Introduction

Historical and contemporary timber constructions are often damaged by biotic factors—wood-destroying insects and fungi. For their reconstruction, it is necessary to locate degraded parts to prepare the reconstruction plan. Recently, a few guidelines and methodologies for timber constructions inspection have been published, supported by several international committees such as RILEM, COST E55, COST IE0601 (Kasal and Tannert 2011; Cruz et al. 2015; Dietsch and Köhler 2010). The fundamental and commonly used diagnostic method is a visual inspection that provides general information and certain qualitative data about surfaces of inspected structure (Calderoni et al. 2010; Piazza and Riggio 2008). Nonetheless, the visual inspection cannot provide information about inner structure of timber elements nor determine any design values such as strength class (Machado 2013).

For the inspection of inner faults inside the wood in construction, semi-destructive methods (MDT) are primarily used to determine mechanical characteristics of wood. One of the most used methods is the resistography which is based on measuring the energy that is necessary for inputting the drilling pin through the wood. The diameter of the drilling pin ranges between 1.5 and 3 mm, and the whole measurement process is stored on an electronic memory or printed to the paper tape (Rinn et al. 1996). The drilling resistance strongly correlates to the wood density, so the statistically different values may indicate various levels of inner damage (Kasal and Tannert 2011; Reinprecht and Šupina 2015). Similar instruments are also used for testing of inorganic materials such as stones and mortars (Tiano et al. 2000).

Another approach to examine wood behavior and its properties is an instrument that measures fracture bending strength and strength in compression parallel to fibers—fractometer (Bethge et al. 1996). The measurement is carried out on drilled radial specimens of 5 mm diameter. Their strength is substantially dependent on loading direction in respect to fiber orientation. Because of its construction, the fractometer is easy to use and delivers very quick information. The same samples as used by fractometer can also be tested in the laboratory using special jaws mounted to standard universal testing machines (Kasal et al. 2003; Drdácký et al. 2005). Radially drilled specimens can then be used to determine more properties than in situ, such as density using microdensitometry (Bergsten et al. 2001), moisture content (MC), elastic modulus and compression strength parallel to fibers.

Disadvantages of techniques commonly used stem from the fact that their results correlate better with physical properties such as density than mechanical ones (strength or stiffness). Moreover, it is often needed to make samples in situ and test them in a laboratory, which increases both time and financial means. Accuracy of determination of the mechanical properties determines the ways of reconstruction design. In case the structural engineer has exact information about strength and stiffness of the particular construction members, it enables to preserve the majority of historical timber, which is one of the goals in preservation of culture heritage.

The global aim of this work was initiated by rapidly increasing requirements of structural engineers who assess mainly historical timber constructions in the Czech Republic and call for accurate and fast (in situ) determination of mechanical properties of structural timber elements. For that reason, the new semi-destructive device was developed and successfully tested on historical wood in a previous study by the authors (Kloiber et al. 2015a, b). The specific objectives of this work are: (a) to test newly developed semi-destructive instrument for in situ measurement of mechanical properties on recent timber; (b) to determine the conventional strength and modulus of deformability; (c) to verify the instrument data based on compression tests in the laboratory providing the strength and stiffness parallel to fiber; and (d) to perform probabilistic contact finite element (FE) analyses that examine the correlations between measured outputs and properties of wood simulating the instrument function.

Materials and methodology

Description of the new device

The device (Fig. 1 left) is designed to measure mechanical properties of wood by semi-destructive investigation of its behavior when loaded by a small-size jack inserted in a pre-drilled hole. The device can be used both in a laboratory and in the field to determine the condition and quality of timber. The device provides the dependence of deformation on the tension (Fig. 1 right) brought about by pressing symmetrically placed jaws apart in a pre-drilled radial hole with 12 mm in diameter.

Fig. 1
figure 1

Left—overall view of the newly designed device, right—detail of the drawbar with the wedge and rounded jaws

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The device is laid on the tested sample by means of a cylindrical shell, which allows measuring in four positions of the pre-drilled hole. The maximal absolute deformation that can be reached on both sides is 1.5 mm. The rounded jaws are 5 mm wide and 20 mm long. The jaws also include flexible arms whose movement during pushing is provided by a push-apart bronze wedge fitted to the lower end of the drawbar by means of a pin and screw. The apex angle of the wedge is 15°. This angle is not self-locking, and to release the jaws, it is sufficient to release the push-apart force (Drdácký and Kloiber 2013). The force of the drawbar drawing is continually recorded. It is calibrated to the real force of the loading jack and simultaneously related to the measured distance of movement of the jaws (Fig. 2 left). The signals are wireless transmitted to a portable computer where they are processed. More information about the device can be found in Kloiber et al. (2015b).

