C., 2000. The influence of loading conditions on punching resistance in fibre reinforced concrete panels. In: International Symposium of Punching Resistance in Concrete Slabs, IABSE, Stockholm, June 8–9. British Tunnelling Society, 2010. Specification for Tunnelling, third ed. Thomas Telford, London, p. 200. Chang, Y., & Stille, H., 1993. Influence of early-age properties of shotcrete on tunnel construction sequences. Shotcrete for Underground Support VI, Niagara-on-theLake, Canada, May 2–6, pp. 110–117. Golser, J., 2001. Behaviour of Early-Age Shotcrete. Shotcrete for Underground Support VIII, Sao Paulo, April 11–15, pp. 83–93. Morgan, D.R., McAskill, N., and Heere, R., 1999. Determination of early-age compressive strength of shotcrete. In: Third International Symposium on Sprayed Concrete, Gol, Norway, September 26–29, pp. 347–372. Potvin, Y., Nedin, P., 2004. Controlling rock fall risks in Australian underground metal mines. In: Villaescusa, E., Potvin, Y. (Eds.), Ground Support in Mining and Underground Construction. Balkema, pp. 359–366.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Influence of geometric factors on the punching load resistance of early-age fibre reinforced shotcrete linings Erik Stefan Bernard ⇑ TSE P/L, PO Box 763 Penrith, NSW 2750, Australia
a r t i c l e
i n f o
Article history: Received 28 September 2010 Received in revised form 1 December 2010 Accepted 15 February 2011 Available online 16 March 2011 Keywords: Ground control Fibre reinforced shotcrete Load resistance Early age Punching shear Testing
a b s t r a c t Understanding the early-age properties of fibre reinforced shotcrete (FRS) is critical to the accurate estimation of the time to safe re-entry under freshly sprayed FRS linings. Previous research in the field has indicated that shear failures dominate early-age load resistance and thereby govern the performance of a lining during the first few hours after spraying. This investigation has examined the influence of several geometric variables on shear resistance in a punching mode of failure. In particular, the research has addressed the influence of the size, shape, eccentricity, and inclination of punching loads on the apparent shear strength of an early-age fibre reinforced shotcrete (FRS) lining. Ó 2011 Elsevier Ltd. All rights reserved.
1. Background In the tunnelling and underground mining industries interest has recently developed into the subject of early-age strength development and its influence on safe re-entry times under freshly sprayed fibre reinforced shotcrete (FRS). This is because cycle times for drive development within mines, and in civil tunnel construction, can strongly depend on the time to safe re-entry and this, in turn, affects progress rates and overall economy. In the present context, the term ‘safe re-entry’ refers to an acceptably low risk of pieces of rock or shotcrete falling onto operators during the first few hours after spraying and resumption of work under a freshly sprayed lining. The majority of research into safe re-entry times has focused on strength development in hardening shotcrete (Golser, 2001; Chang and Stille, 1993) under the implicit assumption that toughness, adhesion to the rock surface, and the ability of the FRS lining to support loose rocks are all related to the strength of the concrete matrix. Evidence to support this assumption has been partially developed through trials conducted at Cliffs, Cannington, Olympic Dam, Argyle, and Cadia mines in Australia (Bernard, 2008). However, these trials have also shown that punching shear is the dominant mode of failure at early ages and that flexural failure mainly occurs at later ages. Compressive failures seldom occur in any FRS linings over hard rock. It is therefore important that factors affecting punching resistance at early ages are well understood. ⇑ Tel.: +61 247255801; fax: +61 247225773. E-mail address: [email protected] 0886-7798/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2011.02.004
Predicting the early-age punching resistance in shear, V, of a FRS lining is presently restricted to the use of simple models such as
V ¼ mpt
ð1Þ
where m is the shear strength of the concrete, p is the critical perimeter, and t is the thickness. This model is based on punching shear behaviour in concrete floors (AS3600, 2010) and the accuracy of the expression has not been rigorously demonstrated for earlyage FRS linings. The present investigation has been developed to extend this simple model of lining capacity and examine the influence of geometric factors on early-age shear resistance. Previous research conducted into early-age shotcrete performance for hard rock applications primarily addressed the rate of strength gain over the first few hours and days after spraying and methods of assessing compressive strength at these ages (Bernard and Geltinger, 2007; Morgan et al., 1999). There has also been a substantial amount of work undertaken addressing strength and stiffness in shotcrete shell linings used in the NATM tunnelling technique through soft ground (British Tunnelling Society, 2010). Data of direct relevance to the estimation of safe early-age re-entry times is presented in Fig. 1 which shows the relation between shear and compressive strengths at early ages. Experiments by Bernard (2008) demonstrated that fall-outs of FRS lining are dominated by the shear mode of failure through the lining thickness. Potvin and Nedin (2004) also showed that early-age fall-outs of shotcrete caused by loose rock are dominated by individual scats and wedges of up to 2 tonnes mass and that larger bodies of mobile rock are rare. This has helped to delineate the 1 MPa compressive strength limit for a 50 mm thick lining as the minimum satisfactory
