Shear Parameters of Rammed Earth Material: Results from Different Approaches

Rammed earth (RE) is a construction material which is manufactured by compacting the soil in a formwork, in different layers. Several recent studies have investigated this material. /e seismic performance of RE buildings is an important topic which needs to be carefully investigated. /e complex numerical model seems a performant approach to investigate the seismic performance of a whole building. To correctly establish the model, the shear parameters of the material, which are the cohesion and the friction angle, should be identified. /is paper first presents experimental studies on the shear parameters of RE through the direct shear tests, at two different scales. /e differences of the results at different scales are analyzed. /en, the obtained experimental values are used in a numerical model to simulate the shear behavior of RE walls which are loaded by a constant vertical stress and pushed horizontally on the top. From the obtained results, the values for numerical models are recommended.


Introduction
Rammed earth is an ancient technique of construction where the wall is built by compacting the soil in a formwork, in different layers. Each earthen layer has thicknesses of about 10-15 cm. More details about this technique of construction are presented in [1,2]. is material is recently experiencing a renewed interest because of its low embodied energy [3], its recycling ability, and a positive hygrothermal behavior which offers an attractive living comfort [4]. Figure 1 illustrates an example of a recent school in France constructed by RE material.
A nonnegligible number of studies on RE material are observed during the last decade, on different topics: mechanical characteristics [5][6][7][8][9], thermal and hygrothermal properties [4,10], and durability [11,12]. For the earthquake performance of RE structures, although several studies have explored this topic [13][14][15][16], different aspects still need to be investigated more thoroughly. In order to study the earthquake behavior of an entire RE structure, robust numerical models are a necessary approach. For the numerical modelling of RE material, two important shear parameters are the friction angle φ and the cohesion c. Due to the superposition of successive earthen layers during the manufacture of RE walls, two kinds of characteristics should be distinguished: characteristics of the earthen layers ("intralayer") and those of the interfaces between earthen layers ("interlayer") [17]. e first scope of the present study is to identify the relevant values of the friction angle φ and the cohesion c for both intralayers and interlayers. e characterization of these parameters is the first important step to create performant numerical models for the seismic evaluation of RE buildings.
Several previous studies in the literature tried to identify these two parameters but important dispersions in the obtained results were observed. Cheah et al. [18] performed triaxial tests on cement-stabilized RE specimens and obtained friction angles from 45°to 56°. Bui et al. [19] used analytical calculations for RE specimens and indirectly obtained for intralayers a friction angle of 51°and a cohesion of 0.1 f c , where f c is the compressive strength. Nowamooz and Chazallon [20] used finite elements modelling with the Barcelona model on small compacted soil specimens and identi ed a friction angle and a cohesion of 41°and 13.4 kPa, respectively. Bui et al. [17] used discrete elements modelling to identify c and φ; the identi ed friction angle was of 45-50°a nd the identi ed cohesion was of 100-150 kPa. Miccoli et al. [21,22] identi ed numerical values of 30-45°for intralayer friction angles. e experimental approach is a feasible way which provides "direct" values, while for the numerical approach, a calibration of the results is needed and the identi ed values are "indirect". e di culty with RE material is that the representativeness of the tested specimens should be insured because of a high inhomogeneity of the material [6]. El-Nabouch et al. [23] present an experimental study on a fullscale direct shear test where the friction angle and the cohesion of the intralayers were of 37.3°and 30 kPa, respectively. e present paper rst presents the results about the cohesion and the friction angle of RE intralayers and interlayers and obtains the following di erent scales: on standard direct shear tests (10 cm × 10 cm × 4 cm) and on the full-scale direct shear tests (50 cm × 50 cm × 45 cm). en, the experimental results are used in a numerical model to simulate the behavior of two RE walls which were tested under a constant vertical stress and a horizontal force on the top of the wall. e results and recommendations will be presented.

