Crushed rocks stabilized with organosilane and lignosulfonate in pavement unbound layers: Repeated load triaxial tests

Abstract

The creation of the new “Ferry-Free Coastal Highway Route E39” in southwest Norway entails the production of a remarkable quantity of crushed rocks. These resources could be beneficially employed as aggregates in the unbound courses of the highway itself or other road pavements present nearby. Two innovative stabilizing agents, organosilane and lignosulfonate, can significantly enhance the key properties, namely, resilient modulus and resistance against permanent deformation, of the aggregates that are excessively weak in their natural state. The beneficial effect offered by the additives was thoroughly evaluated by performing repeated load triaxial tests. The study adopted the most common numerical models to describe these two key mechanical properties. The increase in the resilient modulus and reduction in the accumulated vertical permanent deformation show the beneficial impact of the additives. Furthermore, a finite element model was created to simulate the repeated load triaxial test by implementing nonlinear elastic and plastic constitutive relationships.

Graphical abstract

Keywords

organosilane / lignosulfonate / crushed rocks / pavement unbound layers / repeated load triaxial test / finite element analysis

Introduction

Project background

According to the Norwegian Public Roads Administration (NPRA), the overarching aim of the “Ferry-Free Coastal Highway Route E39” project is to enhance the condition of the existing road network along the coast of southwest Norway by revamping the highway infrastructure present between Trondheim and Kristiansand [1]. This project is highly significant for the Norwegian economic system [2]. The widespread tunneling blasting operations that are being conducted to create new and faster routes generate considerable quantities of crushed rocks. These resources could be employed as aggregates in the unbound courses of the highway itself or other road pavements present nearby, thus curtailing the use of non-local materials, promoting a sustainable construction [3–5], and consequently bolstering Norway’s national goal of becoming carbon neutral during this decade [6].

To avoid the formation of excessive distresses in the road structure [7], the NPRA demands that the aggregates (unbound granular materials, UGMs) meet some qualification tests [8,9] regarding shape [10], flakiness [11], resistance to fragmentation (Los Angeles test, LA) [12], and resistance to wear (micro-Deval test, MDE) [13,14].

Previous research [15] has investigated the geological origin of rocks present along the E39 highway. Three rock types (referred to as M1, M2, and M3) were collected and characterized according to the aforementioned standard tests. The qualification tests are met by M1 (“strong” aggregates), whereas M2 and M3 exceed the limit values of the LA and MDE tests (“weak” aggregates) and therefore cannot be employed in their natural status in the unbound courses of road pavements.

Stabilization technologies

In recent decades, different stabilization solutions for unbound materials have been investigated, e.g., bitumen, cement, fly ash, and lime, just to mention a few [16–23]. Furthermore, two innovative technologies have exhibited preliminary positive outcomes when it comes to enhancing the mechanical properties of “weak” aggregates [24]. These stabilizing agents are based on organosilane and lignosulfonate, and are designated as polymer-based (P) additive and lignin-based (L) additive in this study, respectively. These technologies modify the mechanical performance of aggregates entailing macroscopic enhancement [25–29]. The P agent promotes the creation of strong siloxane (= Si-O-Si=) chemical polar bonds. The L agent is an organic product comprising both hydrophilic and hydrophobic linkages [30,31].

Objectives

The effectiveness of the stabilizing agents was investigated in the laboratory by means of repeated load triaxial tests (RLTTs), which evaluated the resilient modulus and resistance against permanent deformation. The most common numerical models were adopted to describe these two key mechanical properties, thus expanding the research accomplished thus far [32].

Furthermore, a finite element model simulating the RLTT was created. Numerical analyses were carried out to study the behavior of UGMs, and non-linear elastic and plastic constitutive relationships were considered [33]. The experimental and numerical results were compared in terms of vertical permanent deformation.

Materials and methods

Materials tested

Referring to the three crushed rock types (M1, M2, and M3) initially collected [15] to represent the geology spread along the highway alignment, this study focuses on the weak material M2. It has a metamorphic origin and is a fine-grained felsic and micaceous rock. The numerical models adopted and discussed for M2 in the following sections could also be analogously extended to M3 (or other aggregate types).

Repeated load triaxial test

The stiffness and the resistance to permanent deformation of UGMs were thoroughly investigated using RLTTs. The stress level, moisture content, dry density, grading, and mineralogy [34–37] are the most relevant variables that determine the mechanical performance.

