Undercut anchorage in dimension stone cladding

Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos ice | proceedings Proceedings of the Institution of Civil Engineers Construction Materials 166 June 2013 Issue CM3 Pages 158–174 http://dx.doi.org/10.1680/coma.11.00050 Paper 1100050 Received 17/08/2011 Accepted 17/10/2011 Published online 02/08/2012 Keywords: anchors & anchorages/design methods & aids/ stress analysis ICE Publishing: All rights reserved Undercut anchorage in dimension stone cladding Rui S. Camposinhos PhD Coordinator Professor, ISEP, Polytechnic of Porto, School of Engineering, Porto, Portugal This paper analyses undercut anchorage technology, in particular its behaviour and performance as a fixing system for dimension stone cladding of rainscreen façades. Based on a number of mechanical tests using various types of Portuguese stone – three igneous, two sedimentary and one metamorphic – a study was carried out to investigate the relationship between the flexural strength and breaking load of specific and very common stone types. Several physical and mechanical characterisation tests and 130 pull-out tests with 6 and 8 mm cone bolt threads were performed to determine the pull-out load failure on six different stone types: three granite, two limestone and one marble. Finite-element stress analyses were carried out, and the test results were the basis for calibrating a simple formula that can be used to estimate the stone’s breaking load at the undercut anchorage. Stress concentration factors are proposed to take into account the undercut drill hole geometry and the specific properties of each type of stone. Stone specimens from the same batches were subject to pull-out force tests using dowel anchorages, whose values were then compared with the breaking load of undercut anchorages. Results are discussed and conclusions are drawn based on tensile stress values by comparing the test results, the finite-element method and the proposed semiempirical formulations for the same breaking load. Notation Acf du em F Ku r sm t a am wt wu smax st stm sRf sRtf sRf1 sRf2 1. area of the projected cone failure surface anchorage depth minimum edge distance applied force at failure stress concentration factor radius of the specimen (disc) minimum space between anchors thickness of the disc average angle of the cone failure surface average spall angle diameter of the cylindrical drill hole diameter of the undercut actual maximum stress tensile strength of the stone medium tensile stress strength of a brittle material under flexure axial tension flexural strength of specimen with volume v1 flexural strength of specimen with volume v2 Introduction Art and science must come together in the design of stone façades. The beauty and quality of natural stone make it an ideal material for prestigious projects using successful construction methods in many countries. Rainscreen cladding systems, using the more expensive fixing option, in terms of materials and fixing, can offer other benefits resulting in cost and time savings in the overall project. Resistance to lateral loading, mainly wind and seismic action, is usually achieved by means of stainless steel anchors inserted into kerfs or holes that are drilled or cut into the edges of the stone panels. These anchors are mechanically connected to the building’s structure, thus providing the essential mechanical connection between the stone and the structure. One structural weak point in this type of stone construction is to be found at the kerfs or anchor holes on the edges of the stone slabs. These cuts need to leave sufficient stone thickness to provide the necessary strength to resist the various forces or actions to which the stone panels are subject. The failure of any stone panel may have significant consequences. Many engineers and architects have an overconfident attitude toward these issues and, although they may not fully understand the engineering aspects of natural stone and the behaviour of natural stone veneers, this drawback does not seem to be a constraint when they specify the selection, manufacture and use of natural stone as a façade cladding material. This attitude, when combined with a lack of regulatory controls and standards stipulating appropriate practices, has often led to situations of serious flaws in the selection, design, and installation of natural stone cladding panels. 158 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos Developing innovative fastening products requires in-depth knowledge about the physical phenomena involved in the complete process of installation and loading. stainless steel. The sleeve is made of stainless steel or carbon. The nut is in stainless steel or aluminium. Generally, fasteners can be subdivided into three different working principles according to the load transfer mechanism, namely friction, bonding and keying. For friction-type anchors, the tensile load is transferred from the anchor to the base material due to the friction created by expanded segments. For bonding anchors, the tensile load is transferred mainly through the adhesive bond between the anchor rod and the stone which may cause a combined shear and cone type failure. Keying-type anchors carry the tensile load through main keys at the end of the anchor, resulting in a cone shape failure or in the yielding of the steel rod. This is the case of undercut anchoring. This technology, combined with a suitable support framework, allows the engineer to implement a safe and high performance fixing system for stone cladding façades. The main aspects of this technology are described in the next section. 