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shotcrete according to the procedures described by Bernard and Geltinger (2007) who validated these test methods against standard UCS test methods such as cores. The soil penetrometer was 6.0 mm in diameter and could be used to estimate compressive strengths up to about 0.3 MPa. The needle penetrometer comprised a 3.0 mm diameter steel needle at the end of a spring that was forced into the surface of setting concrete. This method is suitable for determining compressive strengths up to 0.8 MPa. The ASTM C116-based beam-end tester (ASTM, 1980; Morgan et al., 1999) was the only early-age strength testing device that involved direct compressive failure of the concrete samples. Beams measuring 75 75 400 mm were produced by spraying shotcrete into an open-ended mould. This device could assess compressive strengths in the range 0.5–8.0 MPa. Unconfined compressive strength tests were conducted at later ages in accordance with AS1012 (1991) using 75 mm diameter cores. 3.2. Shear testing
Fig. 1. Shear strength as a function of compressive strength for FRS (Bernard, 2008).
strength of FRS before re-entry can be considered safe. This benchmark compressive strength happens to coincide with the minimum requirement specified by the Austrian Tunnelling Society (2006) for thick-shell shotcrete although this limit was arrived at by different means. However, these conclusions were based on very simple models of lining behaviour at early ages that require development and validation. 2. Objectives of investigation The primary objective of the present investigation was to determine the punching resistance of early-age FRS linings and establish quantitative evidence of the influence on this parameter of geometric factors in the first few hours after spraying. This information will be used to develop a more comprehensive model of factors controlling punching failure of FRS and help to identify the period of curing required before it is safe to re-enter under freshly sprayed excavated ground while including a reasonable margin of safety against fall-outs. The dominant loading case for early-age failures has been taken to be gravity loading associated with loose individual rocks. 3. Experimental program The project was undertaken through four related series of shear trials conducted to examine the influence of the shape and size of the punching zone, as well as the influence of inclined and eccentric loading, on apparent shear strength. Each of the shear trials comprised a set of experiments in which a FRS mix was cast or sprayed to produce panel specimens that were subsequently tested over a 24 h period to determine early-age shear strength in punching under a variety of conditions. A total of 28 trials were conducted involving 630 specimens. Cast FRS specimens were used in many of the trials in the interests of economy. This research was undertaken as part of an industry-funded project administered by AMIRA International and reported by Bernard (2009). The test methods employed in this investigation are described below.
In order to generate punching shear strength data on FRS, laboratory-based punching tests were conducted in a purpose-built apparatus consisting of a thick steel annular base onto which the FRS panel specimens were placed (Bernard and Harkin, 2001). Load was imposed onto the upper surface of each specimen using a servo-controlled hydraulic piston operating under displacement control so as to cause punching failure through the centre. In the majority of tests, load was imposed through a 100 mm diameter spherical seat resting on top of a 200 mm diameter steel plate. The spherical part of the seat was convex, and matched the design used by Bernard and Nyström (2000). This type of seat allowed rotation of the punching cone during failure, thereby simulating the rotational freedom believed possible for rocks that are punched through a FRS lining. All the specimens were cast or sprayed inside thick steel rings that prevented radial dilation during punching. The use of the steel rings has been shown to effectively prevent the specimen edges rotating or translating during a punching test and thereby simulate the lateral confinement associated with a contiguous lining. The annulus under the panel had a diameter that exceeded that of the loading plate by 250 mm for each ;200 mm punching plug as it was driven through the ;580 mm specimens that were used for the majority of trials (Fig. 2). Given that the specimens were 50 mm thick this ensured that the conical failure surface generated during each test was inclined at about u = 65–70° to the loading axis. This is close to the inclination of natural failure surfaces which form at around u 70°. The load was imposed at a controlled rate of displacement equal to 4.0 mm/min up to a total central displacement of 25 mm.
