Soil compaction is considered the main cause of the physical degradation of agricultural soils (Nawaz et al., 2013). However, soil compaction alone is not always the problem, and therefore a quantification how it affects crop yield and root growth is of high relevance. The effect of soil compaction has led to many debates, especially regarding the establishment of critical limits to plant growth (Moraes et al., 2014; De Jong van Lier and Gubiani, 2015). If there is no chemical or biological limitation, plant growth is mainly directly affected by four physical factors in soils, which are temperature, aeration, resistance, and water content (Letey, 1985). Moreover, it is indirectly affected by several soil characteristics, for example, texture, aggregate structure, and pore size and distribution (Letey, 1985).

Mathematical modeling has become an important tool for describing the functionality of biophysical processes including soil–root interactions, such as water absorption and root growth (Dupuy et al., 2010). The physical conditions of the soil that influence plant growth are dynamic in time and space, and an improvement in the techniques used for the understanding of these conditions is necessary. The use of eco-hydrological models for root growth is, therefore, an important way to increase the understanding of dynamics of soil–plant–atmosphere interactions (Tron et al., 2015). There are many different root system models that can be divided into pure root growth models (Hartmann et al., 2017), such with a focus only on root system’s topology (Berntson, 1997; Pagès et al., 2004) or more mechanistic models (Javaux et al., 2008; Leitner et al., 2010b; Moraes et al., 2018a). The decision to use a specific soil–root model should be related to input data (Bengough, 1997; Javaux et al., 2008; Schnepf et al., 2018), computer power availability (Dupuy et al., 2010), and expected output (Dunbabin et al., 2013). However, there are still very few models describing soil–plant interactions, therefore between the physical (e.g., soil water flow, soil mechanics, gas flow, or solute transport) and biological (e.g., water uptake/release, root system architecture, or shoot and root growth) processes to predict root growth (Vereecken et al., 2016).

The rate of maize root elongation is strongly correlated with soil mechanical resistance to penetration and with the matric potential (Bengough et al., 2011). No functional–structural model of root growth and root water uptake currently addresses the dynamics of those stresses and their effect on maize root elongation during the crop development cycle (Leitner et al., 2010a; Dunbabin et al., 2013; Leitner et al., 2014). In Moraes et al. (2018b), we presented a new model of hydric and mechanical stress effects on root elongation. The model consists of two modules, an extended version of the RootBox model (Leitner et al., 2010a) that reduces root elongation rate due to mechanical and hydric stresses, and a 1D solution of the Richards equation including root water uptake. The model was evaluated with field data for soybean, and we could show that explicitly distinguishing mechanical and hydric stresses induced by dynamically changing soil physical conditions is fundamental for advancing the knowledge of soil–root relationships in soil management. This is because during the crop development cycle, plants undergo a series of phenological changes that affect the transfer of mass and energy in the soil–plant–atmosphere system (De Jong van Lier and Gubiani, 2015).

We hypothesized that maize root growth can be simulated with RootBox model as a function of soil physical condition (mechanical impedance, hypoxia, and water stress) in various compaction levels of an Oxisol. The objective of this work was to evaluate whether this new root growth model can be used to interpret field data of maize grown in a Rhodic Eutrudox in Brazil at different levels of soil compaction. In particular, we aimed to identify the individual contributions of mechanical and hydric stresses to root elongation reduction and thus help to improve soil management at this site. The measurements available from this field site, including the stress reduction function (i.e., mechanical and hydric stresses to reduce root elongation), serve as a reference against which our model is evaluated. As field data for benchmarking root growth models are scarce, we make our results an example of way to serve for benchmarking of other root growth models as well.

The horizontal and vertical variability of soil density in February 2014 can be observed in Figure 2. The compaction levels after soybean cultivation demonstrated the persistence of the differences before the sowing of the second maize crop. Soybean cultivation in the 2013/2014 cropping season, prior to maize cultivation, in association with the effects of the shank-type furrow opener favored reductions in bulk density in the sowing row, mainly in the trafficked areas ( Figures 2C, D), which was important for improved maize root depth in the following crop. The effects of tractor and harvester traffic could be observed up to 30 cm deep, while chiseling had a residual effect up to 20 cm.