2. Undercut anchoring Since anchoring is only a small part of the whole façade system, all other influencing factors must be given an equal amount of consideration for a successful design. However, to comprehend how undercut anchors are used, a basic understanding of the most important issues of this type of technology must be addressed. There are mainly two types of undercut technologies to provide a keying-type anchorage in the interior of the dimension stone or slab’s thickness. Anchors are installed by driving the anchor sleeve against the locking ring, thus forcing it to expand within the undercut hole form and locking it within the stone, which provides a stressfree anchorage under zero applied load. This system is generally identified with the Fischer-type technology (Deutsches Institut für Bautechnik, 2009). The other system consists of a special anchor made of a crosswise slotted anchor sleeve with an internal thread. The anchor’s upper edge has a hexagon formed to it and the respective hexagon bolt with a tooth lock washer formed to it. The anchor sleeve and the hexagon bolt with a tooth lock washer formed to it are also made of stainless steel. The anchor is fitted into an undercut drill hole and, by driving the sleeve in it is deformed (Figure 2). The anchor sleeve is expanded to its original dimension by inserting the screw to a controlled depth, so that the sleeve sits snugly against the undercut section of the hole in the façade panel. This system is identified in general with the Keil-type technology (Deutsches Institut für Bautechnik, 2004). In each case the anchor embedment depth may vary and is directly related to the anchor’s tensile capacity. The greater the embedment depth the higher the load bearing capacity, providing the steel has the required load bearing capacity. The undercut drilling is performed with a proper drill bit and a special drilling device in order to obtain the correct shape and dimension according to the size and type of anchors to be fitted (Figure 3). a One system is illustrated in Figure 1 in which the undercut anchors have a cone bolt, either with external thread or internal thread and generally 6 or 8 mm in diameter, an expansion ring with three or four convolutions, a sleeve and, optionally, a nut. Cone bolts and expansion rings are made of a b a c b c b d c e d Anchor with external thread Anchor with internal thread Figure 1. Undercut anchors with external and internal thread: (a) expansion ring; (b) sleeve; (c) cone bolt; and (d) nut Figure 2. System using a crosswise slotted sleeve and an internal thread with a hexagon bolt: (a) slotted sleeve; (b) hexagon bolt with internal thread and tooth lock; (c) dimension stone; and (d) panel bracket 159 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos t hv du t Z u Figure 3. Typical cross-section of a stone slab showing undercut drilling: wt, diameter of the cylindrical drill hole; wu, diameter of the undercut; du, anchorage depth; hv, constant diameter hole depth; z, variable diameter hole depth; t, panel thickness In general, the undrilled depth (t2du) is equal to or greater than 0?4t. This may be justified by the fact that the undercut anchorage resistance is governed by the stone thickness in tension under negative wind pressure on façades. For positive pressures, the majority of resultant forces are transmitted directly to the frame supporting system and/or the façade backup structure. 2.1 Frame supporting systems In both systems, the screw or nut is screwed in until exerting slight pressure on a panel bracket forming a rigid unit with a backup supporting façade system. The support system for a dimension stone panel in most cases consists of a suitable framework in aluminium or stainless steel. Generally, the framework consists of four brackets attached to the back of the façade panel by means of an appropriate undercut anchor. These brackets are then placed into or onto a corresponding continuous horizontal rail. Stone types and specimens from the same quarry and batch were also used to evaluate the force of dowel anchorages and, thereby, compare the resistance of these two anchorage systems. A semi-empirical formulation is proposed based on results from testing mechanical stone properties and the geometry of the anchorage. Finite-element computer analyses of the stress states induced in the stone panels by the undercut anchorage were also carried out. These analyses were the basis for calibrating a simple formula that can be used to estimate the breaking load of the stone at the undercut anchorage. 3.1 Stone type and specimens A photo with samples of the six studied rock types is shown in Figure 4. A brief lithological description of these stones is a prerequisite to fully understand the study and its results. 3.1.1 The granites The study included three different granites: Cinzento de Alpalhão (C.A.), Pedras Salgadas (P.S.) and Amarelo Real (A.R.). (a) The Cinzento Alpalhão (C.A.) granite is grey with a thin grain and a very uniform background. Its colour varies somewhat, from light to dark grey. It is a hard natural stone containing the following essential minerals: In most cases the horizontal rails are attached to vertical mullions which are fixed to the building’s main structure, structural concrete or masonry. C.A. As for the other fixing systems, it must be possible to adjust undercut anchorage systems both horizontally and vertically. Relative movement between the panel and the framework must also be taken into account. 