Engineering Fracture Mechanics 87 (2012) 62–72

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Engineering Fracture Mechanics

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Experimental determination of the fracture properties of unfired dry earth

Stefano Lenci a,⇑, Francesco Clementi a, Tomasz Sadowski b

a Department of Civil and Buildings Engineering, and Architecture, Polytechnic University of Marche, via Brecce Bianche, I-60131 Ancona, Italyb Department of Solid Mechanics, Lublin University of Technology, Nadbystrzycka 40 str., 20-618 Lublin, Poland

a r t i c l e i n f o

Article history:Received 23 June 2011Received in revised form 31 December 2011Accepted 13 March 2012

Keywords:Dry earth3-Points bending testLinear Elastic Fracture MechanicsTwo Parameter Fracture Model

0013-7944/$ - see front matter � 2012 Elsevier Ltdhttp://dx.doi.org/10.1016/j.engfracmech.2012.03.00

⇑ Corresponding author.E-mail address: lenci@univpm.it (S. Lenci).

a b s t r a c t

The fracture behaviour of unfired dry earth has been investigated by means of an experi-mental approach supported by some numerical simulations. Three-points bending tests,both with monotonic and cyclic loads, have been performed experimentally, and therelated force–displacement diagrams are interpreted theoretically to characterize the frac-ture parameters of the considered material. Both Linear Elastic Fracture Mechanics and aTwo Parameter Model are considered. In the latter case, based on the post-peak softeningbehaviour, the R-curve is determined, which shows how the critical stress intensity factordepends on the fracture length.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Earth has been used for many centuries, together with others natural materials such as stone and wood, in the construc-tion of load-bearing masonry structures, including constructions which are outstanding from a structural point of view, suchas the well-known 10-storey buildings in Yemen [1]. Ruins of earth buildings of the Roman imperial age have been found[2,3], but the use of this material is certainly older. The utilized technologies change with the geographical zone and withthe historical period. Typically, but not exclusively, earth has been used in the form of blocks, which were readily producedby manual compaction. Theirs constituent phases (clay, sand, etc.) can vary, and are somehow related to the building site.

The production of adequate blocks required an able labour, and this was one of the problems that, after the Roman eraand in the middle age, contributed to the marginalization of the construction of earth house in western countries. In fact theybecame non competitive with respect to other buildings materials (masonry of fired clay bricks first, and then steel and con-crete), both in terms of costs and of mechanical properties, and because of the impossibility to standardize the compositiondue to the intrinsic scattering of this material.

Over the past seventy years the use of earth block experiences a sort of revival, and they have been re-developed, or‘‘re-discovered’’, and increasingly used. On the contrary, compressed hearth blocks were continuously used in developingcountries, because earth is cheap, environmentally friend and abundant. Today the world heritage is very rich in all countriesof earth constructions, and it is estimated that approximately 30% of the world population still lives in earthen structures [4].In fact, the use of local materials, in general, and of earth block, in particular, in building of houses is one of the ways to sup-port durable development of the entire planet, because this meets the needs of the present without compromising the abilityof future generations to meet their own needs [5,6].

This trend call for a determination of the mechanical properties on earth blocks, which is the starting point for a modernuse of this old material, according to the current standard safety requirements. Quality control of the compressed earth

. All rights reserved.5

Nomenclature

a0 macroscopically observable crack of length, see Fig. 4a = a0+da effective crack length, see Fig. 4da microscopic (effective) crack of length da, see Fig. 4das value of da at the peak of the force displacement diagramB, W, L, L0 geometrical dimensions of the specimens, see Fig. 4CTOD crack tip opening displacementCTODS

C critical value of CTODE Young modulusF force applied on the midpoint of the specimens, see Fig. 4Fmax maximum value of FKI stress intensity factor in (opening) mode IKIcr critical value of KIKS

Ic critical value of KI in the two parameters modelKIcr(a) the R-curveQ brittleness parameterD measure displacement at the midpoint of the specimensdmax maximum value of drf

cr traction stress in flexurem Poisson coefficient

S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72 63

blocks is also an important issue, and today testing procedures are available and easily performed in a civil engineering lab-oratories [7,8].