The soil water retention curves were altered due to the soil compaction level (Figure 3). Agricultural traffic reduced the total soil porosity, thus altering the frequency and distribution of the pores in the soil (Figures 3B, D, F), and the values of the corresponding soil hydraulic parameters (α and n) of the soil water retention curves (Table 2). Because of agricultural traffic, the water retention was altered, requiring higher tensions for the extraction of water from the soil. For the same matric potentials, between field capacity (−10 kPa) and the permanent wilting point (−1,500 kPa), increases were observed in the water contents due to the increase in the soil compaction level ( Figure 3), increasing the plant-available water capacity in compacted soil (Figure 4 ). The effects of the traffic with tractor or harvester in the no-till system presented increases in soil water retention for all of the layers up to 30 cm in depth, while soil chiseling provided reductions in water retention, principally up to 20 cm in depth (Figure 3).

The dry mass of the shoot of the plant was greater in the no-tillage system and in the soil subjected to tractor traffic (Figure 5A). The increase in compaction by traffic with the harvester or the chiseling of the soil caused reductions in the biomass production of the shoot compared to the soil trafficked with the tractor. Maize grain yield was reduced in the chiseled area and in areas with additional compaction by tractor and harvester traffic compared to the soil under the no-tillage system (Figure 5B).

The growth of the root system of the maize crop was altered due to the soil compaction level (Figures 6 and 7). The root length density ( Figure 6A) and the root dry biomass ( Figure 6B) indicated changes in soil profile due to traffic or soil chiseling. The root length density was altered up to 20 cm deep ( Figures 5 and 6), while for the root dry mass there were changes in the 20–30 cm layer. The chiseling of the soil provided increases in the root dry biomass of maize in the 20–30 cm layer in relation to the tractor trafficked soil. In the 10–20 cm layer, there were reductions in root length in the soil trafficked with the tractor in relation to the no-tillage system. However, in the surface layer (0–10 cm), the soil chiseling reduced root length density in relation to the soil trafficked with the harvester (Figure 6).

The 2D root distribution in the soil profile in relation to the row and interrow of the maize crop was altered due to the soil compaction level ( Figure 7). The increase in the compaction levels in the soil favored increases in the quantity of roots in the soil profile ( Figures 7C, D) in relation to the chiseled soil ( Figure 7A). Principally in the 0–10 cm layer, the harvester traffic (NTC8) provided increases in the root length density in relation to the chiseled soil (Figure 6A). This increase in root length density in NTC8 was conditioned by the higher root concentration near the maize sowing line (Figure 7D).

The modeling of the root growth for the maize crop was performed for the development period between sowing and root sampling, which corresponded to 110 days (Figure 8). The architecture of the maize root system was altered by the compaction level, regarding the number and the length of the roots.

Physical limitations were incorporated into the root growth model. From the 3D explicit root architecture as shown in Figure 8, root length density profiles were computed (Figures 7E–H) and compared to the values that had been measured in the field (Figure 9). In addition, measured root length densities in 2D agreed with simulated values of root length density (Figure 7I). The efficiency of the model in 2D equaled to 0.36, compared to 0.51 in 1D. Among the compaction levels, we observed an overestimate in the reduced tillage system of the root length density in relation to the values measured in the field (Figure 9A). In the other compaction levels, the simulated and measured values were similar. In all treatments, there were reductions of root growth in relation to the potential of root growth without physical stress (Figure 9). Thus, the maximum reduction of root growth at field in relation to a condition modeled without physical stress was reached in the MTC (76%). In addition, simulated root growth in soil profiles considering soil physical condition (stress reduction function) improved the results regarding root length density, and therefore this approach should be used in simulation scenarios that consider water uptake. The relationship between measured and simulated root length density values in 1D (Figure 9E) indicates that the simulated values agreed with the values observed in the field. The Camargo index (d) of 0.86, which evaluates the agreement of simulated and measured values, indicated that the model was adequate for predicting the maize root growth observed in the field.

The modeling of the stresses of root elongation and root growth during the maize development cycle indicated that there were changes in the soil physical conditions during the crop cycle under the compaction levels ( Figure 10). The transpiration rate of maize, during the initial period of development, was lower in the areas with chiseled soil than in the other treatments (Figure 11). The depth of the root system and the root elongation rate were altered due to the water and mechanical stress in the soil profile over a growth season. The time required for the roots to reach at least 50 cm in the soil profile was altered due to the soil compaction level; in the reduced tillage system, this occurred at least 10 days earlier than in the no-till areas (Figure 10). This occurred because of the greater rate of root elongation under conditions of lower soil physical limitation.

