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Jaaranen, Joonas; Fink, GerhardExperimental and numerical investigations of a timber-concrete dovetail splice joint

Published in:Journal of Building Engineering

DOI:10.1016/j.jobe.2021.103179

Published: 01/11/2021

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Published under the following license:CC BY

Please cite the original version:Jaaranen, J., & Fink, G. (2021). Experimental and numerical investigations of a timber-concrete dovetail splicejoint. Journal of Building Engineering, 43, [103179]. https://doi.org/10.1016/j.jobe.2021.103179

Journal of Building Engineering 43 (2021) 103179

Available online 26 August 20212352-7102/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Experimental and numerical investigations of a timber-concrete dovetail splice joint

Joonas Jaaranen *, Gerhard Fink Department of Civil Engineering, School of Engineering, Aalto University, Espoo, Finland

A R T I C L E I N F O

Keywords: Timber-concrete Dovetail joint Numerical modelling Experimental investigations Abaqus

A B S T R A C T

Cross-laminated timber panels offer an effective option for timber structures; they allow biaxial load transfer and have good dimensional stability. However, practical transportation and handling limits size of the panel and a stiff connection between the panels is required to effectively utilise biaxial properties. In this paper, a dovetail splice joint for timber panels is presented using cross-banded LVL with cast concrete grout interlayer. The interlayer allows a tight fit, which is important for stiffness, but also avoiding installation problems due to manufacturing tolerances and moisture-induced dimensional changes. The mechanical behaviour of the dovetail joint was investigated experimentally for various geometries. Furthermore, a numerical model was developed that shows a wide agreement with the experiments, especially in the cases with governing failure in the LVL. Using the numerical model, a parameter study was performed where the influence of the connection length (number of dovetails) and the joint geometry on the strength and stiffness properties was investigated. Besides the optimal geometrical configurations of the dovetail joint, also a significant increase of the strength and stiffness properties with increasing connection length was identified.

1. Introduction

Cross-laminated timber panels, such as cross-banded laminated veneer lumber (LVL) or cross-laminated timber (CLT), can be produced in large sizes, are characterised by a good dimensional stability and allow biaxial load transfer. However, although it is possible to manu-facture very large timber panels or splice them by gluing in the factory environment, on the construction sites the sizes are limited due to handling and transportation issues. Therefore, to utilise biaxial load transfer, adjacent panels need to be connected together with joints that have sufficient stiffness and strength.

Recently, there has been interest towards biaxial timber floors sys-tems that would utilise panels more efficiently or allow discretely sup-ported floors systems. In these studies, different options for in-plane panel connections for continuity have been studied. Zollig et al. [1] investigated the use of butt-jointing timber panel edges by two-component PU glue, reporting characteristic bending strengths up to 20 MPa. Loebus et al. [2] used glued-in reinforcement bars and cast-in-place concrete seam to connect together two CLT-panels for a timber-concrete composite (TCC) slab. According to their tests on the jointed slab, the bending stiffness was nearly equal and bending moment

resistance was around 80% compared to an intact slab. Maurer et al. [3] proposed an edge connection between CLT plates by synthetic reaction resin dovetails that are cast in the pre-made slots in the connected panels. However, no data on the joint performance was provided. Various generic edge to edge connections for CLT panels have been presented in [4] but only few of them are considered to have significant moment-resistant capacity. Asselstine et al. [5] investigated a moment-resisting CLT edge connection with splice plates on the tension side that were connected to the panels by inclined self-tapping screws. Kreis [6] presented a two-way timber-concrete composite plate with beech LVL, tube connectors and intermediate insulation layer to reduce the weight of the slab. Connections between the LVL panels were pro-vided by steel connector that were attached to the panels by glued-in rods and jointed on-site by bolts. In the vibration and bending tests, 43% increase in fundamental natural frequency and 34% decrease in the deflection was observed by comparing two-way plate and one-way plate.

In the study presented here, an alternative panel-to-panel connec-tion, a timber-concrete dovetail splice joint, is investigated. Aim has been to develop a joint that (i) allows axial in-plane load transfer be-tween panels, (ii) requires no metal parts or glues, (iii) its installation is not sensitive to manufacturing tolerances or dimensional changes of the

* Corresponding author. E-mail address: joonas.jaaranen@aalto.fi (J. Jaaranen).

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https://doi.org/10.1016/j.jobe.2021.103179 Received 31 May 2021; Received in revised form 2 August 2021; Accepted 21 August 2021

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panels due to moisture content variations, and (iv) has high stiffness and sufficient strength properties. The joint consists of a dovetail pattern cut to the connected panels and an interlayer that is cast after installation of the panels on-site to ensure tight fit. Basic concept of the joint is illus-trated schematically in Fig. 1.

This study considers application of the joint to the TCC slabs, where the timber panels are located in the bottom layer and are mainly loaded in tension. Therefore, focus is only in the in-plane tensile behaviour of the joint. The paper consists of experimental investigations of the dovetail joint including additional testing for relevant material proper-ties. Furthermore, a numerical model is developed and used to investi-gate effect of the joint length and different geometric parameters on its behaviour.

2. Materials & methods

2.1. Overview & materials

The experimental investigations contain two sets of tests; pretest and validation tests. The pretests included four dovetail joint specimens and were used for the initial development of a numerical model. Using the

numerical model, the influence of the joint geometry on the mechanical behaviour and the failure modes was investigated. For the validation of the numerical model, twelve specimens with the varying geometric parameters were chosen in order to observe different failure modes (validation tests). A summary of the specimens is shown in Table 1.