Great attention has been paid to the experimental determination of the compressive strength, as it represents the mostimportant parameter to evaluate the load-bearing properties [9–12]. A simple model to compute the compressive strengthby means of a 3-points bending test has been proposed in [7], and the results have been compared with experimental data.Results from compression tests at different ages was reported in [13] (24 h, 7 and 28 days after construction) and [14] (7, 14,21 and 28 days after construction). The matter of how properly perform a compression test has been deeply analyzed andreviewed in [8], where the influence of the block geometry, of the test procedure (including those proposed by internationalstandards) and of the basic material properties (dry density, cement and moisture contents) have been discussed.

The effect of reinforcing fibres, both natural (straw) and artificial (plastic and polystyrene) inserted in the earth block as afabric layers are investigated in [15] and [16], while Yetgin et al. [17] have shown that the addition of straw fibres decreasethe compressive strength, a result which is confirmed by [18]. In [19] tensile tests were performed, too. Some indications onthe compressive strength of rammed earth and adobe are reported in the appendix of [19], together with some suggestionson the safety factors to be used. It is also shown how the compressive strength increase by the use of added cement and/orlime. The effect of stabilization with added cement was also considered in [20].

Although to a minor extent, also bending test have been performed, and the flexural ultimate stress has been determinat-ed [7,14,18,20], with results showing that it varies from 1/5 to 1/20 of the compressive strength [19], and that it is muchmore influenced by various parameters such has percentage of straws.

On the contrary, up to the authors’ knowledge, less or no attention has been paid to other important properties of dryearth, such as fracture, the experimental study of which constitutes the object of this paper. The knowledge of this behaviourpermits to enlarge the picture of the mechanical behaviour, which is particularly needed in the applications where fracture,and not strength, represents the critical event for the structure.

Fracture toughness in mode I were investigated in [21] by 3-point bending tests and by considering clays with differentwater content or different dry density. Although not directly related to dry earth, a relevant paper is [22], where 3-pointbending tests are used to determine the R-curve of samples of sandstone. Here the results are also compared with those ob-tained by a two-parameter fracture model [23].

An experimental campaign has been performed at the ‘‘Laboratorio Prove Materiali e Strutture’’ of the Polytechnic Uni-versity of Marche, the results of which are reported in this paper. More precisely, this paper is organized as follows. In Sec-tion 2 the considered earth material is briefly described. Then, the fracture properties have been discussed (Section 3) by a 3-point bending test. In order to achieve information also on the flexural strength of the material, we started by testing unnot-ched specimens. To further assess the fracture characteristics of the material, we have considered specimens with an initialcrack. The results of the experimental tests have been paralleled by numerical simulations performed with Finite ElementMethod to single out the desired fracture parameters (the so-called R-curve [24]) in the context of Linear Elastic FractureMechanics. Finally, a two parameters model [23] has been considered, too.

64 S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72

2. Materials and preparation

The material used in compression tests is made of three different constituents, arranged according to the following vol-ume proportions: 1 volume of ‘‘earth’’, 1/2 volume of ‘‘coarse sand’’ and 1/2 volume of fibres straw. The geotechnical char-acteristics of the constituents are reported in Table 1 and in Fig. 1. According to the ASTM D2487 the ‘‘earth’’ and the ‘‘coarsesand’’ can be classified as ‘‘lean clay with sand (CL)’’ and ‘‘well graded sand (SW)’’, respectively. The fibres of straw have alength which varies from 2 to 8 cm, with an average valued of 5 cm, and they were added since they increase the mechanicalproperties of the material still maintaining the eco-compatibility.