3.1. Early-age compressive strength A soil penetrometer, needle penetrometer, and beam-end tester were used to assess the early-age compressive strength of
Fig. 2. Punching shear test with confinement ring around side and included angle u.
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The calculated punching shear resistance of a concrete plate represented by Eq. (1) requires an estimate of the critical perimeter. The critical perimeter is the perimeter at which the mid-plane intersects a conical surface subtending 45° from the outline of the loaded plug. Note that the conical failure surface was assumed to always act at an angle of 45° from the loaded surface regardless of what the true angle actually was. This must be considered when the resulting estimates of shear strength are used to calculate the load resistance of a lining. 3.3. Production of specimens Two methods were used to produce the specimens tested in this investigation: either by spraying, or by casting. Both methods of production included the use of precision-milled and surface– ground steel plates as a substrate over which polypropylene sheeting was placed to prevent bond to the newly produced specimen. The surface–ground plates were necessary to produce a very flat underside to the specimens so that flexural stresses were minimised during testing. All the panel specimens were round with a 10 mm thick steel ring acting as both a form and a confining ring to prevent dilation of the specimen during shear testing. Contiguous linings do not dilate around a punching plug as the surrounding lining acts to confine the concrete at the failure zone within the plane of the lining. Dilation during a shear test has been shown to significantly reduce the peak shear strength in laboratory tests of punching in plates (Bernard and Curnow, 1999). 3.3.1. Production by spraying Shear specimens were sprayed in a horizontal position while lying on ground steel plates over pallets (Fig. 3). The shotcrete was a 40 MPa mix with 4–5% bwc SA 160 set accelerator placed using manual spraying. After spraying, the surface was screeded and floated to produce a smooth steel-troweled finish. Companion ASTM C116 beams were produced for UCS determination in the range 1 and 8 MPa. The shear panels themselves were used for early-age soil and needle penetrometer tests up to 1 MPa equivalent UCS.
specimens generally took longer to attain the required compressive strength range deemed suitable for testing each specimen in shear. 3.4. Influence of production method on shear capacity In underground applications all linings are produced by spraying an FRS mixture into place. Many of the specimens produced in this investigation were also sprayed. However, spraying is very expensive in a laboratory environment and thus the majority of specimens were cast in order to limit the cost of the investigation. A preliminary investigation was therefore undertaken to determine whether there is a systematic difference in the relation between shear and compressive strengths for an FRS mix that had been sprayed as opposed to cast. Two trials were undertaken using the 40 MPa nominal shotcrete mix listed in Table 1. One of the sets involved spraying 20 shear specimens and ASTM C116 beam-end specimens followed by testing over a 10–12 h period, and the other involved casting the same nominal mix and testing. The results are shown in Fig. 4. The points do not follow exactly the same trend throughout the entire strength range but given the variability typical of specimens tested in this and earlier investigations there did not appear to be a systematic difference in performance between FRS that is sprayed as compared to cast. For the remainder of this trial it has therefore been assumed that the shear-compressive strength relation does not vary between sprayed and cast specimens for a given FRS mixture.
Table 1 The 40 MPa shotcrete used in all trials. Ingredient
Quantity (kg/m3)
Coarse sand Fine sand 7 mm basalt Cement (GP) Flyash Pozzolith 300Ri (LRWR)
500 455 600 380 90 1200 mL
3.3.2. Production by casting When casting was employed as the method of production the specimens were placed in a horizontal position over the ground steel plates. No set accelerator was used during casting, but internal vibration with a 42 mm poker vibrator was applied to consolidate all the specimens. A screed and float were then used to finish the specimens. The absence of a set accelerator meant that the cast
Fig. 3. Spraying shear specimens.
Fig. 4. Relation between shear and compressive strengths for FRS that has been sprayed versus cast.
