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147 Page 4 of 17Regarding the fracture properties of E. globulus, theevaluation of Mode I fracture energy is detailed in [43]and [44] using Double Cantilever Beam (DCB)specimens (Fig. 1a). A mean value of the criticalstrain energy release rate GIc 0.77 N/mm wasderived from the resistance curves (R-curves) following the compliance-based beam method (CBBM) as adata reduction scheme. This method was also appliedto determine the critical strain energy release rate inMode II loading from end-notched flexure (ENF) tests(Fig. 1b), resulting in a mean value of GIIc 1.54 N/mm [45].Table 2 summarises the mean values of theseproperties that will be considered in the differentanalytical models to study the splitting behaviour of E.globulus.2.2 Splitting tests32 splitting tests were conducted on planed E. globulusspecimens of 29 9 116 mm2 cross-section, 580 mmlength and 500 mm span. This and similar crosssections are readily available in this species.Two series of three-point bending tests were carriedout on single and double dowel connections withdifferent arrangements of loaded edged distances (he):(a)A single steel dowel of d 16 mm diameter andof S355 quality placed in the middle of thebeam. Three he were evaluated: 2d ,3d and 4d (32 mm, 48 mm, and 64 mm)(Fig. 2a). The relative height of the connectionis sometimes simplified by the parameter a( he/h). The configurations mentioned correspond to a values of 0.27, 0.41 and 0.55,respectively (test data reported in the literaturehave shown that a values up to 0.7 may fail byFig. 1 a Double cantilever beam test; b end-notched flexure testMaterials and Structures (2022) 55:147(b)splitting [37], with the splitting check restrictedto a B 0.7 in the former German standard [28]).It should be noted that he 4d corresponds tothe minimum loaded edge distance set out inEurocode 5 [30], but there is always thepossibility of execution errors when drillingholes on site, which are particularly relevant instructures with small depth elements, such as theones studied here. Between seven and ninebeams were tested for each configuration.Two steel dowels in a row of d 16 mm indiameter and quality S355, spaced 3d (48 mm)apart between their centres and placed athe 4d (64 mm) as shown schematically inFig. 2b. Eight beams were tested with thislayout.The diameter of the steel dowels was chosen to besufficiently thick to prevent yielding. These wereloaded by two outer plates made of Eucalyptusglobulus with characteristics similar to those of thebeams (note that no embedment damage occurred inthe plates). A load cell of 50 kN maximum capacitywas used. The tests were carried out at a constantcross-head displacement rate of the test device,adjusted to reach failure in approximately 5 min(2 mm/min, 1 mm/min and 0.5 mm/min for he 4d,he 3d and he 2d layouts, respectively, in thesingle-dowel tests; 0.7 mm/min velocity in the double-dowel tests). During the loading process, theapplied load (P) and the displacement (d) wererecorded. For the latter, two Linear Variable Differential Transformer (LVDT) displacement sensors,Solartron AX/10/S, with 10 mm measurementrange and 20 mV/V/mm sensitivity, were used: onewas located on the middle bottom side of the specimenand the other at the top of the steel dowel.