Fig. 2
figure 2

Left—example of the device output: a record of the force needed to push the jaws apart in relation to the measured shift (displacement) of the jaws; right—detail of the device for pin pushing

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Other devices used

Other semi-destructive methods used were the measuring of mechanical resistance of wood against microdrilling and measuring of mechanical resistance of wood against pin penetration (Fig. 2 right). Microdrilling was carried out using Resistograph that examines the resistance of the material against the penetration of a small borer with 1.5–3.0 mm in diameter. Because the Resistograph is well known, the readers are referred to important literature such as Rinn (1994), Rinn et al. (1996) and Drdácký et al. (2006).

The second technique used was measurement of resistance against gradual penetration of an object—a pin (Fig. 2 right)—to a depth relevant for the examined dimensions. The method is based on continuous monitoring and recording of the power related to the measured depth of pin pushing (Kloiber et al. 2012). The device is important for the study because it retains the character of a loading test. The output of measuring provides information on the development of the force necessary for pin pushing. Based on the size of the resistance force, the mechanical resistance of the material can be established. Detailed information about the construction of this device and comparison with destructive timber testing can be found in Kloiber et al. (2014).

Experiment

The verification of the prediction of mechanical properties through measuring by semi-destructive devices was carried out by measurement of sixteen 8-m-long beams made of Norway spruce (Picea abies L. Karst.), commonly used in historical constructions in the Czech Republic. The cross section of the beam was 200 × 240 mm2. After gradual drying of all sixteen beams and their conditioning to 12% moisture content, holes were made by a borer with 12 mm in diameter. Two holes were made in each beam. The boring was done in purely radial direction, and the distance between the holes was 100 mm. The depth of the boring was about 130 mm, which enabled to perform the measurement using the jaw pushing apart in the hole in four layers: layer 1 (5–25 mm), layer 2 (35–55 mm), layer 3 (65–85 mm) and layer 4 (95–115 mm) The measuring part of the device was then inserted into the radial hole, and the device was laid on the tested piece of timber using a cylindrical shell. The jaws were pushed apart parallel to the grain. The prints of the measurement are shown in Fig. 2 left. In total, 128 positions (16 beams, always 2 holes) were measured using the newly constructed device.

Mechanical properties of wood in the holes were determined using measured data—modified form of a stress–strain diagram (Fig. 2 left). Axis x represents the displacement of the jaws; axis y shows the force necessary for inducing displacement of jaws in drilled hole. The maximum force (F max) in Fig. 2—yield point, was established from the intersection of tangents of the elastic and the plastic parts of the stress–strain diagram. Conventional compressive strength (CS C(L)) was determined from the proportion of the ultimate load and the area of the pushed jaws. The modulus of elasticity cannot be calculated directly from the diagram and, hence, the modulus of deformability was established instead using the angle of the curve fit through the linear part of the force record and deformation. In the places adjacent to the bored holes, measurements were performed using the device for pin pushing (pin with 2.5 mm in diameter, 120 mm long). Measured basic characteristics were: work (S) as the area below the curve (N mm) of the force record in dependence of pin displacement, length (L) (mm), time of pin displacement (s) and the maximum and minimum force (N). To assess the mechanical resistance of timber against pin pushing, the average force (F AVG) (N) was used, calculated as the quotient of work (S) and length of displacement L, which best correlates with mechanical properties (Tippner et al. 2011). The Resistograph 2450p recorded the amount of energy needed to keep constant drilling speed. The output—energy consumption or the relative resistance—was evaluated explicitly in order to compare it with physical and mechanical properties. Therefore, a script was designed in MATLAB to calculate a parameter marked as resistance measure RM (Bits), i.e., a resistance value that corresponds to the area below the curve divided by the length of the measured section (Lear et al. 2011).

The function of the semi-destructive devices was verified using standard destructive experiments carried out on the universal testing device Zwick Z050. The results were processed by TestXpert v 11.01. The basic parameters included in the analysis for device verification were: wood density (Density), wood strength in compression parallel to the grain (S C(L)) and the modulus of elasticity in compression parallel to the grain (MOE C(L)). The standard tests were performed in compliance with European regulations using 20 × 20 × 30 mm3 samples taken at individual positions adjacent to places measured by the semi-destructive devices. The samples were made from wood 50 mm aside the drilled holes. Two samples with dimensions of 20 × 20 × 30 mm3 (compression parallel to the grain) were made for each place of measurement by the examined device. The data were further processed in Statistica 10.0 (survey analysis of data, verification of distribution normality, independence of elements of the selection, correlation analysis, linear and nonlinear regressions).