The dovetail joint consisted of two different materials: coniferous LVL and concrete grout. The LVL is a cross-banded product with nine parallel plies and two perpendicular plies. The nominal thickness of the LVL is 33 mm and the mean density is ρmean = 510 kg/m3. The LVL was stored in a climate room with temperature T = 20 ◦C and relative hu-midity RH = 65%. Different LVL batches were used for the pretest set and validation test set, but within both test sets, all the specimens were cut from one single panel. The concrete grout is a non-shrinking concrete grout filler with CEM II A 42,5 R cement and maximum aggregate size 4 mm. The strength class according to the [7] is C50/60-4. Mix ratio of the water and cement-aggregate dry mix was from 1:10.1 to 1:10.3 in all the manufactured specimens.

For consistent comparison of the experimental results and the nu-merical model, good estimates for the material properties are required. For the LVL used in this study, the manufacturer provides only generic properties regardless of the panel layup, only characteristic strengths are given and the properties have been determined on structural sized components. In this study however, the interest is in mean values of the local properties for this specific LVL thickness. Also, for the concrete grout, only minimum performance properties according to standard are reported by the manufacturer. Therefore, additional material tests were performed for both. The material tests consisted of compression, tension and shear tests for the LVL and compression and flexural tension tests for the concrete grout.

2.2. Specimens

The specimens consisted of two LVL panel pieces connected by a single dovetail joint with interlayer of concrete grout filler as shown in Fig. 2. The joint geometry was precut to the LVL parts with a CNC ma-chine and two layers of polyurethane acrylate lacquer were applied on

Fig. 1. Concept of the dovetail joint; (a) parts with the dovetail joint, (b) installation on-site and (c) dovetail joint with cast interlayer.

Table 1 Summary of the dovetail joint test samples and the test results. Orient. refers to the LVL grain orientation with respect to the loading direction, n is number of specimens, Sp. # is specimen number, and the geometries are according to Fig. 2.

Group n Orient. Geometry Test results

L [mm] B [mm] α [o] t1 [mm] t2 [mm] R1

[mm] R2

[mm] Sp. # K04 [kN/

mm] Fu

[kN] Failure type

Pretests (4 specimens) LVL0-P 2 0◦ 100 100 20 16 16 16 32 1 17.1 18.5 LVL shear

2 17.1 16.5 LVL shear LVL90-P 2 90◦ 100 100 20 16 16 16 32 1 21.0 5.9 LVL tens.

2 17.7 6.2 LVL tens. Validation tests (12 specimens) LVL0-1 2 0◦ 100 100 10 16 16 16 32 1 3.4 15.3 LVL shear

2 10.5 14.8 LVL shear LVL0-2 2 0◦ 100 100 30 16 16 16 32 1 14.2 14.9 LVL shear

2 15.6 15.6 LVL shear LVL0-3 2 0◦ 70 150 20 16 16 16 32 2 75.3 5.4 Conc. crack

2 59.5 4.5 Conc. crack LVL90-1 2 90◦ 100 100 10 16 16 16 32 1 13.1 9.3 LVL tens.

2 6.7 9.1 LVL tens. LVL90-2 2 90◦ 100 100 30 16 16 16 32 1 72.8 5.4 LVL tens.

2 81.3 6.0 LVL tens. LVL90-3 2 90◦ 70 150 20 16 16 16 32 1 6.3 8.0 Conc. crack

2 5.9 7.2 LVL tens.

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the contact surfaces to prevent moisture transport from the fresh con-crete grout to the wood.1 The surfaces were sanded lightly with P120 sanding paper between the applied lacquer layers. For casting, the LVL parts were fixed in horizontal position with correct interlayer gap and the grout was poured to fill the entire gap. After casting, the joints were covered with a plastic film to prevent evaporation of the moisture, and after one day, the specimens were stored in the climate room (T = 20 ◦C, RH = 65%) until testing. For the pretest specimens, speckle pattern was applied on one side in order to perform digital image correlation (DIC) measurements. All the specimens were tested when the age of the con-crete grout was between 28 and 31 days. Summary of different dovetail joint specimens is shown in Table 1. In the pretests, the specimens were connected to UTM via perforated steel plates, glued to a grooves at the ends of the specimen. In the validation tests however, to speed up manufacturing, the specimens were held by a steel parts clamped on the specimen (see Fig. 2b).

2.3. Test setup

The dovetail joint tests were performed in an universal testing ma-chine (UTM). Ideally, the tests would have been performed on long joints since the length affect the joint’s behaviour (see also Section 6), but testing joints with large number of dovetails was not practical due to size limitations, and instead, tests were done on a single dovetail while emulating the confinement from the adjacent dovetails by an external steel frame that restricts opening of the joint. The steel frame is referred here as restraining device and it consists of two steel parts, placed on both sides of the joint, connected by four tie-rods with load cell, which could be used to adjust the initial preload and monitor force in the restraining device.

The load protocol in the test was defined according standard EN 26891 [8]. For the pretests, the ultimate load was preliminarily esti-mated, and updated between the samples based on observed ultimate load Fu. In the validation tests, the initial estimate was kept even if it differed from the observed strength (standard requires update if the difference is larger than 20%) since the main objective was the com-parison with the finite element model prediction instead obtaining joint properties from the tests. Prior to test, a total preload Npre = 0.8 kN (equal tension force in all the tie-rods) was applied to the restraining device. A rather high load was selected in order to ensure good contact between the specimen and the restraining device and to prevent detachment of the device in any circumstance.