The rate of root elongation was reduced because of the combination of the stresses attributable to the soil resistance to penetration ( Figure 12B) and to the matric potential ( Figure 12C), which incorporates the effects of excess water (anoxia or hypoxia) or water deficiency. The contribution of the mechanical and hydric stresses on the total stress demonstrated that most of the stresses that caused root growth reduction were determined by mechanical stresses (Figure 12B). Thus, in areas with tractor or harvester traffic, there were greater contributions from mechanical stresses than from the hydric stresses (Figure 12C). In the MTC, the contribution of the hydric stresses presented greater weight and favored the reduction of the root elongation rate through the interaction of the water and mechanical stresses.

Thus, the reduction of the overall values of root elongation ( Figure 12A ) should be interpreted as daily effects for each root at each position in the soil ( Figure 10 ). The frequency and intensity of the stresses for root elongation describe the physical conditions to which the maize roots were subjected during the entire development period of the crop. The soil compaction levels caused changes in the physical condition of the soil resistance to penetration or the matric potential for the root elongation. For most of the crop development period, stress caused by soil resistance to penetration ( Figure 12B ) was the principal reason for the reduction of maize root growth. In some periods, the reduction of the water content in the soil provided increases in hydric stress, and this caused reductions in the stress parameter for root growth.

Hydric and mechanical stress of maize root elongation was successfully incorporated into the root growth model in 3D, into the RootBox (Leitner et al., 2010a; Moraes et al., 2018a). The association of the root growth model with the flow of water in 1D (van Dam and Feddes, 2000) and the absorption of water by the roots due to the matric flux potential (de Jong van Lier et al., 2008) represent an advancement in the understanding of biophysical processes in the soils. The model was able to predict maize root growth due to soil physical conditions ( Figure 8 ). In the future, this model could be associated with other models to predict root growth based on climatic predictions and allow the anticipation of agricultural strategies to prevent limiting conditions to root growth from arising in agricultural crops.

The soil compaction, caused by the harvester traffic, resulted in significant reductions in grain yield and shoot biomass ( Figure 5 ). However, the soil chiseling also reduced these parameters in relation to the no-tillage system ( Figure 5 ). The harvester traffic provided increases in the number of roots in the soil profile, principally in the regions close to the sowing furrow ( Figure 7 ). In general, there were changes in the soil profile in the distribution of the root system, mainly in the 30 cm nearest to the sowing row.

Soil compaction levels increased the physical limitations to root growth, as was described within the model by the frequency of the total stresses ( Figure 12A ). Our simulations enable a quantified hypothesis whether this stress is due to soil penetration resistance ( Figure 12B ) or due to the effect of the water matric potential in the soil ( Figure 12C ). Therefore, the model offers a way to analyze and explain how hydric and mechanical stresses during the development cycle are altered due to the meteorological conditions precipitation and evapotranspiration ( Figure 11 ). This is of high relevance since these factors are responsible for changes in the soil physical limitation to maize root elongation ( Figure 10 ).

The intermediate levels of bulk density, in the no-tillage system, provided the best physical conditions for maize crop production performance ( Figure 5 ), as was described due to soil physical quality in a long-term tillage system (Moraes et al., 2016). Thus, soil structure and its physical quality was damaged due to soil chiseling, reducing the plant-available water capacity in chiseling soil ( Figure 5 ) as it was with soil compaction, with increasing of mechanical impedance, and they both reduced the grain yield of maize. In trafficked soil, there was an increase in plant-available water capacity. That happened due to changes in soil retention curve with higher reductions of macropores but few changes in micropores in compacted soils. Thus, the water storage in the soil was affected by changes in pore size distribution, which decrease larger pores and increase micropores promoting increases in water volume storage in soil profile. Therefore, reduction of macropores in compacted soil affected soil aeration, which affects root growth and grain yield. In a long-term experiment in an Oxisol soil, chiseling reduced the yield grain of soybean (Moraes et al., 2017b). Thus, in loose soil, the main factor to reduce the yield and root length density should be due to the reduction of plant-available water capacity ( Figure 4 ) promoted by reduction of size and stability of soil aggregates (Nunes et al., 2015) in chiseled areas. Thus, there was an increase in the water stress to crop growth ( Figures 10A and 12C ) in chiseled soils.