FE modeling

The finite element analysis was used to predict the behavior of the device and to find out the sensitivity of measured outputs to common factors. This was achieved by using probabilistic analyses to describe the influence of grain declination and properties of materials on obtained reaction force. The influence of the bottom of a hole on reaction forces in the case of measuring near the bottom was analyzed as well. The 3D FE model was made in ANSYS Mechanical APDL 14.5 software by using the Ansys Parametric Design Language. The final unsymmetrical geometry model consists of the wood specimen (cube 50 × 50 × 25 mm3) with a hole of 12 mm diameter and the jaws simplified to prismatic deformable bars. The FE model uses a regular sweep mesh with quadratic hexahedral solid elements (SOLID186) in all domains. The interaction between jaws and wood was defined by symmetric contact pairs using contact (CONTA 174) and target (TARGE170) elements on the surfaces. Material model of specimen was based on the elastic orthotropic properties of Norway spruce with respect to literature data (derived ratios of constants) and the experimentally obtained density and MOE C(L). The material of jaws is considered as elastic isotropic steel (E = 210 GPa, μ = 0.3). Boundary conditions were applied as displacements on back sides of the moving jaws and boundary areas of wood specimen as well. Nonlinear large displacement contact analysis was performed to compute displacements, strains, stresses and reaction forces in 50 sub-steps of load step with the jaws imprint. Parametric definition of model allowed testing the influence of 5% change of grain declination (in all three possible directions, in practice slight turning of the device in the hole, drilling in non-radial direction) on reaction forces, comparison of measurement in different depth of a hole. Further, the ANSYS Probabilistic Design System was used to describe correlation between all moduli of elasticity and reaction forces. Randomizing by Monte Carlo method was used in probabilistic analysis; input range of parameters was defined with Gaussian distribution by average value of parameter and standard deviation (matches coefficient of variance 0.15 in all cases, which corresponds to common variability of mechanical properties of wood). The analysis consisted of 300 cycles.

Results and analysis

Figure 3 illustrates the distribution of displacement (left) and strains (right) in longitudinal slices of the FE model for the measurement near the bottom of the hole. Despite the small contact area of jaws, there is a large theoretical area of impacted material, which suggests a good potential for estimation of non-local properties. Common measurement at a distance of 5 mm above the hole bottom gives unbiased results of reaction forces.

Fig. 3
figure 3

Displacements in the direction of applied forces for the longitudinal slices of FE model for the measurement near the hole bottom (left) and measurement in a high position (right)

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Table 1 shows Spearman rank correlation coefficients between input parameters retrieved by probabilistic FE analysis and output reaction forces. For the values closer to zero, the two variables are weakly correlated; for the values closer to 1, the two variables are highly correlated. Table 1 shows only results for the reaction force in the direction of loading. Reactions in other directions were small: The direction of hole axis is about 0.2% of reaction force in loading direction, and reactions in tangential direction of tested material are slightly higher (about 1%) but still negligible. The values of coefficients of correlations show strong influence of longitudinal modulus of elasticity (R = 0.96). A weak correlation was found for all other parameters. Negligible influence was also described for modulus of elasticity of the jaw material—steel. In practical conclusion: 15% change in material properties causes changes of reaction forces only in the case of longitudinal elastic modulus and other material properties have no effect; 5% change of grain declination caused by turning of the device in the hole or drilling in non-radial direction has also no effect on reaction forces (on the force-based outputs from measurement, respectively). Presented linear analysis was not able to describe all necessary behaviors of the process due the high plasticity of real imprint of jaws to wood. The FE model including plasticity phenomena with description of influence on conventional strength will be subject of further research.

Table 1 Correlation coefficients from sensitivity FE analysis—F R (as reaction force) versus E L, E R, E T (as normal moduli of elasticity), G RT, G LT, G RL (as shear moduli of elasticity), A L (declination in longitudinal direction or turning of device in hole), A T, A R (declination in tangential and radial direction or deviation of hole axis from radial direction)
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Experimental values of the 16 beams (strength in compression parallel to the grain, conventional compressive strength, modulus of elasticity parallel to the grain, modulus of deformability) are presented in Figs. 4, 5 and 6. The analysis results prove statistically significant differences between the beams. Mainly beams 2, 9, 17 manifested considerably higher measured properties of wood than the other beams. Considerably lower measured properties than is common in spruce wood were found in beams 4 and 5. The progress of the values of strength in compression parallel to the grain S C(L) corresponds to the progress of the values of conventional compressive strength CS C(L). Similarly, there is a very good correspondence between values of MOE C(L) and MOD C(L) of all measured beams. Influence of material stiffness (longitudinal elastic modulus) and computed reaction force in relation to displacement was also revealed by sensitivity FE analysis (very strong correlation). The absolute differences between values of the parameters measured on testing specimens and values obtained from the new device could also be explained by sensitivity analysis. The influence of other parameters cannot be neglected in the complicated mode of jaws’ imprint into wood (see correlation coefficients from PDS analyses above). The higher values of properties from “imprint” method probably correspond to high stiffness of material. The similarities between data distributions of standard tests and output parameters were also recorded by the other two semi-destructive devices.