Materials and Structures (2022) 55:147Page 5 of 17147Table 2 Number of specimens (n), mean value, and coefficient of variation (CoV) of the different properties of E. globulusGLR (N/mm2)n10Mean1926CoV (%)24ft,90 (N/mm2)GIc (N/mm)GIIc (N/mm)3613107.5160.77231.5428Fig. 2 Connection geometries: a Single-dowel; b double-dowel3 Analytical models studiedThe considered analytical fracture mechanics modelsfor the analysis of the splitting capacity of beamsloaded perpendicular to grain by connections areshown in Table 3. A comprehensive review of most ofthese approaches can be found in [35, 41]. Therefore,in this work, only a summary of these models will bepresented. Most of the models are related and appearas special cases of a general one, where the failure loadis determined for a linear elastic body loaded with asingle force, based on the energy balance approach[47] and the fracture mechanics compliance methodaccording to Eq. (1):sffiffiffiffiffiffiffiffiffi2GfPu ¼ dCðAÞð1ÞdAbeing A and C the crack area and the modelcompliance, respectively.The different analytical models in Table 3 arederived using Eq. (1) making certain assumptions onhow to calculate the compliance C(A), which leads to agood agreement with the experimental data. Theexternal load is assumed to act at a single point in themiddle of the beam. The parameters considered by themodels are both material and geometrical. The material properties are the fracture energy, Gf (GIc of theMode I loading in most models); the shear modulus ofelasticity, G; the longitudinal modulus of elasticity, E;and the tensile strength perpendicular to the grain, ft.The main geometric parameters are the width of thebeam, b; the height of the beam, h; the distance fromthe connector to the loaded edge of the beam, he; therelative height of the connection, a ( he/h); the shearcorrection factor, bs, which takes the value of 6/5 for arectangular cross-section according to ordinary beamtheory; the number of rows of dowels parallel to grain,n; and the connection width, ar.Jensen [34] formulated one of the most generalmodels as an extended version of the original Van derPut and Leijten model [33], which will be discussedbelow, but without any simplifying assumptions, suchas neglecting the normal forces in the cracked parts ofthe beam. The model was derived considering acracked beam structure modelled by beam elements,all rigidly connected. The failure load is given byEq. (2).Another model which appears as a special case ofthe model expressed by Eq. (2) was later proposed byJensen et al. [35], derived this time from consideringthat the part of the beam below the crack behaves like abeam with fixed ends, of length the crack and depth he.The expression is shown in Eq. (3), which would alsobe arrived at by assuming h ? ? for a finite value ofhe (i.e. a ? 0) in Eq. (2), that is, all beams except thebeam with depth he are assumed to be infinitely stiff.When only shear deformations are considered andthus bending deformations are neglected (i.e., finite G,

147 Page 6 of 17Materials and Structures (2022) 55:147Table 3 Analytical models for the analysis of the splitting capacity of beams loaded perpendicular to grain by connectionsReferenceAnalytical ModelJensen (2005a) [34]Pu ¼ 2bJensen et al. (2015) [35]Pu ¼ �ffiffiffiffiffiffi2GGf heEquation (2)23GEðhae Þ ð1 a3 Þþbs ð1 ��ffiEquation (3)2GGf he23GEðhae Þ þbsqffiffiffiffiffiffiffiffiffiffiffi2GGf hebs ; bs ¼ �ffiffiffiPu ¼ 2bC1 1 hehe ; C1 ¼ 53 �ffiffiffiffiffihePu ¼ 2bk 1 a3 fw fr ; k ¼ 53 GGfEquation (5)Jensen (2005b) [38]Pu ¼ cPu;LEFMEquation (7)Jensen et al. (2015) [35]Pu ¼ cPu;LEFMEquation (8)Franke and Quenneville (2011) [39]Pu ¼ GLarsen and Gustafsson (2001) [36]Van der Put and Leijten (2000) [33]Ballerini (2004) [37]Pu ¼ ��ffiPu;LEFM ¼ 2bC1 he ; C1 ¼ 53 GGf �ffiffiffiffi21þ1; 1 ¼ Cft1 10 GE h1ec ¼ �ffiffiffiffiPu;LEFM ¼ 2bC1 1 hehe ; C1 ¼ 53 �ffiffiffiffiffi21þ1C1c ¼ 1þ1 ; 1 ¼ ft 10 GE h1eb 103GI;normII;normGIc þ GIIc krEquation (4)Equation (6)Equation (9) 1 0:25GI;norm ¼ eðh ð200 10he h ar ÞÞGII;norm ¼ 0:05 þ 0:12 hhe þ 1 10 3 ar(1 for n ¼ 1kr ¼0:6 for n [ 10:1 þ ðarctanðnÞÞE ? ?), the ratio G/E ? 0 and Eq. (3) is reduced tothe form expressed in Eq. (4). This expression issimilar to the solution proposed by Larsen andGustafsson [36] when bs 1 is assumed.A renowned simple analytical model that forms thebasis for the design in Eurocode 5 [30] is the oneproposed by Van der Put and Leijten [33] expressed inEq. (5). Due to the similarity in behaviour, the sameprinciple was followed as in the mechanical fracturemodel for the splitting of beams with notches previously derived by Van der Put [32]. The expression isobtained by analysing the cracked state of a beamunder an energy balance approach when the joint loadis perpendicular to the grain near the loaded edge,using experimental results from the literature ascalibration. Although today it is still the model basisof the normative expression, it has been subject tosubsequent alterations and adjustments by differentresearchers. In this sense, the resulting expressioncould again be seen as a special case of the generalmodel presented in Eq. (2) neglecting bending deformations and taking into account only shear deformations (that is, G/E ? 