Material preparation and mixing was carried out by hand (Fig. 2a). The mixture was manually pressed into formworks ofwood of the dimensions of 32 � 46 � 13 cm. 1/3 (on average) volume of water was added during the manual operations andcompaction to have an adequate lavorability.

After removing the boxes (Fig. 2b), the blocks were dried under stationary thermo-hygrometric conditions (temperature23–26 �C; relative humidity 45–55%). After about 5 months, the blocks were cut by saw to obtain the desired specimens, thedimensions of which are reported in the following. At the end of the tests, it was verified that the moisture contents was lessthan 3–4%, and this guarantees that practically a dry material has been used.

3. Fracture behaviour

In order to analyse the fracture behaviour of dry earth we have performed 3-points bending tests with (Fig. 3b) and with-out (Fig. 3a) an initial notch (see Fig. 4 for a sketch of the specimens). In each case we have applied both a monotonic and acyclic load, so that a total of four cases have been considered. We applied the displacement d (at the midpoint, see Figs. 3 and4) and measure the associated force F to detect the softening behaviour.

0

20

40

60

80

100

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

Grain size [mm]

Pas

sing

[%

]

0

20

40

60

80

100

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

Grain size [mm]

Pas

sing

[%

]

(a) (b)

Fig. 1. Grading curve for (a) the ‘‘earth’’ and (b) the ‘‘coarse sand’’.

Fig. 2. (a) The compaction in the formwork and (b) the final block.

Table 1Physical properties.

‘‘Earth’’ ‘‘Coarse sand’’

Clay (%) 22.4 0.5Silt (%) 49.9 1Fine sand (%) 24.5 61.8Coarse sand (%) 3.2 36.7Liquid limit (%) 26.4Plastic limit (%) 18.4Plastic index (%) 8

Fig. 3. Specimens for 3-points bending tests: (a) without initial crack and (b) with initial crack.

Fig. 4. Geometrical configuration of the 3-point bending tests.

S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72 65

It is initially assumed that plastic deformations are limited and that the material is brittle enough so that the Linear Elas-tic Fracture Mechanics (LEFM) can be applied with a sufficient accuracy. The most important parameter is then the stressintensity factor (SIF) KI, since (opening) mode I is the unique fracture mode considered in this paper. Actually, our first goalconsists in determining experimentally the critical value KIcr, which is a measure of a material’s resistance to crack propa-gation. More precisely, we will determine KIcr as a function of the crack length a, KIcr = KIcr(a), thus obtaining the so-called R-curve [24–26].

For the configuration of Fig. 4 the stress intensity factor KI is given by [25]

K I ¼FL

BW3=2 2:9a

W

� �1=2� 4:6

aW

� �3=2þ 21:8

aW

� �5=2� 37:6

aW

� �7=2þ 38:7

aW

� �9=2� �

; ð1Þ

where a is the crack length measured from the bottom and the meaning of B, W, L and F is illustrated in Fig. 4. It is worth tonote that Eq. (1) does not consider the weight of the specimen, since it is negligible with respect to the applied force F.

Fig. 5. The F–d experimental curve for the 3-points bending test without initial notch and with monotonic load.

66 S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72

3.1. Bending tests without initial crack

Let us first consider specimens without initial crack (Fig. 3a). The principal dimensions of the specimens are (Fig. 4):L0 = 355 mm (length), B = 85 mm (width) and W = 112 mm (height). The specimens lean on two steel cylinders, which arefree to roll (Figs. 3a, 4), at distance L = 255.

The experimental F–d curve for the monotonic test is reported in Fig. 5. This figure shows that the initial elastic range endsat F = Fmax = 2274 N, in correspondence of d = 1.239 mm. As the beam theory does not apply because the specimen is notslender enough, we have used the linear Finite Element Method (FEM) to correlate these data. A commercial FEM softwarehas been used, and the specimen is modelled within the framework of plane elasticity, since the geometrical configurationsuggests (and the experiments confirm) that there are no out-of-plane effects. Standard eight nodes shell elements havebeen employed, and in the next numerical simulations an appropriate mesh, automatically done by the software, is consid-ered around the crack tip, although we do not use the FEM to determine the KI.