During all tests, the load F applied to the specimen, the relative displacement between the LVL parts u and the forces in the tie-rods of the restraining device was recorded. The relative displacement between the parts were measured by LVDTs, placed symmetrically on both sides of the specimen (see Fig. 2b). For the DIC measurements in the pretests, photos over the speckle pattern area were taken through the whole test (interval 3 s), with a camera placed normal to the surface. The images were post-processed in DIC software GOM Correlate [9] to obtain the strain measurements.

2.4. Material tests

The material tests were performed mainly in order to identify pa-rameters for the numerical model and they partially deviate from the test methods proposed in the standards.

2.4.1. LVL - compression tests Compression tests were performed according the procedure for

compressive testing parallel to the grain in EN 408 [10] with adapted specimen dimensions (b x h x l = 33 × 50 × 180 mm3). Although the test is intended for parallel to the grain testing, it was here utilised also perpendicular to the grain. The deformations during the test were

Fig. 2. Dovetail joint test setup and joint geometry.

1 If fresh concrete is in direct contact with wood, moisture transfer can lead to initial swelling and later shrinkage, which decreases tightness of the joint.

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measured by two LVDTs, placed on both sides of the specimen, with the gauge length h0 = 100 mm. A bilinear curve was fitted to the stress-strain curves for each specimen. The MOE, yield strength and plastic modulus were extracted from the fitted curve based on assumed linear elastic-linear hardening plastic behaviour. The fit was extended only up to strain of 1% in order to avoid including effects of global buckling of the specimens that was observed to occur during the tests. Cross-section area in the calculations was taken as the area measured prior to the test.

2.4.2. LVL - tension tests The tensile tests were performed parallel and perpendicular to the

grain using a simple dog-bone specimen shown in Fig. 3b. The test is not based on standards, however load rate was chosen so that the target time of failure is 300 s as in compression tests in EN 408 [10] for consistency. The LVL tensile strengths were calculated based on the ultimate loads and cross-section areas measured prior to the tests.

2.4.3. LVL - shear tests Shear properties of LVL in Europe are determined according to EN

408 [10] as required in EN 14374 [11]. However, the testing method was not considered suitable to determine local shear properties due to required fairly large size of the specimen. Alternatively, block shear specimens have been used to determine shear strength of clear wood in small scale. However, the method has been critiqued for not producing pure and uniform shear stress in the region of interest. Thus, other methods, such as Arcan shear test for wood, have been proposed with the aim producing more uniform shear and better prediction of the actual shear behaviour [12]. Although in other studies the method has been performed on solid wood, the method was adopted to this study assuming it is sufficiently accurate for estimate LVL shear properties for the numerical model. In [13], the method was used to determine shear stiffness of spruce clear wood by estimating the strain field around the notch tip by video extensometry. Similar test setup was adopted in this study except that the specimen was held in the device by clamping it between sand papers as in [14] instead of glueing the device on the sample and only monotonic load up to the failure was applied. The specimen and the test setup are shown in Fig. 3a. All the specimens were tested in parallel to the grain shear. The specimens had a point grid on the face surface and video of this face surface was recorded during the test for extracting strains after the test.

The strains were estimated from the video in Matlab over a 5 × 7 point grid (area 12.5 × 17.5 mm2) using the method described in [13]. In Matlab functions ‘nomrcorrx()’ [15] and ‘dftregistration()’ [16] (code provided by the first author in Github) were used to extract displace-ments of the points in each video frame relative the first frame. From the obtained point displacement, finite element interpolation procedure presented in [13] was used to estimate related average strains. The shear stress τ was calculated by the applied load and shear area at the notch tip with the actual dimensions measured prior to the test. The shear strength τmax was taken as maximum shear stress during the test and the shear stiffnesses were determined by fitting a line to stress-strain curve between 0.1τmax and 0.4τmax.

2.4.4. LVL - moisture content and density The moisture contents and densities of the LVL were determined

from the compression and shear test specimens by oven-dry method and measured dimensions.

2.4.5. Concrete Compressive strength and flexural tensile strength were determined

for each batch of concrete grout that was used to cast interlayers of the dovetail joint specimens according to the standard EN 196-1 [17]. The tests were performed at the age of 28 days. Additionally, stiffness of the concrete grout was determined from a separate concrete batch by testing three ø100 × 200 cylinders according to standard EN 12390-13 [18] at the age of 28 days.

3. Test results

3.1. Load-displacement behaviour

In Fig. 4, load-displacement plots from all tested dovetail joints are shown. In general, two different parts can be distinguished from the diagrams prior to the peak load, initial stiff region and following reduced stiffness region, although the distinction is not very clear in all the cases. In the initial region, it seems that the interfaces between LVL and concrete are completely bonded and no deformations occur in the interface, thus leading to observed high stiffness. After reaching certain load, the interfaces started to debond. At this stage visible gap opening, followed by slip in the diagonal interfaces between wood and concrete, are observed. Debonding can be sudden (accompanied by load drop in the graphs) or gradual (smooth transition in the graphs). However, in all cases, the interfaces were at least partly debonded during the test prior to ultimate load. In the test set LVL0-1, a discontinuous load-slip behaviour is observed after reaching approx. 10 kN. This was inter-preted as stick-slip behaviour in the slipping interfaces. Similar behav-iour was also observed in the friction tests [19] perpendicular to the grain under highest normal stress level with one set of samples. It should be also noted that distinct load-displacement behaviours are obtained from different geometries and the range for maximum displacement before the failure can vary from 1 mm up to almost up to 10 mm depending on the geometry and the grain orientation.