Fig. 4
figure 4

Left—dependence of density and CS C(L) compressive strength parallel to the grain; right—dependence of S C(L) and CS C(L) conventional compressive strength parallel to the grain (both show data from proposed device)

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Fig. 5
figure 5

Left—dependence of modulus of deformability MOD C(L) on modulus of elasticity MOE C(L) parallel to grain (new proposed device); right—dependence of modulus of deformability MOD C(L) on density

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Fig. 6
figure 6

Left—dependence of average force F AVG and density (pin pushing); right—dependence of average force F AVG and S C(L) (pin pushing)

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Correlations between the parameters Density, S C(L), MOE C(L) and those measured by semi-destructive devices, for example CS C(L), MOD C(L), F AVG, RM, are shown in Figs. 4, 5, 6 and 7. In particular, the relation to density can be considered strong for all semi-destructive devices. Compression strength parallel to the grain can be accurately established using the newly constructed device for jaws pushing apart. In addition, the method of pin penetration enables to assess mechanical properties of the timber very well. The resistance measure calculated from the graphical record of microdrilling is a universal parameter, which correlates with density mainly, but the prediction of mechanical properties based on this is not convincing. This behavior of the methods based on resistance drilling can be explained by the principle/mode of material disruption close to timber machining, in contrast to pin penetration, where the loading mode and disruption are closer to loading while testing of mechanical properties, and mainly in contrast to jaws pushing apart, where the loading and the disruption are very close to loading and disruption caused by compression tests parallel to the grain.

Fig. 7
figure 7

Left—dependence of density and resistance measure RM (microdrilling); right—dependence of S C(L) and resistance measure RM (microdrilling)

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The relationship between the conventional compression strength parallel to the grain CS C(L) and the selected properties of wood, Density and S C(L), is described by linear regression (Fig. 4). The coefficients of determination R 2 show very close dependences.

The relationship between the modulus of deformation MOD C(L) and modulus of elasticity parallel to the grain MOE C(L) is shown in Fig. 5 left. The R 2 = 0.76 which is a quite strong prediction using the device. The relationship of MOD C(L) and density shows rather lower prediction (R 2 = 0.37) and is depicted in Fig. 5 right.

Similarly, the density and S C(L) can be derived using the average force of pin pushing (Fig. 6). The density can also be derived well using the resistance measure of microdrilling (Fig. 7 left). Only the compression strength parallel to the grain derived from the resistance measurement seems to be not very convincing (Fig. 7 right).

Conclusion

This paper examines the usage of a new device for in situ assessment of inbuilt timber. The use of the device, which is sufficiently sensitive to natural differences occurring in wood, has been verified. The analysis of relationships between input material properties and output evaluated parameters was performed by probabilistic FE analysis. The main conclusions are as follows:

  1. 1.

    FE sensitivity analysis revealed the longitudinal elastic modulus has the strongest impact on the reaction force that is measured by newly developed device (R = 0.96).

  2. 2.

    Radial, tangential and shear moduli have little influence (R < 0.1). The same holds true for the influence of angle inaccuracy in drilling of hole (<5%) that shows R < 0.1. The FE model also shows a negligible difference in forces obtained by measurement near the hole bottom and measurements in higher positions.

  3. 3.

    Within experimental work, strong correlations were mainly found between CS C(L)—conventional compression strength parallel to the grain, and S C(L)—strength of standard samples (R = 0.92). The relationships were closer described by practically usable linear regression models.

  4. 4.

    The compression strength parallel to the grain correlates with the other explored parameters, for example density (R = 0.87). MOD C(L)—modulus of deformability, correlates very well with MOE C(L)—modulus of elasticity parallel to the grain (R = 0.87). Low correlation was found between MOD C(L) and density (R = 0.61).

  5. 5.

    Resistography provided R = 0.90 between density and RM; between S C(L)—wood strength in compression parallel to the grain, and F AVG —average force R = 0.82; MOE C(L) correlated well with F AVG (R = 0.74). Less significant correlations were found for RM and S C(L) (R = 0.62).

The new device enabled to gain strong predictions of material properties, and because it is light and does not require electric grid, it can easily be used in situ. In contrast to other techniques, the new device enables to establish mechanical properties in the depth profile of the assessed elements very accurately.