Figure 1 displays the preparation procedure for running a RLTT. Initially, 7300 g of aggregates were blended (Fig. 1(a)) considering the selected gradation depicted in Fig. 2 with the reported upper and lower grain size distribution curves for a base layer [7,8]. Water and additive, if necessary, are added to the aggregates, which rest for 24 h to allow the moisture to be distributed uniformly inside plastic bags (Fig. 1(b)). Both organosilane and lignosulfonate were blended with M2 at the optimum moisture content (OMC), which is equal to 5% in mass for the considered grading curve distribution. The quantity of organosilane mixed with the crushed rocks was 0.5% (40 g), and the amount of lignosulfonate added was 1.5% (120 g). The former admixture is effective after application, whereas the latter admixture requires curing to attach to the aggregates. A Kango 950X vibratory hammer (total weight 35 kg, frequency 25–60 Hz, amplitude 5 mm) compacted the specimen layers for 30 s (Fig. 1(c)); the bulk density and dry density were assessed as specified by Ref. [38]. The sample was fully compacted inside the steel mold (Fig. 1(d)); afterwards, it was extracted vertically by means of a dedicated ejecting tool and the specimen was encapsulated in a latex membrane (Fig. 1(e)). In the last step, another latex membrane, two metal end plates, four plastic rings, and two hose clamps sealed the sample, thus avoiding the penetration of the water used to exert the confining pressure (Fig. 1(f)). Three and three linear variable differential transducers (LVDTs) evaluated the axial and radial deformations, respectively (Fig. 1(g)). Finally, the test was ready to run (Fig. 1(h)).

Two types of stresses were applied during the RLTT: uniform confining stress (σ_t, triaxial or confining) and vertical dynamic stress (σ_d, deviatoric); the latter varied following a sinusoidal pattern. According to the multi-stage low stress level (MS LSL) testing procedure, five σ_t values (σ_t = 20, 45, 70, 100, and 150 kPa) defined as many testing sequences: each sequence comprised six steps and each step was characterized by a precise σ_d peak value [39]. Figure 3 reports the stress path for the MS LSL procedure considering σ_d and the bulk stress θ (θ = σ₁ + s₂ + σ₃ = σ_d +3σ_t, where σ₁, σ₂, σ₃ are the principal stresses). One RLTT included up to 30 loading steps; for each of them, the peak value of σ_d was applied 10000 times with a frequency of 10 Hz. The overall results were assessed by testing two replicate specimens for each studied proportioning. For example, Figure 4 shows three investigated samples after completion of the RLTT.

As previously mentioned, the L additive requires curing to attach to the material particles. Therefore, the samples (Figure 1(f)) treated with this agent were conditioned at 50°C for 24 h and subsequently at 22°C for 24 h, reaching a water content of approximately 2%. Their performance was compared to that of untreated samples with water content w = 1% in mass. This is a conservative evaluation as the mechanical properties reduce when w augments [40]. In contrast, the P additive is effective after its application; therefore, these treated samples were compared to untreated samples with w = 5%. Because of the differences in w, the results described in Sections 3.1 and 3.2 are portrayed with two plots each time: one referring to organosilane, and one referring to lignosulfonate.

Resilient modulus

Given a dynamic deviatoric stress Δσ_d and a constant σ_t, the resilient modulus M_R is expressed as

(1)M_{\mathrm{R}}={\displaystyle \frac{\mathrm{\Delta }{\sigma }_{\mathrm{d}}}{{\epsilon }_{\mathrm{v}\mathrm{e}}}},

where ε_ve is the vertical resilient strain. The resilient modulus represents the UGM behavior under repeated traffic loading and is a key parameter for any mechanistically based design method [33,41,42].

M_R can be efficiently described by non-linear relationships considering a variety of different parameters [35]; the equations presented in the following subsections are used to evaluate the M_R of the RLTT samples. All regression parameters are obtained through the least-square method.

Hicks and Monismith model

Hicks and Monismith formulated a simple and effective connection between M_R and θ [43].

(2)M_{\mathrm{R}}=k_{\mathrm{1},\mathrm{H}\mathrm{M}}{\sigma }_{\mathrm{a}}{\left({\displaystyle \frac{\theta }{{\sigma }_{\mathrm{a}}}}\right)}^{k_{\mathrm{2},\mathrm{H}\mathrm{M}}},

where σ_a is the reference pressure (100 kPa) and k_1,HM, and k_2,HM are regression parameters. This relationship proposes a neat evaluation of the mechanical performance in an M_R–θ plot. Owing to its simplicity, this model is mostly used to interpret the resilient modulus of UGMs [35].