From the FEM analysis we obtained E = 160 MPa and rfcr ¼ 0:85 MPa (the Poisson coefficient used in the FEM is m = 0.3, but

this parameter does not influence the results that much). Note that with the beam theory we would get E = FmaxL3/(4dBW3) = 63.7 MPa and rf

cr ¼ 3FmaxL=ð2BW2Þ ¼ 0:82 MPa, the former being not very accurate. In fact, E = 160 MPa is in bet-ter agreement with the Young modulus computed by other compressions tests performed by the authors. On the other hand,rf

cr ¼ 0:85 MPa provides an estimate of the tensile (flexural) strength of the material, which agrees with the valuert

cr ¼ 0:5� 0:8 MPa obtained in [17] by a direct traction test.After the initial elastic range, a pseudo-vertical crack appeared in the middle of the lower side, which instantaneously

propagates toward the upper side (Fig. 6). After the first sudden jump, the crack propagation continues smoothly and a rel-atively long softening branch is observed (Fig. 5), with a final vertical displacement equal to dmax = 10.4 mm.

The results of the bending test with cyclic load are reported in Fig. 7. The initial elastic range ends at F = Fmax = 2131.8 N,in correspondence of d = 0.511 mm. In this case the FEM analysis provides E = 330 MPa and rf

cr ¼ 1:70 MPa (the Poisson coef-ficient is again m = 0.3). The overall shape of the softening branch is the same of the monotonic test, but now it is shorterbecause the test has been stopped for a smaller value of the vertical displacement.

Fig. 6. The crack of the 3-points bending test without initial notch and with monotonic load.

Fig. 7. The F–d experimental curve for the 3-points bending test without initial notch and with cyclic load.

S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72 67

The first unload–reload cycle has been performed in the initial elastic part, at a value of the force F = 1677.9 N, corre-sponding to the 78.7% of the maximum force Fmax. This unload occurs in the elastic regime, and in fact it is almost indinguish-ible in Fig. 7. However, during the reloading there is a compaction, so that the elastic modulus increases and becomes twotimes larger than that of the monotonic test. The subsequent seven unload–reload cycles have been done in the softeningpath, after the crack underwent the initial sudden propagation, which occurs as in the monotonic case. They have been per-formed at almost equal intervals of d: 0.667; 1.074; 1.452; 1.821; 2.28; 3.07; and 3.836 mm. During these cycles the damageof the specimen entails the reduction of the Young’s modulus, which is evident in Fig. 7. There is a decrease in the slope of theunloading–reloading paths, which however leaves some permanent deformations. Thus, this damage is not only due to themain propagating crack, which of course reduces the stiffness of the specimen, but also to an ‘‘intrinsic’’ and spread damageof the material.

Since LEFM is assumed to apply, the crack propagation occurs under the condition KI = KIcr calculated with (1). To fulfilexactly the experimental data, we assume that KIcr is a function of the crack length a, KIcr = KIcr(a), and determine this func-tion, called R-curve [24–26], with the following procedure.

The elastic constants considered in the model are E = 160 MPa and 330 MPa for the monotonic and the cyclic tests, respec-tively, with a Poisson coefficient m = 0.3. For the d-values of the softening branch of Fig. 5 (and of the envelop curve of Fig. 7),we enter the FEM with an arbitrary a and the applied vertical displacement d. Then, we vary a until the force obtained by theFEM becomes equal to the corresponding force measured experimentally. Thus we get the function a = a(d), which providesan estimation of the crack length as a function of the applied vertical displacement. With this function and the experimentalcurve F = F(d), one can compute F = F(a) by eliminating the vertical displacement d. Introducing the function F(a) into Eq. (1)we get finally the desired KIcr(a).

