The main actions to which the eco-trench is subjected during its service life are traffic loads. Depending on the location of the traffic load (or the wheel of the vehicle) relative to the trench, failure may be attributed to different mechanisms. Fig. 3 shows two cross-sections of an eco-trench subjected to traffic loads. In Fig. 3a, the loads are located in the width of the trench and overlap with the original pavement on one side, whereas in Fig. 3b the loads are evenly distributed at both sides of the trench.

In the first case, the traffic loads generate bending forces over the expansive concrete pavement and on the original pavement at one side of the eco-trench. These forces cause tensions at the opposite interface (the interface in contact with the pavement without traffic loads). If the pre-compression caused by the expansive concrete’s internal stresses at the interface are lower than the tensions generated by the traffic loads, the trench could lose contact with the surrounding soil or pavement (see Fig. 3a). In the second case, since the traffic loads are symmetrically distributed in the cross-section, the failure of the eco-trench will not be in the form of a loss of contact. Instead, the critical parameter is the shear strength of the interface. If the tangential stresses generated by the traffic loads are higher than the shear strength, a relative displacement could occur and the trench could subside.

To prevent the tensile failure shown in Fig. 3a, the internal stress generated by the expansive concrete should be equal to or higher than the limit-tension that generates the loss of contact. This is represented through Eq. [1], where σ_e represents the internal stress due to the expansion of concrete and σ_n is the normal limit-tension at which the loss of contact due to the traffic load occurs. Eq. [1] defines a minimum value of σ_e, in order to ensure that the stresses in the concrete are satisfactorily transmitted to the surrounding materials (pavement or soil), thus reducing the loads supported by the pipe.

A shear failure of the trench occurs when tangential stresses (τ) in the interface between the materials reach the shear strength of the interface and a relative displacement takes place (see Fig. 3b). According to the Mohr-Coulomb theory, tangential stresses resisted by the interface may be expressed as indicated in Eq. [2], where μ is the friction coefficient and c is the cohesion.

Stress σ in Eq. [2] may be decomposed in the normal limit-tension at which the loss of contact occurs due to the traffic load (σ_n) and in the internal stress generated by the expansion process of the concrete (σ_e), as indicated in Eq. [3]. As a result, the minimum value of σ_e that ensures contact and avoids shear failure is obtained with Eq. [4], after organizing Eq. [3].

In order to determine the range of values for σ_e that ensures the expansion required in the trench, a parametric study was carried out using finite element (FE) analysis, which is explained in the next section.

Finite element software DIANA 9.1 (13) was chosen to simulate the behaviour of the trench due to its extensive material library and analysis capabilities. A 3D model was selected and the mesh was formed by four-node prismatic elements, which were refined for the area of the trench. Fig. 4 depicts the geometry of the model and the main types of elements that depend on the material properties. The geometry was defined by considering that the surrounding soil may present layers with different properties. The dimensions of the model corresponded to those typically found in practice. For the purpose of this study, asphalt with a thickness of 0.08 m was assumed in the top layer. Below that, two sub-base material (graded aggregate) layers were modelled. The top sub-base was 0.08 m thick and the bottom sub-base was 0.11 m. The layers below the graded aggregate represent the original soil.

The narrow trench was evaluated for two widths: 0.15 m and 0.25 m. The depth and the length of the trench, 1.27 m and 2.0 m, respectively, remained constant in both cases. The top 0.15 m corresponded to the expansive concrete layer and the remaining 1.12 m were filled with reused granular material obtained from the excavation of the trench. The soil modelled at both sides of the trench was 1.0 m wide, so the complete model was 2.15 m wide (or 2.25 m, depending on the width of the trench). The pipe was not included in the geometry of the model since it was assumed that the traffic loads in the eco-trench are borne by the expansive concrete layer and transmitted to the surrounding soil. For this reason, the model assumed that the pipe does not bear loads, which is the worst-case scenario in terms of expansion requirements for the concrete since it means that higher values of internal stress are required.

The boundary conditions set in the model corresponded to a spring support perpendicular to each plane of the model. The spring stiffness (k) assumed was 10⁹ N/mm³. Such a high value was defined to maximize the difference in stiffness and hence the shear stresses at the interface between the expansive concrete and the surrounding material. Failure was expected to occur at the interface between the expansive concrete and the surrounding pavement, which was modelled following a Coulomb friction model. Two types of contact between layers were defined in the model: perfect contact and weak contact. The stiffness values adopted in each case were 10¹⁰ N/m³ and 0.1 N/m³, respectively. In the model, the horizontal interfaces were assumed to have perfect contact, whereas the vertical interfaces (between the trench and the surrounding soil and the original pavement) had weak contact, which is the most unfavourable hypothesis.