3. P.S. A.R Case study The main goal of this study is to investigate the relationship between flexural strength and breaking load at the undercut anchorage and also to gain a better understanding of the undercut anchorage’s rupture behaviour. Hence, several tests were performed to determine the physical and mechanical properties of the different stone types. Pull-out tests were also performed to study the strength behaviour of this anchorage system. ML. S.R. ET. Figure 4. Prismatic samples after flexural strength test: C.A., Cinzento Alpalhão granite; P.S., Pedras Salgadas granite; A.R., Amarelo Real granite; M.L., Moleanos Limestone; S.R., Semi Rijo limestone; E.T., Estremoz marble 160 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 (b) (c) plagioclase (35%); quartz (30%), microcline (20%) and biotite (10%). The Pedras Salgadas (P.A.) granite is of a light grey colour with a thin to medium grain and a uniform background. It is predominantly light grey but also has some brownish and white coloured areas. It is also a hard natural stone containing the following essential minerals: microcline (36%); oligoclase (32%); quartz (25%) and biotite (6%). The Amarelo Real (A.R.) granite is of a white-yellow colour, with a slight brownish tonality, and has a medium to gross grain and a uniform background. This granite varies according to its colour uniformity and grain thickness. It is a medium or medium to coarse-grained whitish-yellow to brownish-yellow granite, showing some porphyroid tendency and a somewhat pronounced weathering and incipient foliation. This granite is also known as Amarelo Vila Real. Its essential minerals are: microcline (32%); quartz (27%); plagioclase (26%); and muscovite (11%). 3.1.2 The limestones The Moleanos Macio (M.L.) and the Semi Rijo (S.R.) were the two studied limestones (a) (b) The Moleanos Macio limestone is whitish-grey to light beige, of an oolitic tendency, calciclastic and bioclastic, with some dispersed darkish spots. The Semi Rijo limestone is white coloured, with thin grain and a very uniform background. It has some small darker spots throughout its surface and may have some slight signs of fossils. It is a soft natural stone and its main variations depend on the amount of darker spots, grain and signs of fossils. 3.1.3 The Marble The Estremoz Branco Extra (E.T.) marble is white coloured, with thin to medium grain and a very discreet bluish coloured vein. It is a fairly hard natural stone, and its main variations depend on the vein intensity as well as the type of white background and structure. 3.2 Physical and mechanical properties Samples were tested both wet and dry. The wet samples were soaked in water at 22 ˚C for a minimum of 48 h and a maximum of 120 h. The dry samples were dried prior to testing in a humidity-controlled oven at 65 ˚C and gradually cooled to 22 ˚C. The samples’ relevant physical characteristics, determined according to EN 13755 (CEN, 2008) and EN 1936 (CEN, 2007b), are shown in Table 1. The stones were tested in accordance with EN 1926 (CEN, 2007a) to determine their unconfined compressive strength Undercut anchorage in dimension stone cladding Camposinhos (UCS). Sixty cylindrical samples were tested in dried conditions. The test results are shown in Table 2. Flexural strength was determined with three-point load tests. These tests were carried out on 54 prism samples with a 50 mm 6 30 mm cross-section and on 54 slab samples with a 200 mm 6 30 mm cross-section in accordance with European Standard EN 12372 (CEN, 2006). Hence, the prism specimens had a total length of 200 mm and were placed on rollers with a 150 mm gap; the slabs had a total length of 400 mm and were placed on rollers with a 300 mm gap. The samples were tested in dried conditions with a gangsawn finish on the lower surface. The bending strength per stone type and the number of tests are shown in Table 3. The pull-out breaking load in undercut tests mobilises mainly the stone’s tensile strength. The tensile strength is a very important characteristic which governs the cracking and thus the rupture. Tensile strength is formally defined as the tensile stress required in order to cause a failure of an unconfined cylindrical or cubical stone specimen, divided by the cross-sectional area of the specimen perpendicular to the axis of loading. This is the direct tensile strength; because of the difficulties related to gripping the specimens, this is a very unusual test. Otherwise, the tensile strength can be found indirectly, that is by relying on another type of test. One of these indirect tensile strength methods is the so-called Brazilian test where a circular solid disc is compressed until failure across a diameter; tensile stresses perpendicular to that diameter plane are developed; as such, compressive loading machines are used in this test. In the Brazilian test a stone’s indirect tensile strength is generally defined as: 1. F sRt ~{ : : prt where F is the applied force at failure; r is the radius of the specimen (disc); and t is the thickness