Material Used.
e earth used was provided by a RE manufacturer company, in the Rhône-Alpes region (France). is soil had been used to build numerous ancient RE buildings in this region. e grain size distribution of the earth is presented in Figure 2. e composition of the soil was analyzed by X-ray powder di raction where the data were recorded on small fractions of specimens that were crushed before the analysis. e di raction patterns were recorded with a Bruker D8 di ractometer. e result (shown in Figure 3) reveals the presence of quartz (72.6%), albite (15.1%), illite (11%), and trace of vermiculite (1.3%) [24]. e Proctor optimum water content is of 12% (by weight), determined following the French standard [25].  [26]. e soil specimen is placed in a shear box that consists of two independent half boxes; the contact between the two half boxes is at the midheight of the specimen. A vertical con ning stress is applied to the specimen, and the upper half boxes are pulled laterally (speed of 1.5 mm/min) until the specimen fails. ree tests (at three di erent vertical stresses) are carried out to determine c and φ following Mohr-Coulomb's theory.  In the present study, the standard shear box (dimensions of 10 cm × 10 cm × 4 cm), which is usually used to identify the friction angle and the cohesion of sand or soil, was also used to test RE specimens ( Figure 4).

Standard Direct
In soil mechanics, specimens are directly fabricated in the shear box. However for RE material, the representativeness of the specimens manufactured in "small" moulds (compared to in situ RE walls) is usually problematic. Indeed, manufacturing a representative RE specimen by a pneumatic rammer in a small box (10 cm × 10 cm × 4 cm) is not easy. at was why the authors decided to take specimens directly from a 1.5 m width × 1.5 m height × 0.25 m thickness RE wall, which will be presented in detail in the next section. e wall was manufactured in a steel formwork with plywood plates. e earth was compacted by a pneumatic rammer, at 12% of manufacturing water content (by weight) and in 12 earthen layers (with 12 cm thick for each layer). Preliminary Proctor tests showed that this water content was the optimum value for the compaction energy of the pneumatic rammer used. e wall was unmolded from its formwork after the manufacturing and then cured at laboratory ambient conditions (20°C and 60% relative humidity, RH) during two months. e specimens for direct shear tests were taken after two months and at a quasi-dry state (less than 3% of moisture content, by weight). Firstly, earthen blocks (about 35 cm × 35 cm × 15 cm) were taken from the wall ( Figure 5(a)). en, a table saw was used to cut specimens into accurate dimensions (10 cm × 10 cm × 3.5 cm), enabling to fit the shear box (Figures 5(b) and 5(c)). Since Bui et al. [6], it has been well known that the density in a RE layer decreased from the top to the bottom. at was why specimens for the standard shear tests were taken at different positions in an earthen layer: at 1 cm from the top ( Figure 5(b)) where the compaction was the most important (dry density measured of 1864 ± 51 kg/m 3 ) and at the middle of the layer ( Figure 5(c), dry density of 1703 ± 45 kg/m 3 ). e specimens at the bottom, close to the interface, could not be extracted because they were too brittle. It is worth noting that due to the fragility of unstabilised RE material, special attentions must be paid to correctly cut the specimens without visible damage (for example, [27]).

Test Results.
For each direct shear test, the maximum shear stress was noted and the experimental results giving the relationship between the shear stress τ and the normal stress σ are summarized in Figure 6. Firstly, note that the tests are consistent with Mohr-Coulomb's theory since the experimental results are on the same straight line (a correlation coefficient greater than 97%). Furthermore, the graph shows that, at a same vertical stress, the specimens from the upper part had a shear resistance greater than that of the lower part. is result is not surprising because the upper part-which is better compacted during the manufacturing-has a greater density and therefore has a strength which is greater than that of the lower part.
Following Mohr-Coulomb's theory, the relationship between the maximum shear stress and the normal stress is determined. e result is presented in Figure 6 for the case of the standard shear box. e apparent friction angle and the apparent cohesion were determined, giving, respectively, φ � 44.1°and c � 264 kPa for the specimens taken from the layers' upper parts, whereas φ � 44.4°and c � 164 kPa for the specimens taken for the layers' middle parts. It is interesting to note that the friction angles obtained were similar for the upper and middle parts of an earthen layer (about 44°). e main difference was the cohesion: the upper part had a more important cohesion (264 kPa), comparing to that of the middle part (164 kPa).