The horizontal interfaces were assumed to have perfect contact. The vertical interfaces between the trench and the surrounding soil were simulated as having weak contact. Conversely, the vertical interfaces between the asphalt pavement and the expansive concrete were assumed to have perfect contact. This assumption accounted for the fact that the stiffness of the interface between the asphalt pavement and the expansive concrete tended to be considerably higher than for the other vertical interfaces. Because the interface would bear the biggest portion of the load, it would be the most likely to fail. Such an assumption was on the safe side since in real scenarios part of the load may also be transmitted through the interface between the trench and the surrounding soils. This reduces the trench’s dependence on the soil type and soil humidity, which is a clear advantage of the new trench solution proposed here.

Regarding the other materials, linear elastic behaviour was assumed since high levels of stress, which entail a non-linear analysis, were not expected. The stress level in each model was verified to assure that the material remained in the elastic regime. In this context, two main parameters defined the materials: the modulus of elasticity and the Poisson coefficient. The properties of the asphalt and concrete pavement are presented in Table 1. The properties of the granular backfill and the surrounding soil were considered variables of the parametric study, and their values are described in subsequent sections.

The traffic load applied in the model was defined according to Spanish traffic regulations, which specify the maximum load allowed per tyre. Considering the critical case of double tyres, the specified maximum load per axis is 115 kN. To be on the safe side, the value of 120 kN was used in all simulations. To simplify the model and reduce the number of elements, the load was concentrated on the generatrix of the tyre instead of the tyre footprint. This assumption represents a more critical situation that should also be on the safe side. Force was applied in 10 load steps equal to 12 kN. Both load profiles depicted in Fig. 3 were simulated. Once the full force was applied, the shear and the tensile stresses of the interface were assessed and the required confinement to avoid failure was calculated using Eq. [1] and Eq. [4] for the tensile and shear failures.

The friction coefficient was calculated assuming a friction angle of 45º. This value assumes that a rough asphalt surface is left after the trencher excavates the original asphalt pavement, leading to an increase in friction at the interface. The cohesion value used in the calculations was 0.5 MPa.

The variables considered in the numerical simulation were the properties of the backfill and of the surrounding soil. Again, the materials are defined by the Poisson coefficient and the modulus of elasticity. However, given that the Poisson coefficient did not have a significant influence on behaviour, it remained constant during the parametric study. Therefore, the study’s variable was the modulus of elasticity, which varied with the nature and the degree of soil compaction and the backfill. Table 1 summarizes the properties of the materials, including the values considered in the parametric study. The graded aggregate sub-base was divided into two layers (as shown in Fig. 4), each with different properties. Based on the modulus of elasticity values presented in Table 1, the parametric analysis of 15 different combinations of soils was carried out, assuming that the upper layers were always less flexible than the bottom layers.

Fig. 5 presents the minimum values of the confinement stress (σ_e) required to avoid tensile failure for the different modulus of elasticity values considered. The values on the horizontal axis correspond to the modulus of elasticity of the surrounding soil (75, 150 and 300 MPa). Below them are the modulus of elasticity values for the bottom surface layer or sub-base (150, 300 and 600 MPa), the top surface layer or sub-base (300, 500 and 1000 MPa), and the backfill (10, 50, 100, 200 and 300 MPa). Each grey column represents the confinement stress, or internal stress, associated with the trio of values for the surrounding soil and sub-bases given for each column and thus represents the minimum confinement σ_e required. The results in Fig. 5a and Fig. 5b reveal that σ_e decreases as the modulus of elasticity for the sub-base decrease and the modulus of elasticity of the surrounding soil increases. This tendency may be attributed to the fact that when the stiffness of the soil increases, the possible bending forces created by the traffic loads decrease and, as a result, the tension at the interface also decreases.

In Fig. 5a, the values of σ_e are not significantly affected by variations in the modulus of elasticity for the backfill material. For example, for a modulus of 10 MPa the values of σ_e for all three combinations of the rest of the materials are similar to those of a modulus of the backfill of 200 MPa. However, in the case of Fig. 5b the difference is bigger. Such an outcome reveals that the influence of the degree of compaction on the tensile failure depends on the width of the trench. For narrower trenches, failure is most affected by the stiffness of the surrounding soil, whereas for wider trenches compaction has larger repercussions. From the results, it may be concluded that the values of σ_e required to avoid tensile failure range between 0.21 MPa and 0.55 MPa for trenches that are 0.15 m wide and between 0.24 MPa and 0.55 MPa for trenches of 0.25 m wide.

The results in Fig. 6 for shear failure show a different tendency from the outcome described for tension failure. In this case, σ_e increases with the modulus of elasticity for the sub-bases and the surrounding soil, and the influence of the backfill is bigger for both trenches (0.15 m and 0.25 m wide).

Such behaviour may be understood by considering that in soils with higher stiffness, the displacements are smaller and distributed within a shorter length of the trench. Consequently, the tangential stresses are concentrated in a smaller area and higher values of σ_e are required in order to bear the loads. Conversely, the displacements in flexible soils are larger and occur along a bigger length of the trench, leading to smaller tensions. Based on the previous analysis, it follows that the degree of compaction of the backfill has a noticeable influence on the results. The minimum values of σ_e needed to avoid shear failure range between 0.28 MPa and 0.75 MPa for the 0.15 m wide trench (see Fig. 6a) and between 0.30 MPa and 0.87 MPa for the 0.25 m wide trench (see Fig. 6b).