of the disc. Yet, it must be said that the above formula for determining the indirect tensile strength of stone, which has been extensively applied in rock engineering and research fields for more than 30 years, is erroneous when the disc has a significant thickness (Yu et al., 2006). Another simple procedure to obtain the indirect tensile strength is via flexural strength tests (Weibull, 1939). The flexural strength of a stone specimen is the maximum tensile stress when it is about to break. This stress is calculated based on the formula for linearly elastic bodies. Yet, what matters is 161 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Rock type Undercut anchorage in dimension stone cladding Camposinhos Stone identification (Figure 4) Water absorption: % (EN 13755) Volumic mass: kg/m3 (EN 1936) Open porosity: % (EN 1936) C.A. P.S. A.R. M.L. S.R. E.T. 0?3 0?4 0?7 2?4 8?0 0?1 2640 2610 2610 2540 2190 2710 0?7 0?8 1?8 6?3 19?1 0?3 Granite Limestone Marble Table 1. Water absorption, volumic mass and open porosity of the studied stones the tensile stress value instead of the flexural strength. It is known that the calculated maximum flexural stress is greater than the actual stress in the test specimen because, during the testing of a stone prism or slab under flexure, a number of factors operate to change the stress distribution in the specimen so as to reduce the maximum stress. It follows that the tensile strength of a stone in the conditions of a flexure test is higher than in direct testing under tension (Burshtein, 1967). The fact that flexural strength is physically greater than axial tension (according to Davidenkov (1947), and Frenkel and Kontorova (1943)) since, during flexure, the maximum tensile stress is experienced only by a filament on the convex surface of the specimen whereas during axial tension all points of the cross-section experience the maximum tensile stress. Based on the statistical theory, Weibull (1939) derived relations between the strength of a brittle material under flexure, sRf, and the axial tension, sRt, if data from specimens of different volumes are known. Thus, for pure flexure the following relation can be applied: 2. 1 sRt ~ ðsRf1 zsRf2 Þ:ð2mz2Þð{1=mÞ 2 Rock type Granite Limestone Marble Stone identification (Figure 4) UCS: MPa (average) Quantity C.A. P.S. A.R. M.L. S.R. E.T. 253 237 83 92 55 97 10 10 10 10 10 10 Table 2. Average unconfined compressive strength of stones studied as per EN 1926 For simple flexure 3. h ið{1=mÞ 1 sRt ~ ðsRf1 zsRf2 Þ:2ð{1=mÞ : ðmz1Þ2 2 where sRf1 and sRf2 are the flexural strengths of specimens with volumes v1 and v2, respectively. The value of m is given by the following formula: 4. m~ln v2 sRf1 : ln v1 sRf2 Considering the values from Table 3, the tested stone’s indirect tensile strength can be estimated by means of Equations 3 and 4. The results are shown in Table 4. 3.3 Undercut anchorage strength tests Axial tension tests were performed on the slab specimens with a nominal thickness, t, of 30 mm to evaluate the anchoring strength with Fischer type anchorages. Two external thread M6 or M8 cone bolts with carbon sleeves (see Figures 1 and 6) were used with a corresponding nominal diameter drill hole, wt, of 11 and 13 mm, respectively. The corresponding undercut diameters, wu, are of 13?5 and 15?5 mm, with a tolerance of 0?3 mm for both undercuts. All anchorage strength tests were performed with a digital pulloff strength tester with a 16 kN capacity (Figure 5). The pulloff tester is fitted with a load cell and a high resolution large digital display unit, thus being suitable for measurements with a resolution of 10 N. The direct tensile force is applied by rotating a hand wheel, through a seat ball which ensures axial and central load application. In order to limit tested slabs from bending along the unit’s three-foot span, they were positioned over a stiff steel plate with a 120 mm diameter circular hole with its centre aligned with the vertical axis of the load cell. The 250 mm 6 250 mm 162 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos Flexural strength (F.S.), coefficient of variation (c.v.) and number of tests (qty) Rock type Granite Limestone Marble Stone identification (Figure 4) Prisms flexural strength: MPa c.v.: % Qty Slabs flexural strength: MPa c.v.: % Qty C.A. P.S. A.R. M.L. S.R. E.T. 21?03 16?82 8?81 15?90 7?40 18?30 4?25 9?74 8?28 8?78 7?00 9?94 9 9 9 9 9 9 15?72 12?85 6?66 11?73 4?97 11?32 6?14 8?12 13?31 7?37 9?10 8?46 9 9 9 9 9 9 Table 3. Flexural strength of tested stones according to EN 12372 square steel plate was 12 mm thick and the 120 mm diameter centre hole was sufficiently large not to interfere with the pulloff resistance of the undercut anchorages. lead to a relevant discrepancy in the anchorages’ bearing capacities. 