Full-Scale Direct Shear
Tests. In a recent study, El-Nabouch et al. [23] have carried out an experimental study on a full-scale shear box (50 cm × 50 cm × 45 cm height) to take into account the scale effects ( Figure 7). e soil used and the manufacturing process were the same as that of the present study. Two types of shearing tests were performed: specimens sheared at the middle of layer (intralayer) and specimens sheared at the interface between the layers (interlayer). Due to the large size of the specimens, there was a high variation of the moisture content inside of the specimens, which was from 3% to 6%, depending on positions (on the surface or at interior).
First, a vertical load is applied on the top of the specimen (by the vertical actuator VA), and then, a horizontal load is applied by the horizontal actuator VH. e results (Figure 8) showed that the friction angle and the cohesion of the intralayers were of 37.3°and 31 kPa, respectively, and that of the interlayers were of 34.8°and 24 kPa, respectively.

Discussion.
e results obtained show that, for a same scale of test, the friction angle does not vary significantly within a RE wall: between the upper part and the middle part in the case of standard shear box tests (about 44°) and between the intralayer and the interlayer in the case of fullscale shear box tests (37.3°and 34.8°, respectively). It is suggested that the friction angle depends on the roughness of earth grains which is similar between the upper and middle parts of a layer. Besides the grain roughness, the density has also in uence on the friction angle, which explains the slightly lower values of the interlayer friction angle, compared to that of the intralayer.
For the cohesion, the di erence is clearer between the upper part and the middle part (264 and 164 kPa, respectively). It is suggested that, with a higher compactness, the dimensions of the micropores in the upper part are smaller than that of the middle part; the smaller micropores give a higher suction which provides higher cohesion and mechanical strength [7,28]. is observation is also valid for the full-scale shear box tests where the interlayer cohesion is about 80% of the intralayer cohesion.  Another important observation is that the results obtained on the full-scale shear box are lower than that of the standard shear tests. Indeed, the shear tests at the midlayer on the standard box were conducted at a similar position with the intralayer shear tests on the full-scale box; for the standard box tests, the friction angle and the cohesion of the middle part are 44°and 164 kPa, respectively, while these parameters obtained on the full-scale box test are 37°and 31 kPa, respectively. e main differences between these two tests are the specimens' size and the moisture content. Indeed, it was observed that the moisture content was not homogeneous in the full-scale specimens and varied from 3% to 6%, depending on the positions, whereas the moisture content played a predominant role on the suction of earthen material which was the main source of the cohesion in earthen material [7,8,28,29]. e influence of the moisture content is also probable because the cohesion obtained on intralayer full-scale specimens were relatively low (31 kPa). For comparison, following the formulas recommended in New Zealand Standard [30] or in [19], the cohesion would be 100-200 kPa for the RE in the present study; or following the values suggested in [22], the intralayer cohesion would be in the range from 132 to 264 kPa in the present study.
e low values of the cohesion and the friction angle obtained through the full-scale shear box are likely due to the effects of the moisture content, but also due to the size effects. Indeed, Flitti et al. [31] observed that when the moisture content increased (from 0 to 3%), the friction angle could decrease about 1°(for a friction angle of 40°). So, it can be suggested that the moisture may act as a lubricant which decreases the friction between the particles, but this phenomenon does not have enough effects to explain the low results obtained. is result confirms the nonnegligible role of the size effects.
From the results of intralayer and interlayer obtained on the full-scale box, the friction angle of the interlayer is 93% of the intralayer and the cohesion of the interlayer is 80% of the intralayer. is is an interesting result which serves for the numerical modelling.