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4. Results 4.1. The influence of the shape of the punching zone on apparent shear strength in punching
4.2. The influence of the size of the punching zone on apparent shear strength in punching
The first of the shear trials involved an examination of the influence of the shape of the punching zone on the apparent early-age shear strength of FRS in punching. The rationale for this assessment is that loose rocks and wedges in a tunnel crown are very unlikely to be circular in shape like the punching zone imposed in the majority of tests undertaken in this investigation. For this reason both square and triangular punching plugs were used in parallel with round plugs in a series of trials to determine whether shape substantially influences apparent shear strength. Shear testing trials were undertaken in which circular, square, and triangular punching plugs were used to load confined panels. The square and triangular plugs had a critical perimeter that was the same as that of the 200 mm diameter circular plug. All the specimens were 50 mm thick, and the mix designs used included both shotcrete and conventional concrete with 10 mm coarse aggregate, and plain, macro-synthetic, and micro-synthetic FRS shotcrete. The results of this investigation are shown in Fig. 5. The trend lines that have been fitted to each set of shape results show that there appeared to be a statistically insignificant difference in shear strength between punching plugs of different shape. At early ages the variability in shear strength for a given compressive strength displayed by specimens tested for a particular shape of punching plug was much greater than the difference between shapes. This must be qualified by the observation that only 200 mm diameter round plugs and square and triangle plugs of equal critical perimeter were included in the present trials. While it is likely that the lack of a shape effect also applies to larger punching zones, the absence of shape influence on shear resistance in the present tests does not necessarily extend to much larger punching zones. However, in the absence of information to the contrary it has tentatively been concluded that the shape of the punching zone has a negligible influence on apparent shear strength.
The second of the shear trials involved an examination of the influence of the size of the punching zone on the apparent earlyage shear strength of FRS in punching. This trial included a number of tests in which sets of 20–24 shear panels were cast ranging in size from ;400 to ;1200 mm. The punching plugs were round and ranged in diameter from 16 to 700 mm. The diameter of the supporting annulus was always 250 mm greater than the loading plug so the conical failure zone had the same inclination angle. The tests were undertaken over the first 6–24 h after production of the specimens so the testers were faced with the problem that the compressive strength increased relatively rapidly over this period. Since the objective was to isolate the effect of punching zone size from the effect of compressive strength change on shear capacity, each set of 4–5 tests was undertaken within a short period of time so that the UCS was approximately equal within this interval. Compressive strength was monitored and the shear strength results within each set were linearly adjusted relative to the result obtained for the 200 mm diameter specimen. Similarly, the shear strengths obtained for each set of ;16 to ;700 mm specimens were adjusted linearly relative to the strength obtained for the 200 mm diameter specimen. This relative strength has been expressed as a Capacity Ratio (hSE = sR/s100, where sR is the punching shear strength of a plug of radius R, and s100 is the punching resistance of a plug of 100 mm radius) and is plotted as a function of the logarithm of the normalised punching zone radius in Fig. 6. The reason for the reduction in apparent strength as the size of the punching zone increased is due in part to the probability that there is a greater statistical likelihood that a critical flaw will occur within the highly stressed area around the zone of failure as the size of the failure zone increases (Bazˇant and Planas, 1998). The presence of a flaw will typically reduce peak capacity. This phenomenon is known as the size effect and has been well studied in concrete materials. When conventional size effect laws are considered for the range of specimen sizes tested in this investigation the capacity reduction factor hSE can be expressed as
Fig. 5. Effect of punching plug shape on relation between shear and compressive strengths for FRS.
Fig. 6. Size effect on relative shear strength of FRS for present data set.
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hSE ¼
1n R 100
ð2Þ
in which n lies in the range 2–3 (Bazˇant and Planas, 1998). The data presented in Fig. 6 indicates that n = 3 offers a good fit to the present results for R > 50 mm. Below this, the capacity of the shotcrete in shear is lower than predicted by this generalised size-effect relationship, but this is not of major concern since this region involves shear failures of insignificant size. A secondary size-dependent effect on the present results may have been associated with the roughness of the surface of the specimens. The loading plates were 20–40 mm thick and made of steel so these rigid plates did not bend and thereby cause flexural stress in the specimens during testing. However, detritus and small bumps on the surface of each specimen possibly gave rise to a combination of flexural and shear stress through the thickness of some specimens and this influence is likely to have been more prominent for the larger specimens due to the larger lever arm between each bump and the edge of the punching zone. Bumps may approximate the effect of loose rubble giving rise to a combination of flexural and shear stresses in a large failure zone compared to a smaller failure zone. 4.3. The influence of eccentric loading on apparent shear strength in punching The third of the shear trials involved an examination of the influence of eccentric loading on the apparent early-age shear strength of FRS in punching. The reason why eccentricity was examined is that the centre of gravity for a loose rock or wedge is unlikely to exactly coincide with the centre of load resistance provided by the FRS lining (Fig. 7). When an eccentricity between load and resistance occurs there arises a couple between the two forces that increases the shear stress on one side of the conical failure zone through the FRS lining compared to the other. The result is likely to be a reduction in the peak load resistance exhibited by the lining. The magnitude of this reduction in capacity, and the relationship between eccentricity and the reduction in capacity, are of interest to designers of FRS linings. In the current investigation the eccentricity has been expressed as a ratio x/R where x is the offset between the centre of loading and resistance and R is the radius of the round plates used to load the specimens. Two sizes of punching plug were used: 300 mm and 400 mm in diameter. The supporting annulus was 250 mm greater in diameter than the punching plug in all the tests. A 150 mm high concrete block was placed between the spherical seat and plate to approximate
Fig. 7. Eccentricity between load and resistance in tests undertaken to examine the relative shear strength of FRS.