The changes in the architecture of the maize root system ( Figure 8 ) in the soil profile ( Figure 7 ) were the result of the physical-hydric stress levels during the development cycle ( Figure 10 ). The increase in the root length under the highest degree of compaction was associated with pore connectivity in the soil profile (Bengough, 2012a) which promotes reduction in root diameter and increases of root length (Duruoha et al., 2007). The increase in root length density, mainly in the 0–10 cm layer ( Figure 6 ), is principally due to the confinement of the roots in the sowing furrow ( Figure 7 ), where there were better physical conditions for root growth. This confinement of the roots due to increasing compaction levels directed the roots to sub-superficial layers (∼30 cm depth) nearest to the sowing line ( Figure 7 ). Thus, this root system confinement in compacted soil reduced the soil volume explored in superficial soil layers and increased the volume in deeper soil layers. This affected water uptake by the root system, as previously observed in structured subsoil by White and Kirkegaard (2010). In addition, the soil type and management must be considered and are likely to be more important factors than genotype to promote increased rooting depth (Gao et al., 2016).

The modeling was efficient at predicting the maize root growth ( Figure 8 ) observed in the field ( Figure 7 ) in 1D ( Figure 9E ) at the soil profile, and was useful for observing the effects of hydric and mechanical stress during cultivation. However, root system length distributions in 2D in the field was not very well simulated by the model ( Figure 7I ), especially for loose soil (MTC). Materechera et al. (1991) showed in a study with many monocotyledons and dicotyledonous that root elongation of maize in compacted soil (0.44 mm day⁻¹) was higher than all other cereals (barley 0.31 mm day⁻¹; oats 0.32 mm day⁻¹; rice 0.31 mm day⁻¹; sorghum 0.34 mm day⁻¹; wheat 0.41 mm day⁻¹). This higher penetration of maize roots was due to an increased root diameter (maize with 1.39 mm day⁻¹) compared with other cereals (barley 0.066 mm day⁻¹; oats 0.076 mm day⁻¹; rice 0.056 mm day⁻¹; sorghum 0.078 mm day⁻¹; wheat 0.076 mm day⁻¹). Roots of maize grew slower than dicotyledonous in compacted soil (e.g., lupine 0.71 mm day⁻¹, pea 0.70 mm day⁻¹, faba bean 0.68 mm day⁻¹, soybean 0.57 mm day⁻¹, and cotton 0.45 mm day⁻¹). Materechera et al. (1991) suggest that there was a significant positive correlation (r=0.78, p<0.05) between root diameter and elongation over all the species in stressed plants. In addition, the study showed that dicotyledonous species were more able to elongate in the strong medium than monocotyledons due to the higher root diameter of dicotyledonous. Thus, the higher diameter of crown roots of maize can facilitate root penetration in harder soils better compared to other cereals (Materechera et al., 1991). This indicates that grasses experience better developmental conditions under soil compaction, principally because of the adventitious seminal roots that are emitted from the crowns of the stem above the surface of the soil. In addition, in a dicotyledonous architecture, the taproot, which determines the growth direction of root system, is more affected by soil physical limitations that can alter the root direction in the soil profile. However, there was an overestimate of the root length density in loose soil (MTC) ( Figure 9 ), probably because the water stress was greater in field than that simulated in the model. This discrepancy should be due to soil structure changes due to soil chiseling (Moraes et al., 2016), which affect the storage ( Figure 4 ) and flux of the water in the soil profile, and this is not reflected well in the soil water retention curve ( Figure 3 ). In addition, there are other factors (e.g., hydraulic root resistance, root radial and axial conductivity, root mucilage and rhizosphere hydraulic properties) that were not included in this model, as well as biological (e.g., rhizosphere microorganisms) and chemical factors (e.g., chemical signals, redox potential, and nutrient available) (Vereecken et al., 2016) that could affect the root growth.