3.2. Failure behaviour

Observed failures are divided in to three different types; LVL shear failure, LVL tensile failure and concrete (interlayer) cracking failure. The failure types for each tested specimen are presented in Table 1 along with the corresponding ultimate loads. Photos of joint regions after the failure from the validation tests are shown in Fig. 5 for additional clarification. Each type of failure is accompanied with different post- peak behaviour as well. The shear failure leads to gradual softening after the peak load whereas the tensile failure is brittle, leading to im-mediate complete loss of stiffness. The cracking failure also has a sudden load drop when the cracks appear. However, the stiffness was not completely lost and the joint still carries load through remaining

Fig. 3. Material test samples with nominal dimensions: (a) shear test with the setup in the UTM below and (b) tensile test. The plain white surface of the sample is from the face side of the panel.

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stressed contact interfaces.

3.3. Digital image correlation

A detailed example of different stages during the test is illustrated in Fig. 6. It displays DIC measurements of maximum principal strains over the connection area at different load levels. It should be noted that high strains in the interfaces are actually gap openings and slips being interpreted as strains by the software. However, it appeared to be an effective way to identify mobilisation of different interfaces. First, hor-izontal interfaces between LVL and concrete start opening up, followed by mobilisation of the diagonal interfaces. At this stage, the load can be transferred only through the diagonal interfaces and the stiffness has clearly decreased. As the load increases, cracks form in the interlayer. However, no clear effect on the stiffness is seen. In the illustrated example, reaching the ultimate load was preceded by vertical shear cracks appearing in wood as well as additional cracking of the interlayer. It is hard to exactly specify mode of failure in this case, but it appears that after the shear cracks in the LVL, the load could not increase any further.

3.4. Material test results

Results from all the LVL as well as concrete material tests are sum-marized in Table 2. For additional illustration of the LVL behaviour, stress-strain curves with fitted lines for the compression and shear tests are shown in Fig. 7.

4. Numerical modelling

4.1. General

The dovetail joints were simulated in Abaqus [20] using a 2D model (see Fig. 8). The model consists of two LVL parts, a concrete interlayer and a support block, which represents the restraining device attached to the specimens. All parts were meshed with quadrilateral quadratic 8-node plane stress elements (CPS8).

Mesh density varies over the model, it is densest in the joint region and sparsest at the ends of the specimen. These mesh sizes were set to 1.5 mm and 16 mm, respectively. As shown, only half of the specimen is modelled due to symmetry. The contacts between LVL and concrete

Fig. 4. Load-displacement graphs from the dovetail joint tests and comparison with the numerical results.

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were modelled with the interface model [21] implemented as Abaqus user subroutine (UINTER) [20] with parameters based on tests in [19] with additional calibration based on the pretests. Linear interpolation was used to estimate the interface properties in directions that are different to parallel and perpendicular to the grain orientation. The linear interpolation was used due to simplicity, since no off-axis data of the properties were available to evaluate more advanced interpolation schemes. The interface model parameters related to cohesive shear strength were calibrated manually against the pretest results due to

observed differences between debonding loads in initial numerical model and experimental results. In addition, no test data for normal direction properties were available, so they were estimated initially and calibrated also. The simulation results with initial and calibrated pa-rameters are shown in Fig. 4 and the calibrated interface properties are presented in Table 3.

The LVL-to-steel (support block) contact was modelled using the built-in interface model with linear pressure-overclosure behaviour and Coulomb friction. The friction coefficient was set to μ = 0.4 and the same

Fig. 5. Comparison of experimental and simulated failure patterns (indicated by largest maximum principal strains in red in FEM). (For interpretation of the ref-erences to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 6. Maximum principal strains at different load levels determined by DIC from LVL0-P, specimen 2. Plot on the lower right corner shows corresponding location on the load-displacement graph.

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normal stiffnesses as between the LVL and concrete was used. Stiffness of the restraining device in the model, i.e. support block, is controlled by the linear elastic spring element between the support node and the block. The stiffness of the spring was estimated by combined measure-ment of connection rod stiffness and analytical calculations. The connection between the specimen and the UTM was not modelled in detail; instead loads are applied to the end of the specimen directly. This was justified by the distance between the joint and plates that is large enough to ensure that the load application method has no significant effect on the stresses around the joint.

The simulations were run under the same loading protocol as in the actual tests. However, direct force control was not possible due to decreasing branches in the load-displacement responses. Instead, the simulation was run under displacements control, defining turning points when the force reaches set values in the load protocol, using user- defined amplitude subroutine (UAMP) [20]. The predefined displace-ment is applied to a node on top edge of the model, coupled with rest of the top edge. The preload was applied in two steps; first preload Npre is applied to the support node in preload step and then the node is locked in place in the beginning of the load protocol step. The preload level Npre = 0.8 kN, corresponding to the preload in the experimental in-vestigations, was used.