0) and bs 6/5 for rectangularcross-section. In the cases where he/h ? 0, the van derPut model would lead back to the solution presented inEq. (4).Ballerini [37] proposed a semiempirical modelgiven by Eq. (6), in an effort to better fit theexperimental data than using the van der Put andLeijten formula for single-dowel connections. Thework also provides an approach for multiple-dowelconnections and is further elaborated with parametricnumerical analysis by Ballerini and Rizzi [48]. Itconsiders the influence of the connection width anddepth using correction functions applied to the singledowel formula. In particular, the correction factor toaccount for the influence of the width of the connection is fw 1 ? 0.75(lr ? l1/h) B 2.2, where lr is thespacing between the dowels and l1 is the distancebetween the dowel clusters (this correction function

Materials and Structures (2022) 55:147will be applied in the case of double dowel connections studied in the present work).Jensen postulated other analytical models based onthe beam-on-elastic foundation (BEF) [38]. In thiscase, the crack plane is modelled by springs to whichthe fracture properties are assigned. After cracking,the beam below the fictitious fracture layer is considered as a beam resting on elastic Wrinkler springsconnected to the upper part, which is assumed to beinfinitely rigid (foundation). For a single load actingfar from the end of the beam and small crack lengths,the failure load is given by Eq. (7), where c is theeffectiveness factor. Unlike the models mentionedabove, this expression includes the tensile strength ft inthe parameter f, and the splitting failure load is notproportional to the square root of the fracture energy.Therefore, solutions cannot be encompassed withineither linear elastic fracture mechanics (LEFM) ornonlinear fracture mechanics (NLEFM). They belongto quasi-nonlinear fracture mechanics, and LEFMsolutions are considered special cases.Assuming E ? ? or ft ? ? in the analyticalapproach of Eq. (7), the solution Pu Pu,LEFM wouldbe obtained. The same solution could also be derivedfrom Eq. (4) for bs 6/5, and from Eq. (5) when he/h ? 0. Therefore, it seems feasible to use, as Pu,LEFMin Eq. (7) the linear elastic fracture mechanics solutiongiven by Eq. (5). In this way, the analytical modelexpressed by Eq. (8) is obtained. When he/h ? 0,Eq. (8) leads to Eq. (7), and when E ? ? or ft ? ?it becomes Eq. (5). Equation (8) is therefore a semiempirical generalization of Eq. (7) that considers theeffect of the total beam height.Franke and Quenneville [39] presented a completeapproach based on a quadratic failure criterion inwhich fracture modes I and II for tension and shear areconsidered using the corresponding fracture energiesGI and GII. It should be noted that virtually all fracturesare, in fact, mixed-mode fractures, but the mixedmode ratio is not considered by the aforementionedcompliance method. As the GI of wood is usuallymuch lower than the GII, the GI is usually consideredin most splitting models as a conservative assumptionand reasonably accurate approximation, but themixed-mode fracture energy would represent the mostrealistic situation. The Franke and Quenneville formula also takes into account the width of theconnection and the number of rows of dowels, andthey found that the geometry of the connectionPage 7 of 17147influenced the ratio between fracture modes I and II.The design proposal is given by Eq. (9) as a result ofan experimental and numerical investigation by finiteelement analysis of more than 100 different connection arrangements.All of the above models are similarly acceptable from a modelling perspective. From a practicaldesign point of view, simple and robust models seemto be more attractive.4 Results and discussion4.1 Experimental failure loadsThe failure behaviour of the series of specimens withone and two dowels in a row and different distancesfrom the loaded edges subjected to splitting tests isherein presented.In the single-connection tests, a main crack couldalways be observed growing from both sides of thedowel (Fig. 3a). This crack developed at slightlydifferent positions, starting at the mid-down part of thedowel contact. The smaller the loaded edge distance,the faster the crack developed with respect to themaximum load capacity. In these test groups, the cracknever reached the ends of the beam.Some of the specimens with the largest loaded edgedistance (4d) showed embedding deformations underthe dowels, but no bending of the dowels, as well assome cracks with small lengths beside the dowel(Fig. 3b). The beams with 2d and 3d loaded edgedistances did not exhibit any significant embedmentunder the dowels. In any case, the brittle failure wasalways characterised by one main crack.Regarding the double-dowel tests, a similar crackgrowth process was observed as for the single-dowelbatches in the sense that just one main crack developedon both sides of the beams. However, in all tests, thecrack reached the beam ends, producing a completeseparation of the specimen into two parts with a verybrittle and sudden failure (Fig. 4a).No embedment deformations were observed underthe two dowels (Fig. 4b, unlike in the case of a singledowel for the same loaded edge distance (4d), as thebearing area increases with the two closely spaceddowels.These failure modes are well represented by thecorresponding load versus displacement curves