Uzan model

The Uzan model considers the presence of three parameters, namely, M_R, θ, and σ, as in Ref. [44]

(3)M_{\mathrm{R}}=k_{\mathrm{1},\mathrm{U}\mathrm{Z}}{\sigma }_{\mathrm{a}}{\left({\displaystyle \frac{\theta }{{\sigma }_{\mathrm{a}}}}\right)}^{k_{\mathrm{2},\mathrm{U}\mathrm{Z}}}{\left({\displaystyle \frac{{\sigma }_{\mathrm{d}}}{{\sigma }_{\mathrm{a}}}}\right)}^{k_{\mathrm{3},\mathrm{U}\mathrm{Z}}},

where k_1,UZ, k_2,UZ, and k_3,UZ are regression parameters. In addition to the formulation proposed by the Hicks and Monismith model, the one suggested by Uzan considers the bulk stress and deviatoric stress at the same time. These two factors are the most important factors affecting the resilient modulus of UGMs [35]. The Uzan model enables a useful comparison in a three-dimensional M_R, θ, and σ_d plot. It is also worth mentioning the Uzan and Witczak model, which takes into consideration the octahedral shear stress τ_oct instead of the deviatoric stress σ_d in order to include full three-dimensional conditions [45]. Nevertheless, the application of the Uzan and Witczak model is of limited interest in this study, as τ_oct can be easily correlated to σ_d as follows: τ_oct = \sqrt{2}σ_d/3, for σ₂ = σ₃ (condition valid for the performed RLTTs).

Accumulated permanent deformation

The deformational response of UGMs can be divided into two parts: elastic (or resilient) and plastic (or permanent). The latter, occurring due to the wearing and crushing of the grains, may lead to pavement distress (rutting, potholes, cracking, etc.) [36]. Moreover, the UGM permanent deformation consists of two phases. In the first phase, there is a rapid increase in permanent strain with the application of load; in the second phase, the deformation rate becomes constant and is characterized by volume change [46,47]. The permanent deformation increases with moisture content, as water reduces the effective stress and friction [40].

A number of formulations can be employed to describe the development of vertical permanent deformation ε_vp based on the applied load pulses N or as a combination of one or more of the following parameters: mean bulk stress θ_m (θ_m = θ/3), mean deviatoric stress σ_d,m (σ_d,m = σ_d/3), and vertical resilient deformation ε_ve [48].

(4){\epsilon }_{\mathrm{v}\mathrm{p}}=f_{\mathrm{1}}(N)f_{\mathrm{2}}\left({\theta }_{\mathrm{m}},{\sigma }_{\mathrm{d},\mathrm{m}},{\epsilon }_{\mathrm{v}\mathrm{e}}\right)\mathrm{.}

This study takes into consideration the models described in the following subsections. All regression parameters are obtained through the least-square method. As illustrated in Section 2.2, an RLTT is composed of 30 steps (or, equivalently, 30 stress-paths); the data obtained for each step are fitted, which may create discontinuities between the end of a step and the beginning of the following one, as displayed in the images in Section 3.2.

Coulomb model

The Coulomb formulation considers that the mobilized angle of friction ρ and the angle of friction at incremental failure ϕ describe the degree of mobilized shear strength and the maximum shear strength, respectively [49]. Consequently, these two angles define the material according to three types of performance (elastic, elasto-plastic, and failure) as presented in Table 1, in which each loading step is classified based on the average strain rate \dot{\epsilon } developed between the cycles from 5000 to 10000 [49].

The elastic limit and the failure limit are defined by the following equations, respectively:

(5){\sigma }_{\mathrm{d}}={\displaystyle \frac{\mathrm{2}\sin \rho \left({\sigma }_{\mathrm{3}}+a\right)}{\mathrm{1}-\sin \rho }},

(6){\sigma }_{\mathrm{d}}={\displaystyle \frac{\mathrm{2}\sin \varphi \left({\sigma }_{\mathrm{3}}+a\right)}{\mathrm{1}-\sin \varphi }},

where the apparent attraction a is specified as 20 kPa [37].

Barksdale model

Barksdale studied the UGM behavior by means of RLTTs and found that the accumulation of permanent vertical strain ε_vp is proportional to the logarithm of the number N of load cycles [50] as follows:

(7){\epsilon }_{\mathrm{v}\mathrm{p}}=a_{\mathrm{B}\mathrm{A}}+b_{\mathrm{B}\mathrm{A}}\mathrm{Log}\left(N\right),

where a_BA and b_BA are regression parameters.