The curves a(d) are reported in Fig. 8a, while the R-curves KIcr(a) are given in Fig. 8b.Fig. 8a confirms the sudden opening of the crack, which undergoes the so-called ‘‘snap-back’’ phenomenon in both cases.

For the monotonic case the elastic part ends at d = 1.239 mm and the crack starts at d = 1.315 mm (in-between there is thesnap and we have no data), where it suddenly reaches the length a/W = 0.51, i.e., almost the half of the height, so that thespecimen is rapidly damaged. The same qualitative behaviour is observed in the cyclic test, but with different vertical dis-placement at jump, d = 0.605 mm, and with similar crack extension, a/W = 0.47.

After the initial jumps, the cracks continue to growth smoothly, with a decreasing slope, up to the final value which isabout a/W = 0.90. Due the large extension of the cracks, both the experiments and the FEM simulations become unreliablein this final range, mainly because of the interactions between the stress concentration at the crack tip and the stress con-centration just below the upper roller. This fact is confirmed by Fig. 8b, where the R-curves show some particular behaviours

Fig. 8. The curves (a) a(d) and (b) KIcr(a) for the unnotched case.

68 S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72

for a/W > 0.75. It is necessary to point out that the real crack is not rectilinear (see Fig. 6), so that the simulations based onrectilinear crack would be in any case approximate, and particularly in the final stage of the deformation process.

It is worth to remark that we are dealing with unstable crack propagations, which are seen only because we applied dis-placements and measure the forces.

Fig. 8b shows that the critical stress intensity factor is a fairly varying function of the crack length, this being an a pos-teriori confirmation that in this case the LEFM can be applied satisfactorily. For the monotonic test the average value isKIcr = 7.67 N/mm3/2, which is practically equal to the experimental points in the range 0.50 < a/W < 0.80. For the cyclic testwe have a slightly higher value due to a compaction in the elastic range, that lead to the average value KIcr = 9.1 N/mm3/2,which is very close to the each experimental point in the range 0.45 < a/W < 0.90. These two values provide an estimateof the crack resistance of the considered earth material.

Fig. 9. The crack of the 3-points bending test with initial notch and with monotonic load.

Fig. 10. The F–d experimental curve for the 3-points bending test with initial notch and with monotonic load.

Fig. 11. The F–d experimental curve for the 3-points bending test with initial notch and with cyclic load.

S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72 69

3.2. Bending tests with initial crack

To further assess the fracture characteristics of the material, we have performed other two 3-points bending tests onspecimens with initial cracks (Fig. 3b), again monotonically and cyclically loaded. Here we have considered a slightlydifferent material composition (1 volume of ‘‘earth’’, 1/2 volume of ‘‘coarse sand’’ and 3/4 volume of fibres straw) and aslightly different geometrical dimensions (L0 = 360 mm, L = 320 mm, B = 84 mm and W = 113 mm, see Fig. 4).

The initial crack length is a0 = 44 mm, i.e., a0/W = 0.4, for both samples (Fig. 9). The experimental data for the monotonictest are reported in Fig. 10. From this figure we can see that there is no longer the sudden jump as in Fig. 5, and the prop-agation is continuous from the starting point F = Fmax = 636 N, which occurs in correspondence of d = 0.544 mm. Further-more, the initial crack now induces an almost rectilinear propagation of the crack, as shown in Fig. 9. A long softeningbranch is observed also in this case.

The results of the cyclic test are reported in Fig. 11. The initial elastic interval ends at F = Fmax = 736.5 N, in correspondenceof d = 0.454 mm. The successive envelop curve of the softening branch is very similar to that of the monotonically loadedcase (compare with Fig. 10). As in the unnotched case, we observe a decreasing slope of the unloading–reloading paths,and market residual strain which proves that there is a spread damage of the material in addition to the damage due tothe main propagating crack.

The analysis of this case is analogous to that of the previous subsection. From the initial elastic part of the curves we getE = 330 MPa (and we still assume m = 0.3 in the FEM simulations) for both types of test, according to the fact that in this casewe have not performed an unload–reload phase in the elastic range, so that up to the peak the specimens undergo the sametime load history.