545
a solid mass of rock so that the rotation characteristics during failure resembled a real wedge or scat. The results of the investigation of the effects of eccentricity are shown in Fig. 8. This graph indicates that peak load resistance during punching shear tests diminishes as the eccentricity in loading increases. The relation between the relative load capacity hecc and the eccentricity x/R was found to be well represented by
hecc ¼ e1:5ðx=RÞ
1:5
ð3Þ
for which 0 < x/R < 0.5. This expression has been plotted as the curve in Fig. 8. The large scatter in results in this figure is possibly due to variations in strength between panel specimens because each point represents the relative load resistance of an eccentrically loaded panel compared to another symmetrically loaded specimen tested at approximately the same age after production. The reduction in punching load resistance for x/R = 0.5 compared to x/R = 0.0 was about 41%. 4.4. The influence of inclined loading on apparent shear strength in punching The last of the shear trials involved an examination of the influence of inclined loading on the apparent early-age shear strength of FRS in punching. This part of the investigation was prompted by the observation that FRS linings normally span the entire arc of a tunnel invert, and often include the walls, and thus gravity loading may be imposed on the inclined side of a lining as well as the horizontal crown. Ground stresses may also induce intrusion of rocks at an angle to the plane of a lining. The angle of inclination between the plane of the lining and the gravity load associated with loose scats and wedges will typically range from 0–45°. In the present investigation a series of shear trials were executed in which an inclined test bed was used to mount the supporting annulus under each test specimen. The test bed had the capacity to be inclined at between 0–45°. Four sets of 24 50 mm thick panels measuring ;580 mm were tested in the device using the ;200 mm punching plug and a ;450 mm support annulus. The concrete used in each batch was the standard 40 MPa mix (Table 1) with
Fig. 8. Effect of eccentricity x/R of the punching zone on the relative shear strength of FRS.
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6 kg/m3 of Barchip Shogun fibre. The tests were carried out for a compressive strength range of 0.2–4.0 MPa, and the results are plotted in Fig. 9. This data shows that inclination angle appears to have very little effect on the relation between shear and compressive strength of FRS at early ages, at least for angles in the range 0–30°. Tests could not be done at larger inclination angles because the loading plate slid down the face of the specimen rather than punch through the concrete. While there appeared to be some local differentiation between test results for different angles of inclination there was no consistent trend across all strengths up to 3–4 MPa compressive strength. It has therefore been concluded that inclination angle has a negligible influence on punching shear resistance for angles of inclination in the range 0–30°. 4.5. Combined influence of all geometric factors When all of the results presented in Sections 4.1–4.4 are considered together it is apparent that a single expression can be developed and used to predict the punching shear resistance of early-age FRS. In doing so it has been assumed that the influence of each variable is independent of the influence of all other variables but the effect of each is also multiplicative. In order to prevent collapse the shear resistance V of a lining must exceed the imposed shear load P by a suitable margin u such that
V
u
PP
ð4Þ
in which
V ¼ hSE hecc mpt
ð5Þ
where, for shotcrete reinforced with normal dosage rates of macrofibre and no micro-synthetic fibre, we have
m ¼ 0:28fc0:60 0:11
ð6Þ
in which fc is the mean compressive strength of the shotcrete (in MPa). The size effect correction factor hSE was given in Eq. (2) in which n = 3, and the eccentric loading correction factor hecc was given by Eq. (3).