4. This procedure limited splitting of the specimens by bending, even though splitting occurred in a few cases and the consequent results were obviously rejected (Figure 6). Results Fifty pull-out tests with M6 cone bolts and 81 pull-out tests with M8 cone bolts were performed to determine the pullout load failure on the six stone types. The typical failure mode was brittle with a detaching radial cone shape and eventually, spall (Figure 7). The load was applied at a constant rate of approximately 0?02 kN/s and all specimens were tested after being kept in dry storage for over 1 week, without any additional wetting or drying procedures. The diameter of the cylindrical drill hole, wt, the anchorage depth, du and the slab thickness were measured before the load was applied. Cone bolt anchors of sizes M6 and M8 with external thread were used. The cone bolt and expansion ring were made of stainless steel and the sleeve was made of carbon. The anchors were placed in the undercut drill holes whose typical dimensions are shown in Table 5 according to Figure 3. It is worth pointing out that the difference in the geometry of the drills for M6 and M8 cone bolt threads is very small – a 2 mm variation for the diameter of the cylindrical drill hole, wt and for the diameter of the undercut, wu – and probably will not After a cone type failure, the medium length of the spalls and their thickness was measured in order to determine the average angle of the cone failure surface a as illustrated in Figure 8. The results for the M6 and M8 thread cone bolts are presented in Tables 6 and 7, respectively. Both tables also indicate the coefficients of variation (c.v.) of the breaking load and the spall angles. Flexural strength (F.S.) and estimated tensile strength (T.S.) (mean values) Rock type Granite Limestone Marble Stone identification (Figure 4) Prisms flexural strength: MPa Slabs flexural strength: MPa m (Equation 3) Indirect tensile strength: MPa (Equation 1) C.A. P.S. A.R. M.L. S.R. E.T. 21?033 16?824 8?810 15?900 7?396 18?300 15?720 12?850 6?662 11?730 4?967 11?320 6?946 8?495 7?037 6?946 5?290 4?311 9?16 8?05 3?88 6?88 2?71 5?81 Table 4. Flexural and indirect tensile strength of tested stone according to Equations 2 and 4 163 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos Figure 6. Splitting failure in a limestone slab and undercut anchorage cone bolt after split failure Substituting the value of the average spall angle, am, in Equation 5, the minimum edge distance, em, for anchorage depths of 15 mm will be given by: . Figure 5. Digital pull-off strength tester and stiff steel plate to deter bending of the specimens For the M8 cone bolts, since it was not possible to obtain samples of Estremoz marble from the same quarry and batch, there is no available data. which is in good agreement with the value recommend in the ETA document (Deutsches Institut für Bautechnik, 2009). With this minimum space between anchors, sm, may be derived: 6. A preliminary observation to the results reveals that the breaking load does not vary with the thread size for the same stone type, as was expected. For each stone type, a global appreciation of the breaking load values and the respective mean value is shown in the graph of Figure 9. The gross horizontal lines indicate the average of the breaking load values shown in Tables 6 and 7. It must be noted that the spall angles are very similar in all the tested specimens, even for the six stone types. The observed mean value for all stone types is of 18?1 ˚ with a coefficient of variation of 9?84%. These values are slightly inferior to the 20 ˚ value reported by Lammert and Hoigard (2007). The characteristic spall angle value (5% lower percentile), assuming a normal distribution, will be given by: 5. ak ~am :ð1{1:64|9:84%Þ&0:839am em ~15|cotð0:839|180 Þ&55 mm sm ~2hv :cotð0:839am Þ A suitable substitution in Equation 6 makes sm equal to 7?4hv, which is practically the same as the recommended value in the Fischer ETA document, 8du (Deutsches Institut für (Bautechnik, 2009). 4.1 Breaking load in the dowel hole comparison For the same stone types and batch, 10 samples of each type were used in tests designed to determine the breaking load at the dowel hole in terms of EN 13364 (CEN, 2002). The samples, measuring 200 mm 6 200 mm, were prepared from slabs with a nominal thickness of 30 mm. The holes were located 100 mm from either side, measured to the nearest 0?5 mm. The thickness of stone between the edge of the hole and the two sides was 12 mm, measured to the nearest 0?5 mm. The holes were 8 mm in diameter and 35 mm deep. The load was exerted in a direction perpendicular to the axis of the dowel at a maximum distance of 2 mm from the edge of the sample and using the system shown in Figure 10. 164 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 External thread gauge M6 M8 Undercut anchorage in dimension stone cladding Camposinhos wt: mm wu: mm du: mm z: mm 11 13 13?5 15?5 15 15 4 4 Table 5. Undercut drill geometry for M6 and M8 diameter thread applied to tested anchorages The dowel hole failure mode is characterised by a brittle detachment of a wedge. A sample, after being tested, is illustrated in Figure 11. found that the average anchorage capacity of undercut anchors was three times greater than that of the dowel hole. 4.2 Semi-empirical formulation The mean breaking load values at the dowel load are compared with the mean breaking load values with undercut anchorages for the six stone types. The results are shown in Figure 12. In this section, the undercut geometry and the pull-out test results were used to develop a formulation of the maximum tensile stress installed in the stone’s anchorage zone. The comparison is quite clear and, as expected, the anchorage capacity with undercut holes is much superior to the dowel hole at the slab’s edges. This fact has been already referred to by other authors (Camposinhos, 2009; Camposinhos and Camposinhos, 2009; Lammert and Hoigard, 2007; Stein, 