Sweere model

Sweere also performed a series of RLTTs on UGMs and found that the logarithm of permanent vertical strain ε_vp is proportional to the logarithm of the number N of load cycles [51] as follows:

(8)\log \left({\epsilon }_{\mathrm{v}\mathrm{p}}\right)=a_{\mathrm{S}\mathrm{W}}+b_{\mathrm{S}\mathrm{W}}\mathrm{Log}(N),

where a_SW and b_SW are regression parameters.

Time hardening approach for Barksdale and Sweere models

Both the Barksdale and Sweere models have been developed to fit the data of a single-stage (SS) RLTT. The results are plotted in a graph with the number N of load repetitions along the x-axis and the accumulated vertical permanent deformation ε_vp along the y-axis, where the first value is equal to zero. In a multi-stage (MS) RLTT, the first ε_vp of each loading step is different from zero (except for the first RLTT step). As this study performs MS RLTTs, the time hardening approach is adopted to describe the experimental data [52,53]. According to the time hardening approach, the ε_vp values corresponding to each loading step are treated as the last part of as many curves; each of them ideally corresponds to an SS RLTT, in which the first ε_vp is zero. This study calculates 30 curves (one for each loading step). Each curve is evaluated using the least-square method with a third-order polynomial expression. The data used to evaluate this third-order polynomial curve are the experimental ε_vp values for the specific step. Finally, for each loading step, the parameters of the chosen model (a_BA, b_BA for the Barksdale model or a_SW, b_SW for the Sweere model) are calculated through a least-square regression considering the experimental ε_vp values of the specific loading step and the first point of the ideal curve (with the first ε_vp value equal to zero).

Hyde model

Hyde established the following formulation for permanent vertical strain ε_vp encompassing the mean deviatoric stress σ_d,m and triaxial stress σ_t [54]:

(9){\epsilon }_{\mathrm{v}\mathrm{p}}=a_{\mathrm{H}\mathrm{Y}}{\displaystyle \frac{{\sigma }_{\mathrm{d},\mathrm{m}}}{{\sigma }_{\mathrm{t}}}},

where a_HY is a regression parameter.

Shenton model

Shenton proposed the following formulation for permanent vertical strain ε_vp including the maximum mean deviatoric stress σ_d,m,max, and triaxial stress σ_t [55]:

(10){\epsilon }_{\mathrm{vp}}=a_{\mathrm{SH}}{\left({\displaystyle \frac{{\sigma }_{\mathrm{d},\mathrm{m},\max }}{{\sigma }_{\mathrm{t}}}}\right)}^{b_{\mathrm{SH}}},

where a_SH and b_SH are regression parameters.

Finite element method RLTT modeling

The RLTT is modeled using COMSOL Multiphysics software [56]. The goal is to describe the accumulation of vertical permanent deformation, and the numerical and experimental results are compared. Figure 5 shows a portion of the model; the problem is two-dimensional axisymmetric, and quadrilateral elements are used in the mesh (height 180 mm, radius 75 mm, Poisson’s ratio 0.3, and density 2300 kg/m³). A fixed boundary constraint was applied at the bottom.

Different models can describe the UGM behavior: non-linear elastic [33,57] and plastic [58,59] relationships have been used by researchers to interpret the UGM behavior. The following subsections detail the constitutive relationships implemented in this study.

A time-dependent analysis is performed and the total time is 30000 s, which is the actual duration of an RLTT. Each loading step, as reported in Section 2.2, corresponds to a specific combination of σ_t and σ_d and lasts for 1000 s; the repetition of the deviatoric pulse is not considered.

Modeling non-linear elasticity

COMSOL Multiphysics enables the implementation of a non-linear elastic model by specifying the elastic modulus law. The resilient moduli obtained by the Hicks and Monismith and Uzan models are implemented.

Modeling plasticity

Tresca and von Mises yield criteria are used to model the associated flow plasticity. Each model requires the definition of two parameters, the initial yield stress σ_y and plastic tangent modulus, to define the linear isotropic hardening. The initial yield stress σ_y is equal to the deviatoric stress σ_d of each loading step because plastic deformation takes place from the beginning of each step. The plastic tangent modulus is evaluated as a secant value using the least-squares method in a graph displaying σ₁−σ₃ along the y-axis and ε_vp along the x-axis for the Tresca model or (2/3)·ε_vp along the x-axis for the von Mises model, as illustrated in Figs. 6 and 7, respectively.