After elaborating the descend paths we obtain the functions a(d) and the R-curves KIcr(a), which are reported in Fig. 12aand b, respectively. The curves of the monotonic and of the cyclic cases are remarkably close between each other, a fact thatconfirms the reliability of the results and which is likely favoured by the fact that the specimens undergo the same load his-tory in the elastic part.

The most important characteristic of the R-curves is that they are no longer ‘‘constant’’, as in Fig. 8b, but they are nowalmost linearly increasing functions of a. The average slope is about 11.5 N/mm3/2. As in the previous case, the final partof the curve is unreliable due to the crack-roller stress interaction.

From Figs. 8b and 12b we see that the critical stress intensity factor of the cyclic load case is systematically larger thanthat of the monotonically loaded case, both in the notched and unnotched cases, although the difference is modest (espe-cially in the notched case) and belongs to the range of experimental approximations. We believe that this difference isdue, at least partially, to the benefic effect of compaction due to the unloading–reloading phases.

Fig. 12. The curves (a) a(dv) and (b) KIcr(a) for the notched case.

70 S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72

In order to have a unique reference value for KIcr, we consider the average values of the R-curves, which are also reportedin Fig. 12b. In the monotonic case the average value is KIcr = 6.8 N/mm3/2, while in the cyclic case it is KIcr = 7.25 N/mm3/2.These values are smaller than the correspondings values of the unnotched case, according to the fact that now the materialhas a macrospic damage.

3.3. A two parameters model

The LEFM model employed in the previous subsections to interprete the experimental results is clearly the simplest one,though it provides quite reliable results. However its validity to cementitious (e.g. concrete) materials has been seriouslychallenged by the lack of experimental evidence suggesting a unique size independent fracture toughness value. This sizedependence has been largely attributed to the presence of a process zone ahead of the crack tip [27]. Because the unfireddry earth has some features of cementitious materials, since the clay provides some cohesive properties as the cement doesin concrete, it is worthy to apply a fracture mechanic model developed for cementitious material to deepen inside the inter-pretation of the experimental data.

The Jenq–Shah two-parameter model [23] is employed. It is different form the LEFM only if in the initial part of the exper-imental force–displacement curve, before the peak where crack starts to propagate, a nonlinear behaviour is observed – justcaused by the cohesive behaviour of the material. In the present case the pre-peak nonlinearity is small (meaning that thecohesiveness is small and confirming that LEFM is satisfactory as a first approximation), but it can be observed in a finerobservation.

With the considered model it is possible to circumvent the problems associated with the nonlinear behaviour of the pro-cess zone by introducing the concept of the ‘‘effective crack extension’’, which practically permits to use LEFM mechanictools and thus it is relatively easy to be applied. The idea is that ahead the macroscopically observable crack of length a0

there is a microscopic (effective) crack of length da (see Fig. 4), whose extension is undetermined a priori and which ‘‘sum-marizes’’ the effects of the process zone.

In the two-parameter model it is assumed that, when the load increases and when the macroscopic crack yet does notpropagate, i.e., when we are below the force peak, a slow microscopic crack grows ahead the macroscopic crack tip. This sim-ulates the development of the process zone, and occurs up to a certain (microscopic) crack extension das, which actually cor-responds to the maximum load applied to the specimen. This critical situation is assumed to happen when, at the peak loadand for unstable geometries (i.e., increasing KI with increasing crack length a), the following two conditions are simulta-neously satisfied:

Table 2Results

MonCyclMonCycl

KI ¼ KSIc; ð2Þ

CTOD ¼ CTODSC ; ð3Þ

where the right hand side values are now considered size-independent material properties, and where the apex S refers to theJenq–Shah model.