2000). In the present case, the difference in percentage varied from 245% for C.A. granite to 78% for S.R. limestone. This difference increased with the stone’s tensile strength as revealed when compared with the breaking load values with the tensile strength values in Table 4. For the six studied types, it was Hence, the spalls created during the undercut cone bolt anchor tests were traced, digitised and the projected spall area calculated. By projecting the failure surface in a plane perpendicular to the cone axis and assuming a uniform distribution of the tensile strength over an equivalent circular idealised area according to Figure 13, it is possible to establish a relation based on the maximum principal stress theory (Rankine, Lamé) which is satisfactorily applicable to brittle or quasi-brittle materials, such as stone. The theory is based on limiting normal stress. Failure occurs when the normal stress reaches a specified upper limit. Failure is predicted when the principal stresses equal the ultimate strength of the material. The presence of cuts, grooves, holes, etc., modify stress distributions, which are obtained through elementary stress design formulas and are based on the members having a constant section or a section with a gradual contour change, so that localised high stresses occur and are measured by a stress concentration factor (Albrecht and Yamada, 1977; Pilkey and Pilkey, 2007). In this case, a stress concentration factor must be considered for the given geometry of the undercut drill hole. This factor, Ku, is defined by the ratio between the actual maximum stress, smax, and the medium stress, stm according to Figure 14, Ku is given by Equation 7 as follows: t du Figure 7. Typical cone mode failure in two tested specimens t Figure 8. Cone mode failure and spall angle a 165 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos Breaking load Stone identification C.A. P.S. A.R. M.L. S.R. E.T. Spall angle Number of tests F: kN c.v.: % a: ˚ c.v.: % t: mm wt: mm du: mm 5 5 7 8 5 20 10?26 7?71 3?86 5?64 2?34 4?92 2?80 4?83 8?92 22?24 3?70 8?02 17?79 19?94 15?44 18?62 19?12 15?14 12?4 15?0 9?6 19?7 14?0 13?4 31?8 30?9 32?9 29?7 28?5 30?7 10?9 10?9 10?9 10?9 10?9 10?8 15?2 15?2 15?3 15?3 15?3 15?3 Table 6. Number of tests for each stone type, breaking load and mean spall angle values and coefficient of variation with M6 thread cone bolt anchors 7. Ku ~ smax stm 10. In Figure 13, the area of the projected cone failure surface, Acf, is represented and may be given by: 8. h i Acf ^p ðhv : cot azðwu =2ÞÞ2 {ðwu =2Þ2
~p h2 : cot2 azhv :wu : cot a Ku ~
st : 2 : 2 p hv cot azhv :wu :cota Fu The chart in Figure 15 shows, for each stone type, the concentration factor value obtained from Equation 10 with the average values for Fu, a and hv taken from Table 6 and the diameter of the undercut wu from Table 5. The tensile strength values from Table 4 were substituted in Equation 10, respectively. v The breaking load Fu value may then be expressed as follows: 9. Fu ~ st : Acf Ku where hv is the maximum spall thickness equal to (du2z), see (Figures 3 and 13); st is the tensile strength of the stone; Acf is the area of the projected cone failure surface; and Ku is the stress concentration factor for the undercut. By substituting Equation 8 into Equation 9 and expressing the result for Ku, we obtain: Table 8 reveals that the same stone type showed no relevant differences in the concentration factor values, which leads to the conclusion that the thread size of the cone bolt anchors and the dimensions of the drilled hole do not affect the said values. The medium to gross grain granite (A.R.) shows a higher stress concentration factor and a smaller spall angle when compared with the other granites, namely the C.A. and P.S. granites. Similarly, but obviously for other reasons, the Estremoz marble, E.T., which has a large degree of recrystallisation has a smaller spall angle and a higher concentration factor in comparison with the noncrystalline stones such as M.L. and S.R. limestone. Breaking load Stone identification C.A. P.S. A.R. M.L. S.R. Spall angle Number of tests F: kN c.v.: % a: ˚ c.v.: % t: mm wt: mm du: mm 12 25 25 9 10 10?53 9?14 4?42 5?41 2?45 7?22 12?63 10?17 13?85 18?69 18?76 19?23 15?92 19?22 19?93 22?5 16?8 10?8 21?7 9?7 31?7 31?0 32?9 29?3 28?5 13?0 13?0 13?1 12?9 13?0 13?0 13?0 13?1 12?9 13?0 Table 7. Number of tests for each stone type, breaking load and medium spall angle values and coefficient of variation with M8 thread cone bolt anchors 166 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos 12.00 11.00 (C.A. 10.45 kN) 10.00 9.00 (P.S. 8.90 kN) 8.00 kN 7.00 6.00 (M.L. 5.52 kN) (E.T. 4.92 kN) 5.00 (A.R. 4.30 kN) 4.00 3.00 (S.R. 2.41 kN) 2.00 1.00 C.A. P.S. A.R. M.L. S.R. E.T. 0.00 Figure 9. Mean anchorage breaking load values per stone type with Fischerß cone bolt anchors 4.3 Finite-element stress calculation method A finite-element stress analysis was carried out to investigate stress distribution near the undercut and along the observed spall surface. The material properties used in the model were assumed to be linear-elastic, isotropic and homogeneous in behaviour, even though dimension stone, as a naturally occurring material, is often heterogeneous and anisotropic. However, the model was used to verify the induced stress state, namely the maximum principal stress for the observed pull-out