Even if UGMs derive the bulk of their strength from friction, and the Tresca and von Mises criteria contain no frictional strength components, these models can represent the cohesion generated by the stabilizing additives.

Furthermore, UGMs are not regarded as viscous materials in the sense that applying a constant load does not cause a time-dependent deformation. It may be worth mentioning that models for viscosity could be adapted to account for the gradual increase in ε_vp per RLTT load cycle [60].

Test results and discussion

Resilient modulus

Figures 8(a) and 8(b) display M_R based on the Hicks and Monismith formulation. The black and magenta colors correspond to untreated and treated materials, respectively.

In addition to the Hicks and Monismith model, the Uzan model takes into consideration the deviatoric stress σ_d as a further parameter to characterize M_R. The three-dimensional plots reported in Figs. 9(a) and 9(b) refer to P and L additives, respectively.

Table 2 presents the values of the regression parameters for the Hicks and Monismith and Uzan models.

All the models clearly show that the additives are effective solutions to enhance the resilient modulus M_R of the aggregates.

Accumulated permanent deformation

The use of the stabilizing technologies also leads to significative improvements when it comes to the deformation properties of the aggregates. Figure 10 shows the mobilized angle of friction ρ and the angle of friction at incremental failure φ for the untreated and treated materials; both angles, ρ and φ, are enhanced by applying the additives. Table 3 details the values of the boundary angles.

The accumulated vertical permanent deformations evaluated according to the Barksdale and Sweere models are shown in Figs. 11 and 12, respectively. These criteria fit the experimental data corresponding to each single loading step with the time hardening approach discussed in Subsection 2.4.4. The treated materials show considerably less permanent deformation than the untreated materials.

The Hyde model results are displayed in Figure 13. Each loading sequence corresponds to a straight line; therefore, five straight lines correspond to the MS RLTT.

Table 4 reports the regression parameter a_HY corresponding to each RLTT loading sequence.

The Shenton model results are displayed in Fig. 14. Each loading sequence corresponds to a curve; therefore, five curves correspond to the MS RLTT.

Table 5 reports the values of the regression parameters a_SH and b_SH for each loading sequence. All the models adopted to describe the accumulation of permanent deformation indicate that the treated aggregates perform better than the untreated ones.

Finite element method RLTT modeling

The aim of the modeling is to evaluate the permanent vertical deformations ε_vp and compare the numerical and experimental results. The choice of the nonlinear elastic model (Hicks and Monismith, Uzan) is irrelevant, as this part does not entail plastic deformations. The first modeling attempt implements the Tresca plasticity criterion. Figure 15(a) displays the results for the P additive, whereas Fig. 15(b) shows the results for the L additive.

The second modeling attempt implements the von Mises plasticity criterion. Figure 16(a) displays the results for the P additive, whereas Fig. 16(b) displays the results for the L additive.

The Tresca plasticity criterion tends to overestimate the results, whereas the von Mises plasticity criterion tends to underestimate them. Table 6 reports the values of the plastic tangent modulus.

Conclusions

This study investigated the use of two stabilizing agents based on organosilane and lignosulfonate to enhance the mechanical performance of aggregates to be employed as construction materials in unbound courses of road pavements. The investigation was achieved by means of RLTTs.

The experimental data obtained were analyzed according to the models available in the literature regarding both the resilient modulus and accumulated vertical permanent deformation. A finite element model was developed to simulate the actual RLTT and compare the numerical and experimental results in terms of accumulated vertical permanent deformation. Non-linear elastic and plastic constitutive relationships were implemented. The following conclusions can be drawn.

1) The outcomes of the RLTTs indicate that both the P and L agents remarkably improve the mechanical properties of the aggregates, and the enhancement includes both the resilient modulus and the development of permanent deformation.

2) The models used to interpret the experimental data referring to the resilient modulus (Hicks and Monismith, Uzan) and vertical permanent deformation (Coulomb, Barksdale, Sweere, Hyde, and Shenton) highlight that the investigated additives are effective technologies for enhancing the mechanical properties of crushed rocks.

3) In the finite element simulation of the RLTT, the Tresca plasticity model tends to overestimate the experimental results of permanent vertical deformation, whereas the von Mises plasticity model tends to underestimate them.

4) Both organosilane and lignosulfonate show promising results in stabilizing “weak” aggregates. The objective of future research could, for example, deal with accomplishing full-scale tests. Moreover, the finite element model can be expanded to the analysis of an actual road.

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