4.2. LVL (material model)

Large variety of different material models for wood has been developed during the past decades, a comprehensive review on them can

be found in e.g. [22]. However, no model for cross-banded LVL espe-cially has been introduced. In [23], failure of plywood in compact ten-sion tests was simulated by modelling the plies individually using elastic material with continuum damage and interface between the plies by cohesive elements. Clouston and Lam [24] utilised layer-wise model with elasto-plastic material to stochastic strength modelling of angle-ply timber composites and found good agreement with the experimental data. However, adopting layer-wise models to the dovetail joint model would lead to additional complexity and obtaining material (and possibly glueline) parameters would require extensive testing. There-fore, LVL was modelled as a homogeneous material, allowing identifi-cation of the properties directly from tests on LVL and use of more common material modelling approaches. It is clear that this simplifica-tion neglects some aspects of the behaviour and cannot perfectly present material response, but it was assumed that it is possible to reach reasonable accuracy just with suitable choice of material properties.

The material model is formulated in terms of orthotropic linear elasticity (plane stress) combined with hardening plasticity to account compressive crushing and continuum damage to account brittle failure modes under tension and shear. The damage and plasticity are coupled by using similar damaged-plasticity formulation as in [25]; the plastic strains and damage are evaluated effective (undamaged) stress space and both are accounted when calculating the actual stresses.

The two brittle modes are (1) failure under tension parallel to the grain (crack across the grain) and (2) failure under combined tension perpendicular to the grain and shear (crack along the grain). Smeared crack approach was adopted and the effects are accounted by damaged

Table 2 Summary of the material test results, all parameter values in [MPa]. In the header, n presents number of measurements for each parameters, x is the sample mean and COV is the coefficient of variation. The LVL average moisture contents and densities were MC = 10.4%, ρ = 513 kg/m3 (pretest, compression samples) and MC =10.2%, ρ = 513 kg/m3 (validation test, compression and shear samples).

Parameter Symbol Pretests Validation tests

n x COV n x COV

LVL tensile test Tensile strength parallel to the grain ft1 – – – 15 45.4 0.15 Tensile strength perpendicular to the grain ft2 – – – 13 8.9 0.24 LVL compression test Compressive strength parallel to the grain fc1 6 36.6 0.03 12 36.4 0.08 Compressive MOE parallel to the grain E1 6 11180 0.07 12 11920 0.07 Compressive strength perpendicular to the grain fc2 6 9.2 0.07 12 8.3 0.08 Compressive MOE perpendicular to the grain E2 6 1720 0.16 12 2210 0.11 Compressive plastic modulus perpendicular to the grain Hc2 – – – 12 177 0.25 LVL shear test Shear strength fv – – – 14 4.7 0.12 Shear modulus G12 – – – 14 471 0.29 Concrete test Flexural tensile strength fct, fl 6 10.3 0.03 3+3a 13.5/12.9 0.04/0.01 Compressive strength fc 12 89.0 0.04 6+6a 80.6/82.4 0.02/0.05 Stabilised secant modulus Ec, s

b – – – 3 39400 0.01

a Two concrete batches. b Determined from a separate concrete batch according to EN 12390 [18].

Fig. 7. Stress-strain curves from the compression tests parallel to the grain (left), compression tests perpendicular to the grain (centre) and shear tests (right). In the plots for compression test, bilinear fit to data is presented. In the parallel to the grain tests, softening branch presented by dashed line involved localised kink band failures. In the shear test, estimated linear fit for shear stiffness estimate is displayed.

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stiffness matrix as in [22]. However, modified initiation criteria and damage evolution functions were utilised in this study. The initiation criteria for damage are defined as

⟨ϵe1⟩

ft1/E1= 1,

(⟨ϵe

2⟩ft2/E2

)2

+

(γ12

fv/G12

)2

= 1 (1)

where ϵe1, ϵe

2 and γ12 are elastic strain parallel to the grain, elastic strain perpendicular to the grain and total shear strain, respectively, and ⟨⟩ are Macaulay brackets defined as ⟨x⟩ = 0 if x < 0 and ⟨x⟩ = x otherwise. Evolution of damage is accounted by linear softening law where the complete failures in these two modes defined by linear fracture energy criteria:

GI,1

GIc,1= 1,

GI,2

GIc,2+

GII

GIIc= 1 (2)

where G is fracture energy, indices I, II refer to opening and shear modes in fracture, index c refers to critical fracture energy and indices 1, 2 refer

to failure modes 1 and 2. The model assumes stiffness recovery under compression, i.e. damage is accounted only for those axial stiffness components that are under tension. For shear stiffness, no recovery is assumed, i.e. damage is accounted regardless of the stress state.

The compressive failure is modelled by hardening plasticity, using a single surface quadratic yield criterion, requiring only uniaxial strengths and hardening moduli as material parameters. The yield surface is defined by (

−⟨ − σ1⟩fc1 + α1Hc1

)2

+

(−⟨ − σ2⟩

fc2 + α2Hc2

)2

= 1 (3)

where σ1 and σ2 are effective stresses, i.e. calculated using undamaged stiffness matrix. Hardening is controlled by accumulated compressive plastic strains α1 and α2 and compressive hardening moduli Hc1 and Hc2. The material model has been implemented in Abaqus as an user material subroutine (UMAT) [20]. The plastic calculations were done using the cutting-plane algorithm [26] and numerical differentiation was used for evaluating the tangent stiffness matrix.