loads. A three-dimensional computer model was generated using solid elements to investigate the stress distribution present in Figure 10. Testing rig and arrangement for breaking load at the dowel hole Figure 11. Specimen edge after the test according to EN 13364 167 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos 12.00 10.00 kN 8.00 6.00 4.00 2.00 0.00 Undercut anchorage dowell hole C.A. P.S. 10.45 3.03 8.90 2.67 A.R. 4.30 M.L. 5.52 1.36 1.76 S.R. E.T. 2.41 1.36 1.98 4.92 Figure 12. Breaking load values comparison – undercut cone bolt anchorage and at dowel hole the typical undercut anchorage configuration load tested by the author, as described above. Fu hv t hv cot u For this analysis, the eight-noded hexahedron element type was chosen. Although not relevant for this study, different values of the modulus of elasticity ranging from 40 000 to 60 000 MPa were used for each type of rock studied. A constant value of 0?3 for the Poisson ratio was considered adequate for all rock types. max tm Acf Figure 13. Spall configuration and detachment angle in slab Figure 14. Stress concentration factor as the relation between the actual maximum stress, smax and the medium stress stm 168 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos 10.00 9.00 8.00 7.00 Ku 6.00 5.00 4.00 3.00 2.00 1.00 0.00 C.A. P.S. A.R. M.L. S.R. E.T. 6 mm 4.92 4.69 7.16 6.75 5.62 8.96 8 mm 4.82 4.44 6.32 6.96 5.27 Figure 15. Stress concentration factor, Ku, for the six stone types studied with M6 and M8 cone bolt undercut anchorages For simplicity, the load was applied directly to the solid element nodes at the nodes in contact with the expansion ring of the cone bolt thread assuming full contact along the stone surface. In the finite-element model (FEM), the advantages of the symmetry are put to use. The computational model is taken as a volumetric structure modelled using isoparametric volumetric finite elements, of the eight-node brick type (Figure 16). Rigid supports were defined at all nodes according to the test setup. At the nodes belonging to the symmetry face, the degrees of freedom were blocked accordingly. Stone identification Fine to medium grain size granite Fine to medium grain size granite Medium to gross grain size granite Limestone Limestone Marble Concentration factor Spall angle a: ˚ C.A. P.S. A.R. M.L. S.R. E.T. M6 cone bolts M8 cone bolts Mean Ku 17?79 19?94 15?44 18?62 19?12 15?14 18?76 19?23 15?92 19?22 19?93 – 18?28 19?59 15?68 18?92 19?53 15?14 4?87 4?56 6?74 6?85 5?45 8?96 Table 8. Spall angles and stress concentration factors, mean values 169 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Undercut anchorage in dimension stone cladding Camposinhos 4 mm 30 mm 11 mm Construction Materials Volume 166 Issue CM3 mm 7. 3 60 Y mm Z X Figure 16. Finite-element mesh for a quarter-sample of the studied slab area Stress contour maps Fu = 10 454 N Figure 17. Three-dimensional stress maps for the C.A. granite breaking load equal to 10?45 kN and FEM calculated maximum tensile stress equal to 10?20 MPa 170 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Undercut anchorage in dimension stone cladding Camposinhos Nodal stresses were averaged from the stresses evaluated at the standard 2 6 2 6 2 Gauss integration points. is desirable to compare the values obtained through both methods, such that the stress value found in this manner may be compared with the semi-empirical formulation derived from Equation 10 as follows: Figures 16 and 17 show, respectively, a three-dimensional view of the geometry and a stress map, Figure 18 shows a two-dimensional section cut according to the calculated stone’s maximum principal tensile stresses. Stress concentrations are present in the vicinity of the hole and dissipate quickly, suggesting that anchorage failures are influenced by a non-uniform stress distribution over the failure surface. The direction of the maximum principal stresses located adjacent to the hole are approximately perpendicular to the failure surface observed in tests, meaning that failure initiates at this location, as was expected. One run for each breaking load value was performed with the corresponding value for the six different stone types as reported in Figure 9. 5. Discussion The universal availability of powerful, effective computational capabilities, usually based on the FEM, has altered the need for and the use of stress concentration factors. Nevertheless, it 11. st ~ : p Fu Ku
h2v :cot2 azhv :wu :cota A comparison between the maximum calculated tensile stress using the FEM method and the stone’s indirect tensile strength obtained via flexural tests is shown in Table 9. The stress values for both cases are also plotted in Figure 19. It must be emphasised that the difference in the stress values were 12?6% superior for granites and 12?0% inferior for the limestone and marble stone types. These stress value differences may be considered acceptable, considering the variations in the breaking load test results (Tables 6 and 7) and the stone’s flexural strength or its indirect tensile strength (Table 4). Nevertheless, note the unavoidable shortcomings of the finite-element modelling, in particular the geometry discretisation and material constitutive law. Fu = 4924 N Max stress contours Radial section cut Figure 18. Stress maps, two-dimensional view of a radial section cut of the drilled region for the E.T. marble’s