Models of root growth, because of soil hydric and mechanical stress on the elongation of roots, are dynamic in time and space and are, therefore, useful for the interpretation of the soil alterations that can affect plant growth. Mechanical stress for root elongation can be changed due to soil structure (e.g., presence of biopore and pore continuity) (Bengough, 2012a). Thus, in this root growth model, the mechanical stress to root elongation is represented by the soil penetration resistance curve, which can be used to estimate the relation between root resistance and penetrometer resistance (Bengough and Mullins, 1991). Also, an age-hardening effect of soil tillage over time can be included into the model by modifying the soil penetration resistance curve (Moraes et al., 2017a). These studies with root growth modeling (i.e., different root systems) (Tron et al., 2015) can help to understand the root contribution to produce biopores in the soil profile, especially in areas under no-tillage. The root system of maize crop was influenced only little by soil compaction, presenting high resilience to overcome the problems caused by the agricultural traffic in this Rhodic Eutrudox. In addition, maize root growth was not limited by compaction due to machine traffic in an Ultisol, and there were increments of grain yield due to increment of soil water retention in sand soils with traffic (Moraes et al., 2018b); this indicates that maize could be an option to use in compacted soils.

Observed root length density profiles follow an exponential decay shape as commonly known for maize (Pagès et al., 2004). They reach a depth up to 2 m (Canadell et al., 1996), and the highest root length density was observed near the sowing furrows in the soil trafficked by the harvester ( Figure 7D ), with values up to 6 cm cm⁻³. These values are close to the maximum root densities observed in the literature (Bengough, 2012b). Because the physical properties that limit root elongation (soil resistance to penetration, aeration, and water content) are heterogeneous and dynamic in time, the only way to infer their effect on overall root development and root water uptake was through modeling ( Figure 10 ).

In line with results of, e.g., Nosalewicz and Lipiec (2014), actual transpiration (i.e., root water uptake) ( Figure 10 ) was reduced with increasing soil compaction. Biopores decrease the axial pressure on the root tip, while still exerting radial pressures on the root in narrow pores (Bengough, 2012a) decreasing the root diameter (Jin et al., 2013). In the chiseled soil, which has a higher macropore density (Moraes et al., 2016), maize plants experienced greater periods of hydric stress. Continuous pores and biopores in soil profile improved water availability to plants, but macropores in chiseling soil are not very well connected in the soil profile (Pires et al., 2017). Thus, macropores in chiseled soil do not help to improve rooting depth due to changes in the soil water retention (Rabot et al., 2018) with faster water drainage (Armindo and Wendroth, 2016) and reduced unsaturated hydraulic conductivity (Ghanbarian-Alavijeh and Hunt, 2012).

As a result of the alteration of the soil structure by chiseling (Moraes et al., 2016), the roots of the crops were more susceptible to periods with hydric stress, increasing the frequency of days with greater reductions in root elongation due to the soil water matric potential ( Figure 12 ). As a result, reductions in shoot biomass production ( Figure 5A ), grain yield ( Figure 5B ), and root length density ( Figures 6A and 7A ) occurred in relation to the soil under no-tillage system.

Maize root growth modeling, including soil physical limitations (mechanical and hydric stress), can be used for the analysis of architecture development associated with soil water flow models, increasing the fundamental understanding of stress that acts on the growing roots. Experimental data showed that the no-tillage system provided the best soil physical conditions for maximum maize yields. In the other scenarios, yield was reduced due to soil chiseling and/or through the excessive level of compaction caused by harvester traffic. Our simulations and analysis showed that the contribution of the mechanical stresses to the reduction of maize root growth was more important in areas with agricultural traffic; however, in areas with soil chiseling, the hydric stresses were the most important component of the total stresses on root elongation of maize, due to the increase of pore diameter and reduction of soil water retention. The root system of maize crop showed the potential of root length density increases due to increased soil compaction. The hypothesis of this work was confirmed that maize root growth could be simulated including mechanical and hydric stresses in the RootBox model. Our results improve the understanding of root growth in soils with physical limitations. As such, they facilitate the application of benchmarking models of root system development and water uptake. We showed that compared to the baseline scenario, explicit consideration of mechanical and hydric stresses improved the agreement between model and data.

MM, HD, and JF designed the field experiment and performed data analyses. MM and JB performed the field sampling and analyzed the soil and roots. DL and AS performed the root growth code. MM performed the root growth modeling. MM wrote the first draft of the manuscript. All authors contributed to manuscript revision, read and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.