147 Page 8 of 17Materials and Structures (2022) 55:147Fig. 3 a Representative failure behaviour of single-dowel test series; b detail of the local failure around the dowel for the three loadededge distancesFig. 4 a Representative failure behaviour of the double-dowel test series; b detail of local failure around the dowelsmeasured at the top of the dowels. The results of thesingle-dowel splitting tests are shown in Fig. 5a,which reveal the different failure behaviour of theinvestigated connection arrangements.As can be seen, the load–displacement curvesobtained from the beams with the greatest edgedistance (4d) show a ductile behaviour characterisedby embedment stresses and yielding followed byhardening. The connection is still able to force asplitting failure after considerable slip, althoughsplitting is not the primary failure mode. On theFig. 5 Load–displacement curves. a Single-dowel splitting tests with 2d, 3d and 4d loaded edge distances; b double-dowel splittingtests with 4d loaded edge distance

Materials and Structures (2022) 55:147Page 9 of 17contrary, a brittle failure response is displayed forlower edge distances (3d and 2d).The load–displacement curves of the double-dowelsplitting tests with a 4d loaded edge distance areshown in Fig. 5b. In this case, a clear brittle behaviouris observed in all specimens for the a-value studied.Failure loads (Pu) achieved in all splitting tests forthe beams with single- and double-dowel arrangements as well as the mean value, the standarddeviation (SD) and the coefficient of variation (CoV)are compiled in Table 4.As can be seen from the results of the single-dowelbeams, the load-carrying capacity increases withincreasing loaded edge distance.The failure loads reached by the beams with twodowels are not necessarily twice as high as thoseachieved by the beams with a single dowel arrangement at the same loaded edge distance 4d (a 0.55),but the mean value is only slightly higher (21%higher). These results are in agreement with thoseobtained by Quenneville and Mohammad [49], whotested different connection arrangements on sprucepine glulam beams, including series of one and twofasteners spaced horizontally 5d apart, with a 0.6.The mean maximum loads in the case of doublefasteners were found to be 23% higher compared to thesingle connection. Previous experimental investigations by Reshke [50] for the same material and jointgeometry as specified for [49], also resulted in a smalldifference of approximately 14% higher failure loadTable 4 Failure loads fromthe single- and doubledowel splitting tests147for specimens with two dowels compared to those withone dowel.The fact that two closely spaced dowels givebasically the same splitting failure load as a singledowel was also stated by Kasim and Quenneville [51]using the concept of cluster (group) of fasteners. Intheir research, the capacity of two rows of boltsseparated 4d in the direction parallel to the grainturned out to be lower or statistically not different fromthat of one row of bolts on spruce glulam beams witha 0.44 and a 0.70. As the spacing of the rowsincreased, so did the splitting capacity of the connection. The two-row joint behaved almost as twoseparate single rows if the spacing between the rowswas C 2he (75% of twice the capacity of the one-rowconnection was obtained). The angle of load distribution from a bolt towards the loaded edge was estimatedto be 45 . In this regard, the former German code [28]limited to less than 0.5h the distance between groupsof fasteners in the direction parallel to the grain to beconsidered as one group. For distances C 2 h betweenthem, they are treated as separate groups. For distancesbetween 0.5h and 2h, the groups are considered as onegroup, but a reduction factor is applied. Quennevilleand Mohammad [49] stated that a connection can beassumed to be one cluster if the distance parallel to thegrain between the rows of bolts does not exceed he.The assumed angle of load distribution was 638 in thiscase.1 dowel2 dowelshe 2d 32 mmhe 3d 48 mmhe 4d 64 mmhe 4d 64 mmnamePu (kN)namePu (kN)namePu (kN)nameP

hardwood products, mainly glued laminated products [e.g., 2-4]. In this regard, Eucalyptus globulus Labill (also known as southern blue gum) stands out as a high-