Numerical Modelling of RE Shear Walls
For the numerical modelling, due to the simplicity, the earthen layers are usually assumed homogeneous and the interfaces are added between layers [17]. However, the above experimental results showed that there was a difference in the cohesions and the friction angles between the upper and middle parts of an earthen layer. So it is important to take the pertinent values for homogenized earthen layers (in numerical models) which represent the real inhomogeneous layers. On the contrary, it has already been observed that the most adapted values for a numerical model may sometimes be slightly different from the intrinsic characteristics of the material [32]. at was why a finite element (FE) model was built and simulated two horizontal loading tests in order to find the recommended values for the modelling of RE material.

Horizontal Loading Tests.
Two walls (called wall A and wall B) were used for the numerical modelling of the present study. e walls having 1.5 m width × 1.5 m height × 0.5 m thickness ( Figure 9) were manufactured with the same soil and the manufacturing process as the specimens presented above. e walls' moisture contents obtained after the test were 2.5-3% (i.e., the same as the specimens tested in the standard shear box). e RE wall was directly built on a concrete beam. After the RE wall manufacturing, a second concrete beam was installed on the top of the RE wall, by applying a lime mortar. ese walls were subjected to the pushover test which is a reliable approach to evaluate the walls' earthquake performance. First, vertical loads were applied on the top of the wall by means of two vertical actuators (VE1 and VE2 (Figure 9)).
ese loads corresponded to a vertical compressive stress of 0.3 MPa, which simulated the stress due to the vertical loads in a building (dead and live loads). en, the horizontal pushing load was applied from a horizontal actuator (VH) with a displacement control (0.01 mm/s). e digital image correlation (DIC) technique was used to measure the displacements of the walls during the tests. In the DIC technique, the displacement fields are determined by comparing the images taken after and before loading (reference image). A professional camera with a resolution of 16 M pixels was used. e test was recorded by the camera, and the data processing was performed with the 7D software [33]. e bottom concrete beam was fixed to the steel frame by four steel brackets that could be mechanically adjusted ( Figure 9). Another steel prop (B on Figure 9) was used as support to prevent the beam sliding when the top horizontal displacement is applied. e bottom concrete beam was also maintained by vertical tie rods (T on Figure 8) to avoid the beam rocking. ree displacement sensors M1 and M2 were installed to verify if there were any movement (vertical and horizontal) of the bottom concrete beam. e displacement sensor M3 was used to verify the accuracy of the results obtained from DIC. Figure 10 shows the horizontal forces in function of the horizontal displacements on the top of both walls. ese displacements were obtained from the DIC. Two walls tested exhibit similar initial stiffness and a nonbrittle behavior; the maximal horizontal load was 40-43 kN. Figure 11 illustrates the crack propagation of wall A through the results of the major principal strains obtained from the DIC process. For the tested walls, three types of cracks were identified: first, a horizontal crack was observed at an interface between two earthen layers at the left-lower part of the wall. Second, inclined cracks which represent the diagonal compressive strut. ese cracks appeared when the horizontal load reached about 80-85% of the maximal load.
ird, the rocking of the walls at their base was also noted at the end of the tests (on the right side of the wall on Figure 11). is code has di erent advanced options for the earthquake studies and was used to model di erent important and complex structures such as nuclear power plants. e initial aim of the authors of this paper is to rst validate the numerical model at the wall scale and then apply for entire RE structures for further studies. e well-known Drucker-Prager's model was chosen. In fact, Drucker-Prager's model does not directly use c and φ as parameters, but a conversion from Mohr-Coulomb' parameters is necessary. However, Drucker-Prager's model was used in the present study due to its robustness (working in 3D) and its simplicity by comparing to other advanced models. Drucker-Prager's yield criterion is written as follows:

Numerical
where I 1 tr(σ) is the trace of the stress tensor, σ eq is the second invariant of stress, and α is a function of the friction angle: R(p) is the value taken by the criterion for tr(σ) 0, a function of the cumulated plastic strain p. e variation of R with the material plasticization presents the hardening. e parabolic hardening is chosen for this model. e parameter σ y is written in the function of φ and the cohesion c: Figure 12 illustrates the geometry and the meshing. e wall was modeled with 12 layers of 11.4 cm each (named "intralayer") and thin layers of 1 cm (named "interlayer") between the earthen layers. Indeed, the role of the interlayers may not be predominant in the case of vertical loads but important in the cases where the interfaces are more solicited [17]. In the present study where the walls are subjected to horizontal loads, the e ects of interlayers on the model might have a signi cant impact on the results. In fact, the interlayers represent the bottom part of an earthen layer where the soil was less compacted than the upper part, and consequently, its mechanical properties are lower. e thickness of the interlayers was chosen following observations by DIC during compression tests where the thickness of the weak layers (excessive displacements compared to other parts) was about 1 cm. Modelling these two layers is a simple way which enables to consider each intralayer and each interlayer with di erent parameters. Each intralayer   Advances in Materials Science and Engineering and each interlayer are considered as homogeneous and isotropic. e bottom of the bottom concrete beam is considered as embedment.

Intralayer and Interlayer
Characteristics. For the intralayers, Young's modulus was taken of 500 MPa that was measured by DIC during the vertical loading phase of the experiment, by using the vertical displacements at the walls' central part. Poisson's ratio was taken equal to 0.23, following the results of a previous study [7].
As mentioned above, the moisture content of the tested walls is similar to that of the specimens tested in the standard shear box, so the intralayer characteristics were taken following the results of the standard shear box. e interlayer characteristics were taken in percentage of the intralayer characteristics, as obtained on the full-scale shear box tests. erefore, the intralayers were modeled with φ intra 44°and c intra 164 kPa, which are the values of the middle part of a layer because the numerical model considered each earthen layer as a homogeneous material. e interlayer friction angle was taken as 94% of the intralayer, corresponding to φ inter 40°; the interlayer cohesion was taken as c inter 130 kPa which represented 80% of the intralayer cohesion.

Numerical Results and Discussions.
e numerical results are illustrated in Figure 13. From this gure, the numerical model could reproduce the maximum force of the experiments, the experimental initial sti ness, and the global elastoplastic behavior. e experimental second slope before the maximal load was less well reproduced; this result is probably due to the limited number of parameters used in the Drucker-Prager model, compared to other more sophistical models which use more parameters [32]. Figure 14(a) illustrates the major principal strains for the model, which show the strain concentration at the left base of the RE wall on the diagonal line. e slight rocking at the right base is also observed. ese strain concentrations correspond to the damages observed during experiments (Figure 14(b)).
If a pushover analysis following Eurocode 8 is carried out to assess the in-plane seismic performance of these walls by using the numerical curve of horizontal load-horizontal displacement (more details can be found in [13,35]), the position of the numerical performance point will be close to the experimental performance point. is result means that the numerical model can provide satisfying results for the pushover analysis.

Conclusion
In the present paper, the shear parameters of RE material were rst experimentally investigated by standard direct shear tests. For the standard direct shear tests, two types of specimens were tested: specimens taken at the upper parts of an earthen layer and specimens taken at the middle parts.
e results obtained for the upper part were φ layer 44°and c layer 264 kPa, and for the lower part, they were φ layer 44°and c layer 164 kPa. e interesting nding was that the friction angles obtained for the upper and middle parts of an earthen layer were similar because of the similar roughness of earth grains and that the upper part had higher cohesion than the middle part due to a higher suction.
en, the results obtained on a full-scale shear box were also presented to provide information about the interfaces between earthen layers. e results showed    that the interlayer friction angle was 93% of the intralayer and that the interlayer cohesion was 80% of the intralayer. Finally, these experimental results were used for a numerical simulation of two RE walls subjected to horizontal loading tests. e numerical model could reproduce the maximum force of the experiments, the experimental initial stiffness, the global elastoplastic behavior, and the crack evolution during the experiments. ese results showed the relevancy of the shear parameters used in the numerical model and that the model could be directly used for the pushover analysis on the seismic performance assessment of RE structures.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.