The material properties for LVL (summarized in Table 4) were taken from the experimental investigations (see Section 3.4) or estimated based on the literature. In those cases where the elastic properties of the LVL plies are required for the estimation, Norway spruce properties in LT-plane from [27] were adopted.

Poisson’s ratio ν12 was estimated by homogenisation using the en-ergy equivalence approach presented in Ref. [28] using nominal di-mensions of the panel layup. The analysis yields Poisson’s ratio 0.095 which was rounded to ν12 = 0.1 for FEM analyses. Although LVL compressive tests showed post-peak softening behaviour parallel to the grain, small hardening was assumed parallel to the grain to avoid

Fig. 8. Dovetail joint model geometry, boundary conditions (BC), applied loads and contact conditions (left) and mesh (right).

Table 3 Interface model parameters for contact’s tangential direction parallel to grain (par.) and perpendicular to grain (per.).

Parameter Units par. perp.

KcN,t [MPa/mm] 35 35

KcN,c [MPa/mm] 0 0

KcT [MPa/mm] 13 27

σ0 [MPa] 0.3 0.1 τ0 [MPa] 2.0 0.6 GIc [J/m2] 15 15 GIIc [J/m2] 700 60 Kf

N [MPa/mm] 40 200

KfT,max [MPa/mm] 46 153

μs0 1.07 1.21 μk0 0.47 0.65 αs,r 0.52 0.57 αk,r 1.0 0.88 αmax [mm] 2.6 2.7 uc

T [mm] 1.9 2.1 p0 [MPa] 100 14 pref [MPa] 0.7 6.7

Note: initial compressive stiffness is equal to KcN,c + Kf

N

Table 4 LVL material properties used in the FE simulations.

Parameter Parameter

E1 11.2 GPa E2 2.2 GPa ν12 0.1 G12 0.5 GPa ft1 60 MPa fc1 36 MPa ft2 15 MPa fc2 8.5 MPa fv 5 MPa GIc,1 2300 J/m2

GIc,2 500 J/m2 GIIc 1000 J/m2

Hc1 0.001 GPa Hc2 0.2 GPa

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Journal of Building Engineering 43 (2021) 103179

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convergence issues, choosing Hc1 = 1 MPa for the simulations. Since the compressive stresses parallel to the grain remain well below the strength in the simulations, this choice is considered to have only minor effect on the results.

Fracture energies were estimated from properties of the wood ma-terial in the LVL. In the tensile modes, it is assumed that fracture energy depends only on the plies oriented parallel to the load, thus it is calcu-lated from the across the grain mode I fracture energy of the wood by weighting it by the relative number of plies orientated normal to the crack. Fracture energy of the wood was estimated by fracture toughness according to [29] assuming wood density ρ = 500 kg/m3 and trans-forming it to fracture energy (see e.g. [30]) based on the elastic prop-erties. After weighting, estimates GIc,1 = 2300 J/m2 and GIc,2 = 500 J/m2 were obtained. In the shear mode, all layers are assumed to contribute to the fracture energy, thus fracture energy equals that of the wood material. Mode II fracture energy of Norway spruce in LT-system (crack systems, see e.g. [31]) is about 1000 J/m2, based on collected values in [32], which was taken as the estimate for GIIc in the model.

The neck region of the dovetails (thinnest part of the dovetail, see Fig. 2), where the tensile failure occurs, is considerably smaller by volume compared to the tensile test specimens. Therefore, the strength values for the model were adjusted based on the Weibull weakest link theory [33]. Assuming 2-parameter Weibull distribution, the mean strengths of two uniformly stresses volumes V1 and V0 are related by [34].

fV1

fV0

=

(V0

V1

)k

(4)

where the shape parameter k needs to be determined experimentally. Here, the parameter was determined from the means and variances of the tensile strengths in material the tests. The shape parameters corre-sponding to tests parallel and perpendicular to the grain are k = 0.13 and k = 0.21, respectively. Volume in the tests was assumed to be equal to the straight part of the specimen, that is V0 = 71.3 cm3. As an estimate for the failure region in the neck of a dovetail, 10 mm long and 20 mm wide area was assumed, giving volume V1 = 6.6 cm3. Based on the calculation, values ft1 = 60 MPa and ft2 = 15 MPa were adopted for the FE analyses.

4.3. Concrete (material model)

The interlayer was modelled using a built-in concrete damaged plasticity material (CPD) model in Abaqus [20]. It combines isotropic damaged elasticity with isotropic tensile and compressive plasticity to present the inelastic behaviour of the material. In-depth investigation of the material model for the interlayer were outside the scope of this study and the choice was deemed sufficient for the model.

The concrete compressive strength is considerably higher than that of the LVL, thus compressive behaviour is almost linear within the stress range of interest. Therefore, a simple linear elastic-ideal plastic uniaxial compressive behaviour was defined, taking yield strength as fc = 80 MPa. The modulus of elasticity was taken from the test data (see Table 2), rounded up to Ec = 40 GPa, and the Poisson’s ratio was set to νc = 0.2 as recommended in [35].

In tension, the behaviour is assumed linear up to the tensile strength. The tensile strength was taken as fct = 5 MPa based on conversion from flexural strength fct,fl by [35] and consideration of increased brittleness due to high strength of the concrete. By comparison, it is close to tensile strength calculated from the compressive strength, 5.2 MPa, according to [35]. The softening was defined bilinear softening law [35] in terms of crack opening displacement, which depends on the tensile strength and fracture energy. The fracture energy was taken as GF = 100 J/m2 using the formulas in [35] and considering the increased brittleness due to the small aggregate size of this particular concrete. For the rest of parame-ters, default values suggested by the Abaqus manual [20] were used.