The parametric study shows that the most critical failure mode is shear, since higher internal stress values for the expansive concrete are required in this case. Moreover, a range of values for σ_e may be defined in order to prevent any type of failure in the trench. In terms of the displacements generated by the traffic loads, the FE model indicates that the highest displacement in the top surface of the trench occurs for the most flexible soil, and this displacement is lower than 1.0 mm. This value may be considered negligible since it does not affect the comfort of drivers, pedestrians or the functionality of the trench. Once the ranges of confinements required to assure stability are determined, it is necessary to verify whether the material is capable of generating such confinement.

In ordinary Portland cement, the hydration process is governed by the reactions between the main constituents of clinker (C₃S, C₂S, C₃A and C₄AF), gypsum and water. Most of the hydration reactions of the clinker components are exothermic. As occurs in the case of clinker, the hydration of calcium oxide (CaO) releases heat, approximately 155 Kcal/kgCaO (14). However, this reaction is not only highly exothermic but also expansive. The increment in volume due to the transformation of CaO is twice the initial volume of the reactants.

The increase in temperature caused by adding CaO to the concrete mix might accelerate the speed of the chemical reactions. This depends on the size of the particle or the presence of agglomerates since these may vary the speed of the CaO hydration and thus the temperature. Accordingly, bigger particle sizes may lead to lower hydration temperature values and smaller CaO particles could accelerate the reaction. If CaO particles have a specific surface that is similar to cement particles or are similar to them in terms of size, they would both compete to combine with the water. In such cases, the mixing order of the concrete components should be modified in order to improve the material’s response to shrinkage.

As noted in the previous section, the main effect of adding CaO to concrete mixes is a volumetric expansion of the material. However, the numerical simulation run to determine the requirements for the expansive concrete that would ensure an acceptable response from the eco-trench does not provide a value for volume increment. In fact, the expansive concrete layer is under confined conditions that restrain expansion, and therefore the model yields a range of internal stresses in the concrete.

This situation requires a test method that is capable of measuring the internal stresses generated in the concrete due to the presence of CaO under confined conditions. The ASTM International includes two standards with test methods for evaluating the restrained expansion of expansive cement mortar (15) and concrete (16). Nevertheless, these methods do not evaluate the internal stresses and they restrict the measurement of the expansion to one dimension. In fact, to the best of the authors’ knowledge, there are no methods given in standards or in the literature that are dedicated specifically to the confinement stresses of concrete with CaO.

Considering this, a new testing method was developed at the Universitat Politècnica de Catalunya to evaluate the confinement stress that mortar or concrete experiences at early ages due to the addition of an expansive admixture. This method uses a metallic ring that has a 110-mm radius (R), is 1 mm thick (e) and 40 mm tall and is instrumented with extensometer gauges attached to the ring in the perimeter direction in order to measure its deformation (see Fig. 7a). Given that the properties of the ring are known (see Table 2), it was possible to determine the stress generated by the confined concrete expansion over time.

Besides the deformation of the ring (ε_s), the temperatures for the mix, the environment and the ring were also registered in order to assess their influence on the deformation (see Fig. 7b). The ring was kept in a curing room at 20°C and 100% relative humidity. The confinement stresses were calculated over time in the test using Eq. [5]. In this equation, E_s is the modulus of elasticity of the ring’s steel, R is the ring’s radius, e is the ring’s thickness, ∆t is the variation of the temperature the ring has experienced since the beginning of the test, and α_s is the thermal expansion coefficient.

Fig. 8 shows the σ_e values obtained for the mortars via the proposed testing method. The curves indicate that the highest stresses were generated in the MCR mortar, followed by the MCN and MCL mortars. Furthermore, for the early stages of the setting (up to 8 or 12 hours, depending on the mix), no stresses were measured. At this moment, the mortars were still in a plastic state, and the potential expansion was not converted into stresses due to the low or null stiffness of the material. After setting, the expansions resulted in the stresses shown in Fig. 8. In this regard, the mortar that required the longest amount of time to develop the stresses was the one containing MCL.

The kinetics of the reaction may be analysed through the slope of the curves, which reveal that the rate at which the stresses developed during the first 24 hours was not the same for all mixes. In fact, the mix containing MCR showed a faster reaction than the mixes with MCN and MCL. In terms of the maximum confinement stress registered, the mortars with CaO reached values between 0.2 MPa and 0.7 MPa. The FE model indicated that the range of minimum stress values required to avoid shear failure go from 0.30 MPa to 0.87 MPa, which is the most restrictive condition. Therefore, the value of 0.9 MPa for internal stress may be established as a reference value for avoiding failure and transmitting stresses to the adjacent ground.

The experimental results confirmed that including CaO in the mortar mixes makes it possible to generate the confinement required for eco-trenches. Depending on the type of CaO used in the concrete mix and the environmental conditions, the CaO content should be increased slightly to ensure the minimum value of 0.9 MPa.