The quantity defined in (2) can be calculated by (1) using the measured maximum load and the critical effective cracklength. The second parameter defined in (3), the crack tip opening displacement (CTOD), can be calculated at the originalnotch tip of the specimen by [26]

CTOD ¼ 6FLa

EBW2 fa0

a;

aW

� �; ð4Þ

where the quantities are represented in Fig. 4. We refer to [23] for more details on the two-parameter model.The critical values KS

Ic and CTODSC can be computed in the following way from the experimental data. From the first (half)

part of the pre-peak experimental curve, where the microcrack is assumed to have not yet developed, we determine theYoung modulus E with the help of the FEM, where the initial value a0 of the macrospic crack (a0 = 0 in the unnotched case,a0/W = 0.4 in the notched case, see Section 4.2) is set. With this value of E, we enter the FEM and modify the crack length untilthe force and the displacements are equal to the values Fmax and d at the peak of the experimental curve. We then have theeffective crack lenght a = a0 + da. Inserting a0, a, E, Fmax in (1) and (4) we can finally compute KS

Ic and CTODSC (as well as a, i.e.,

the effective crack length at macroscopic propagation), which according to [23] are supposed to be size-independent, andthus a property of the material and not of the specimen. The results of the computations are obtained in Table 2 and theKS

Ic are plotted in Figs. 8b and 12b.

of Jenq–Shah two-parameter model for dry earth.

a (mm) KSIc (N/mm3/2) CTODS

C (mm) Q (mm)

otonic without initial notch 37 9.06 0.261 190.52ic without initial notch 27 7.66 0.548 165.93otonic with initial notch 55 5.12 0.078 25.2ic with initial notch 48 4.56 0.041 10.7

S. Lenci et al. / Engineering Fracture Mechanics 87 (2012) 62–72 71

From Fig. 8b it is possible to see that KSIc , for monotonic and cyclic tests without initial notch, are comparable with the

average value of the two R-curves. These are behaviours similar to that observed in the literature [23]. The same situationdoes not occur for notched beam (Fig. 12b) where the fracture toughnesses determined with the two-parameter model haveminor values in comparison to the averages of the two R-curves.

Finally, the Young’s modulus E and the two fracture parameters describing the material fracture properties can be com-bined in the parameter [23]

Q ¼ E � CTODSC

KSIcr

!2

; ð5Þ

which is related to the brittleness of the specimen and which is also reported in Table 2. It has the dimension of a length andit is used as material length to normalize the model predictions. In fact, for large Q the material exhibits a high brittleness.

Before ending this section it is worthy to note that while in the determination of the R-curves (Sections 3.1 and 3.2) thesoftening parts are mainly utilized, in the present case we have used only the initial, pre-peak, part of the experimentalcurves, exploiting its (actually minor) nonlinearity.

4. Conclusions

We have investigated the fracture behaviour of the unfired dry earth. This has been initially done by considering thematerial brittle enough so that the LEFM can be applied with sufficient accuracy. We have analysed four different 3-pointsbending tests, one without and one with the initial crack, loaded in monotonic and cyclic manner. In each case we havedetermined the R-curve of the material, i.e., it resistance to crack propagation, and we have proposed some average valuesof the fracture toughness to be used in first approximation analysis.

Then, a more accurate cohesive model of fracture has been applied, and the relevant critical threshold determined fromthe experimental results. The ‘‘corrections’’ of this model to the critical stress intensity factors have been reported, providinga better understanding of the whole fracture process.

Acknowledgements

The authors wish to gratefully acknowledge the valuable assistance of the Laboratory technicians Franco Rinaldi, UmbertoTaddei and Andrea Conti. The help of the Geotechnical Laboratory of the Polytechnic University of Marche is alsoacknowledge.

The research leading to these results has received funding from the European Union Seventh Framework Programme(FP7/2007–2013), FP7-REGPOT-2009-1, under grant agreement No: 245479; CEMCAST.

The support by Polish Ministry of Science and Higher Education – Grant No. 1471-1/7.PR UE/2010/7 – is alsoacknowledged.

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