4.4. Mesh-sensitivity study

Mesh-sensitivity of the model was investigated by a convergence study with nine different minimum element sizes (dmin, joint region), and two different maximum element sizes (dmax, ends of the specimen). The minimum values were spaced logarithmically between 1 and 10 mm. The maximum values were 8 and 16 mm, and they were included to check whether meshing of the far regions from the joint has influence on the results. The study was performed on two specimen types, LVL0-P and LVL90-P, and the convergence was monitored by comparing stiffnesses K04 and strengths Fu, determined according to standard EN 26891 [8]. The meshing were performed using ‘advancing front’ algorithm. Three remarks were made: (1) full convergence is not reach within the element sizes (up to 6% variations in the results within mesh sizes dmin = 1.5–4 mm), (2) the results are insensitive to maximum element size dmax and (3) failure mode predictions were the same regardless of the mesh density. Most of the deviations are related to the initiation of the slip (affects K04) and damage propagation (affects Fu).

The convergence behaviour was also investigated with Abaqus meshing algorithm ‘medial axis’, and different element types, but none of them displayed clearly more consistent results.

Due to computational limitations, the simulations were performed on minimum and maximum element sizes 1.5 mm and 16 mm. Resolving the mesh-dependency completely would potentially need developing more advanced meshing strategies or use of non-local formulations for the material and interface models, which were out of the scope in this study.

5. Comparison of numerical and experimental results

The comparison between the experimental investigation and corre-sponding FE simulations is illustrated in Fig. 4 for load-displacements and Fig. 5 for the failure patterns. In Fig. 4, the pretests were included in order to display calibration of the interface model parameters. However, since the tensile or shear strengths were not determined for the pretest specimens, pretests cannot be used for validating accuracy of the model. Therefore, the comparison presented in this section con-centrates on the validation tests only.

In overall, a wide agreement between the experimental and simu-lated load-displacement behaviour was observed. The model is able to closely capture the load-displacement behaviour of the specimens although some discrepancies exist at the load level where the stiffness starts to decrease, i.e. slipping begins. The only larger deviation was observed for specimens LVL0-3 after slipping initiates. There, the model predict the failure after a significantly larger displacement, that is con-nected to the overestimation of the ultimate load. In the simulation, there remains a load path that allows the load to increase opposed to the tests where opening of cracks prevented further load increase. In the simulation, the failure is ultimately accompanied by damage and plastic strains in the LVL part, although not visible in the figure due to high cracking strains in the interlayer. Reason for the discrepancy might be that the concrete material model is not well suited for such an thin concrete layer or the selected parameters were not suitable. Trials with varying concrete material parameters and interface parameters were made but no clear improvement was obtained. Further studies on interlayer modelling should be done in the future.

Also, the comparison to the failure pattern shows the efficiency of the model. In specimens LVL0-1 and LVL0-2, a vertical shear crack in the dovetail, and in specimen LVL90-1 and LVL90-2, a tensile failure in the neck of the dovetail was observed and simulated. For the specimens LVL90-3 two different failure modes were observed: concrete cracking and tensile failure of the LVL. In the simulation, ultimate load was reached after cracking of interlayer combined with a shear crack in dovetail. In specimen LVL0-3 the simulation model predicts interface gap opening but in different locations than experimentally observed.

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6. Application of the numerical model

6.1. Length effect

The joint behaviour is length-dependent, i.e. the longer the joint, the higher the stiffness and strength per dovetail. The tests and the nu-merical simulations have been performed on a single joint with the restraining device that aims to emulate the confinement by the adjacent dovetails. Obviously, a single joint can not perfectly represent the behaviour of a long joint, and the preload, which has been applied purely for practical reasons, does not appear in a real-life joints. Therefore, the joint was simulated with varying number of dovetails without the restraining device to investigate effect of the length under practical conditions.

Two simulation models were utilised: finite length joint with varying number of dovetails N and theoretical infinitely long joint (Fig. 9). The infinitely long joint can be considered an upper bound solution for the long joints. The simulations were performed on the joint type LVL90-1 with uniform displacement load. Length of the sample was reduced to 400 mm and minimum element size was set to 3 mm to reduce computational time. No significant differences were detected in the re-sults compared to longer specimen and smaller element sizes.

Results of the simulations are shown in Fig. 9. Here, the joint displacement is defined in Eq. (5), where utot is total displacement, FFEM is load from the model, l is total length, E is elastic modulus in load direction and A is cross-section area of the modelled part.

ujoint = utot −FFEM⋅l

E⋅A(5)

The results show the length-dependency very clearly; with low number of dovetail the stiffness and strength are significantly lower and increase monotonically with increasing number of dovetails. With a single dovetail (N = 1), ultimate load is reached already at the initial debonding. The load-displacement curves with increasing N seem to converge towards the theoretical upper bound, although it is not reached within the simulated number of dovetails. It is clear that for the effective application of the joint, it should have sufficient length. However, no recommendations for required length are given since the length-dependency might depend considerably on the materials, joint geometry and loading conditions.