breaking load equal to 4?92 kN and FEM calculated maximum tensile stress equal to 5?04 MPa 171 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Rock type Granite Limestone Marble Undercut anchorage in dimension stone cladding Camposinhos Stone identification Average breaking load values (Figure 9): kN Indirect tensile strength (Table 4): MPa FEM stress values: MPa C.A. P.S. A.R. M.L. S.R. E.T. 10?45 8?90 4?30 5?52 2?41 4?92 9?16 8?05 3?88 6?88 2?71 5?81 10?20 9?10 4?40 5?64 2?58 5?04 Table 9. Breaking loads, tensile strength and stress values from the FEM calculation of tested stone Finite-element method Tensile strength Semi-empirical (Equation 11) Cinzento Alpalhão (C.A.) 10.000 8.000 Estremoz (E.T.) 6.000 Pedras Salgadas (P.S.) 4.000 2.000 0.000 Amarelo Real (A.R.) Semi Rijo (S.R.) Moleanos (M.L.) Figure 19. Calculated stress with the FEM method and Equation 11 compared with tensile strength for the studied stone types (values in MPa) 172 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174. Construction Materials Volume 166 Issue CM3 Rock type Undercut anchorage in dimension stone cladding Camposinhos Stone identification Indirect tensile strength (Table 4): MPa Finite-element method stress calculated values: MPa Stress calculated values Equation 11: MPa C.A. P.S. A.R. M.L. S.R. E.T. 9?16 8?05 3?88 6?88 2?71 5?81 10?20 9?10 4?40 5?64 2?58 5?04 9?72 8?80 4?18 7?70 2?83 5?97 Granite Limestone Marble Table 10. Comparison between maximum stress from the FEM and Equation 11 with indirect tensile strength For the geometry of the undercut drill hole, hv, was regarded as equal to 11?3 mm and an average value of 14?5 mm was applied for wu. Using the FEM with linear-elastic material properties, together with the maximum principal stress failure criteria, has proven to be an appropriate design procedure for estimating the breaking load. To make use of Equation 11, the medium spall angles and stress concentration factors were taken from Table 8. Observation of the test results allows for some further conclusions. Table 10 shows the comparison between stresses calculated (i) using the FEM (ii), Equation 11 and (iii) the indirect tensile strength. (a) As for the semi-empirical approach in Equation 11, the calculated values appear to be conservative. On average they are 7?8% superior for the granites and 6?4% superior for the limestone and marble stone types, when compared with the indirect tensile strength. (b) (c) (d) (e) A plot of the three groups of stress values from Table 10 and per stone type is shown in Figure 19. 6. Conclusion This paper examined the relationships between material strength, anchorage strength and induced stress states for the undercut anchorage. The findings are based on a significant number of tests performed on six stone types, three granites, two limestones and one marble. The breaking load does not vary with the thread size for the same stone type. Anchorage embedment depth is directly related to the anchor’s tensile capacity. Based on the semi-empirical formulation for the same tensile strength, it can be shown that the greater the embedment depth the higher the load bearing capacity. Spall angle measurements made it possible to define a minimum space between anchors and distance to edges. For the studied specimens, it was found that the medium anchorage capacity of the undercut anchors is three times greater than that of the dowel anchorage type. Acknowledgements The author wishes to thank Dr Roland Unterweger for his support and the back-up provided by the Fischerwerke GmbH & Co. KG in supplying the hardware and the specimen undercutting drills. REFERENCES Anchorage failure can be described as inducing a cone-shaped spall. The projected area of the stone failure surface is of a somewhat circular shape. The average surface failure angle was found to be of approximately 18 ˚. The maximum principal stress theory is applied satisfactorily to a limiting normal stress. Failure occurs when the normal stress reaches a specified upper limit. Based on this assumption, and on the described failure area and angle, the breaking load value at the undercut hole can be estimated with sufficient accuracy based on the indirect tensile strength estimated from flexural strength tests. Albrecht P and Yamada K (1977) Rapid calculation of stress intensity factors. Journal of the Structural Division, ASCE 103(2): 377–389. 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Yu Y, Yin J and Zhong Z (2006) Shape effects in the Brazilian tensile strength test and a 3D FEM correction. International Journal of Rock Mechanics & Mining Sciences 43(4): 623–627. WHAT DO YOU THINK? To discuss this paper, please email up to 500 words to the editor at [email protected]. Your contribution will be forwarded to the author(s) for a reply and, if considered appropriate by the editorial panel, will be published as discussion in a future issue of the journal. Proceedings journals rely entirely on contributions sent in by civil engineering professionals, academics and students. Papers should be 2000–5000 words long (briefing papers should be 1000–2000 words long), with adequate illustrations and references. You can submit your paper online via www.icevirtuallibrary.com/content/journals, where you will also find detailed author guidelines. 174 Proceedings of the Institution of Civil Engineers - Construction Materials 2013.166:158-174.