The radius of the expected punching zone R must be normalised to a 100 mm radius zone because all of the data obtained and presented in Fig. 1, for example, was obtained in tests conducted using punching plugs of this radius. The critical perimeter p and thickness t have been defined earlier. The capacity reduction factor u can assume a value somewhere in the range 1.1–1.5, but typically for short-term construction requirements would equal about 1.3. A more rational choice for the magnitude of u must await a formal risk analysis. Note that the angle of inclination is taken to have no effect on punching shear resistance for angles of inclination up to 30°. The shape of the punching zone is similarly taken to have no influence on the punching resistance of the lining in shear as long as the critical perimeter is used in Eq. (5). It must be noted that the distributed loading case was not considered at present because it has been assumed that loose clumps of fragmented rock capable of imposing a distributed load on a lining are removed by scaling prior to spraying of a lining. It has therefore been assumed in all of the calculations listed above that induced flexural stresses are low compared to shear stresses. This is a reasonable assumption given that observed early-age failures in the field have primarily comprised individual intact rocks rather than fragmented material (Potvin and Nedin, 2004). 5. Design calculations In the process of FRS lining ‘design’ for early-age re-entry under freshly sprayed ground, it must first be determined whether potentially loose ground acts under the influence of gravity alone or ground stresses. The estimation of localised forces acting on a lining as a result of ground stress is beyond the scope of the present investigation. However, if gravity is assumed to be solely responsible for ground mobility then it will only be necessary to take into account the loose rock that presents the potential of collapse, its perimeter, and the possibility of eccentric load imposition onto the FRS lining. As an example of the process by which the minimum compressive strength of FRS required before re-entry is safe can be calculated, consider the following. For simplicity, take the mass of a loose rock to assume the shape of a hemisphere and the direction of gravity to be acting at less than 30° inclination to the plane of the lining. The shape of the punching zone will be round, and with the area estimated to be 1.0 m2 the radius will be R 564 mm. The magnitude of u is taken to be 1.3, n is 3, and the eccentricity of loading is assumed be no worse than 0.2. Thus the size effect factor is hSE = 0.562 and hecc = 0.8744. The critical perimeter is 3700 mm and the mean minimum thickness of the lining is taken to be 50 mm. The density of the rock is assumed to be 2800 kg/m3 and that of the shotcrete lining 2350 kg/m3. It is necessary to solve the following expression to obtain the minimum shear strength required before entry is possible, thus
P6
1
u
hSE hecc mpt
ð7Þ
in which the force acting on the lining, P, is found as volume multiplied by density for both the rock and lining, that is P = 4pR3qRock/6 + pR2tqFRS = 11,461 N. We take V P uP and thus
mP
uP ¼ 0:164MPa hSE hecc pt
ð8Þ
Referring to Eq. (6) for the relation between shear and compressive strength for the FRS, we find that the minimum required compressive strength is Fig. 9. Effect of load inclination on the relation between shear and compressive strength of FRS.
fc P
1 0:164 þ 0:11 0:60 ¼ 0:96MPa 0:28
ð9Þ
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A similar process can be used to develop general estimates of the minimum mean compressive strength of concrete fc required before re-entry is safe. For a cone or pyramid the volume of mobile ground to use can be based on the model proposed by Barrett and McCreath (1995) in which the subtended angle between rock bolt and inclined surface of the failure zone is taken to be 30°. Hence the height (or depth) h of the unstable rock mass is h = R tan(60°) = 1.732R and Vcone = pR2h/3, or Vpyramid = 4R2h/3. Calculations indicate that most failure zones comprising a loose rock under gravity loading (with competent adhesion and no other ground stresses acting) of up to 500 mm equivalent radius can essentially be supported in the short term using a 50 mm thick FRS lining of 1.0 MPa compressive strength even with u = 1.3 and x/R = 0.2. 6. Conclusions An experimental investigation of the influence of geometric factors on the punching shear resistance of FRS at early ages was undertaken to assist in the development of a rational approach to the estimation of safe re-entry times under freshly sprayed shotcrete. The work has identified a number of factors that appear to strongly influence punching shear capacity at early ages, and several factors that have a negligible influence. A relatively simple expression has also been developed to quantify the influence of the significant geometric factors on punching shear resistance at early ages. Among geometric factors of possible influence on punching capacity, the shape of the punching zone did not appear to influence shear strength at least for punching zones of around 200 mm span. The angle of inclination between the lining and imposed force also appeared to have an insignificant influence on capacity for angles in the range 0–30°. In contrast, the size of the punching zone and eccentricity of loading both had a substantial influence on capacity. Punching resistance was found to be significantly reduced as the size of the loaded zone increased and as eccentricity between the imposed load and centre of resistance increased.
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