6.2. Parameter study

The model was used to study effects of the geometric parameters on the strength and stiffness. The study was conducted only for the joint loaded perpendicular to the grain, since joining panels parallel to the grain has a limited practical interest. The number of possible parameter combinations is vast, making it unpractical to cover the whole design space or illustrate the results in a convenient manner. Therefore, only dovetail the width (B) and inclination angle (α), which were considered the most influential parameters, were varied and the other parameters were same as in specimen LVL90-1. The model with infinitely long joint was used for the simulations with the minimum mesh size 1.5 mm. The range for α was set between 2.5◦ and 32.5◦. The upper bound for B was chosen as 160 mm. The lower bound constraints for B were set so that dovetail neck width is ≥ 10 mm and any other physical dimension must be positive. In total 313 points, scattered uniformly over the parametric range, were evaluated, and joint stiffnesses K04 and strengths Fu were calculated according to standard EN 26891 [8]. Due to some noise in the results, especially in the strength values, they were smoothed over the parametric range using Matlab [15] curve fitting toolbox with locally weighted regression using option ‘loess’. The results are presented in Fig. 10 with the constraints and maximum values. As seen, the most effective solution is obtained at fairly low inclination angle α, less than 10◦, but the value of B depends on whether the maximum strength or stiffness is required. For the strength, a lower angle is more effective as the width of the dovetail neck is larger. For the stiffness, the optimum is at the lower bound which is purely due to the parametrisation and choice of the other parameters. E.g. decreasing the radii R1 and R2 would allow lower values of B and potentially higher maximum stiffness.

The stiffness Kmax = 196 kN/mm/m can be considered relatively high value, allowing significant biaxial behaviour as long as spacing of the joint in the structure is large enough. The MOE of the base material (LVL perpendicular to the grain) is E2 = 2.2 GPa. Assuming spacing s between the joints, equivalent reduced MOE of the panel layer, which accounts the additional deformation due to the connection, is calculated by

E2,red =

(1E2

+t

sKjoint

)−1

(6)

where t is thickness of the panel. As an example, if there are joints with 2 m spacing (stiffness Kmax), the reduced MOE is E2,red = 1.86 GPa, which

Fig. 9. On the left: models for simulating long dovetail joints with the corresponding boundary conditions on the edges. On the right: load-displacement plots for simulated long joints with varying number of dovetails (N) and infinitely long joint (N = ∞).

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Journal of Building Engineering 43 (2021) 103179

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only 16% less than the MOE of the panel. Comparing the maximum tensile strength from the parametric study Rmax = 115 kN/m and tensile strength of the panel Rt2 = tft2 = 495 kN/m, the strength of the connection is approx. 23% of the strength of the base material. However, design of the flat plates is usually governed by serviceability limit state criteria and the strength may be multitudes of higher than the ultimate limit state loads. Therefore, low strength of the joint may not require increasing in the plate cross-section in general. It is likely, that further improvements on the strength and stiffness can be obtained by optimi-sation over the other parameters as well, since only a small fraction of the design space is covered in the here presented parametric study. However, as seen, the maximum stiffness and strength do not coincide in the parameter space. Therefore, multi-objective optimisation is required to control the trade-off between the strength and stiffness.

7. Conclusion

In this paper, a novel dovetail splice joint for in-plane connection of biaxial timber panels, such as plywood, cross-banded laminated veneer lumber (LVL) and cross-laminated timber (CLT), is presented. Tight fit of the joint, which is important for stiffness, is provided by an interlayer that is cast on-site, avoiding problems with manufacturing tolerances and moisture-induced dimensional changes. Behaviour of the joint have been investigated experimentally on joints made with cross-banded LVL and concrete grout interlayer, accompanied by additional material testing. The test results were used to develop and validate a numerical model to simulate behaviour of the joint. In overall, a good agreement with experimental and numerical results was obtained. However, failure due to cracking of the interlayer was not correctly captured, leading to discrepancies that should be given more attention in the future. In addition, the simulation results involved mesh-dependency that could not be completely avoided with the meshing and element sizes used in the study. Nevertheless, it is shown that it is possible to simulate com-plex behaviour of the dovetail splice joint, involving multiple materials and contacts, to a good degree.

As a case study, the model is used to simulate behaviour of a long joint with varying lengths. The results show a strong length-dependency of the joint; strength and stiffness, normalised for a single dovetail, in-crease along with increasing length of the joint. Therefore, it is concluded that this kind of joints needs have sufficient length for good performance. However, no specific recommendation of the length are given since the behaviour is affected multiple aspects like used mate-rials, joint geometry and load conditions.

The primary intended application is in timber-concrete composite slabs, where concrete is a natural option for the interlayer fill. Most efficient the joint would be in large structures, in which the interlayer

width can be large enough so that joint gets filled simultaneously when the concrete slab is cast. However, any other castable material, able to fill the gap, and having adequate stiffness and strength after hardening, could be used. For adequate performance, the joint should be used with cross-layered panels, like CLT, plywood and cross-banded LVL, whereas unidirectional panels lack transverse stiffness and strength required for biaxial behaviour.

As a follow-up, experimental investigations on two-way timber- concrete composite plates and transverse plate strip with the dovetail splice joints are on-going. The aim is to further investigate the behaviour of the joint and effect on the structural performance in the large scale structures.

Credit author statement

Joonas Jaaranen: Conceptualization, Writing – Original Draft, Writing – Review and Editing, Methodology, Investigations, Formal Analysis, Software, Visualization, Project Administration; Gerhard Fink: Conceptualization, Writing – Review and Editing, Project Administration, Funding Acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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