**1. Introduction**

Soft soil is widely distributed in coastal areas with many defects such as large natural moisture content, excessive compression capacity, and poor bearing capacity [1–3]. In geotechnical engineering, deep mixing method is generally adopted to improve the strength of soil by adding cement to the soil [4–8]. The soft soil is reinforced to impart higher strength through a series of reactions between raw materials and curing agent [9–16]. In addition to the traditional cement curing agent, researchers are constantly looking for some novel materials such as nano materials to improve the bearing capacity of the soft soil layer [2,3,14,15,17–20].

Nano cemented soil refers to the cement-soil mixture which is improved by adding nano materials as admixtures into the mixture of water, cement and soil [20–22]. At present, the nano materials for enhancing cemented soil mainly include nano titanium oxide, nano montmorillonite, nano magnesia, nano silicon, nano alumina, etc. Previous experimental results show that adding nano admixtures can improve the performances of cemented soil such as its soil strength and anticorrosive properties. Based on some recent studies [2,3], nanometer magnesia (Nm) can be added into cemented soil to improve its mechanical performance.

In the past few years, mathematical models have been adopted to study the stress–strain response of soils [23–31]. In term of the stress–strain behaviors of cemented soil, a large number of researches have been reported [2,3,5,6,13–18,32–37]. However, the reported mathematical models have some limitations particularly in the modeling of the constitutive behavior of nano magnesia-cement-reinforced seashore soft soil (Nmcs) which manifests different stress–strain behaviors under varying conditions [2–4,17,18,38,39].

This study aims to propose a REP (reinforced exponential and power function)-based mathematical model to simulate the various stress–strain behaviors of Nmcs under varying circumstances. The mathematical characteristics of di fferent constitutive behaviors are firstly examined. Then, the conventional mathematical models for stress–strain behavior of cemented soil are discussed. Based on the mathematical characteristics of various stress–strain curves and the features of di fferent conventional models, a new REP model for characterizing hardening behavior, modified falling behavior and strong softening behavior is proposed. Furthermore, a CEL (coupled exponential and linear) model improved from the REP model is also proposed which is able to simulate the S-type stress–strain behavior of Nmcs. Comparisons between conventional models and the proposed REP-based models are made which verifies the feasibility of the proposed models.

#### **2. Mathematical Characteristics of Stress–Strain Constitutive Relations of Nmcs**

#### *2.1. Materials and Samples*

The seashore soft soil discussed in this study was collected from coastal areas in Shaoxing, Zhejiang Province, China. Its specific gravity, liquid limit, and plastic limit were 2.6, 43.5%, and 30%, respectively. According to American Society of Testing Materials, ASTM (1994), it belongs to silty clay [2]. In direct shear test, the thickness of the shear plane is assumed to be zero which means the corresponding shear strain cannot be calculated; thus in this case shear displacement is applied to represent the strain behavior. In the following, a more general symbol δ is therefore used to represent shear deformation characteristics, i.e., shear displacement or shear strain.

The soil samples were prepared under a standard maintenance temperature of 20 ◦C with a relative humidity of 95%. The mechanical tests were performed after 28 days' standard curing time. For the tests considering sulfuric acid erosion, after the standard curing the samples were immersed in sulfuric acid solution for another 14 days.

#### *2.2. Mathematical Characteristics of* τ*-*δ *Behavior*

The shear stress–shear strain (τ-δ) behavior of Nmcs typically comprises four types [2,3,17,18]. They are strain-hardening behavior, falling behavior, S-type falling behavior and strain-softening behavior. According to Wang et al. [17] the strain-softening behavior can be well captured using a generalized mathematical model, so it will not be discussed in this study. In order to establish the constitutive model characterizing the shear stress-displacement curve, it is necessary to analyze the mathematical characteristics.

#### 2.2.1. Strain-Hardening τ-δ Behavior

The typical shear stress-shear strain (τ-δ) curve for strain-hardening behavior of Nmcs is shown in Figure 1. As can be seen, the strain-hardening process can be divided into three stages: elastic stage (OA), plastic stage (AB), and failure stage (BC). In the elastic stage, the τ-δ curve shows a straight line and the shear stress increases linearly with the shear strain at a gradient of initial elastic modulus *E*0. In the plastic stage, the tangent modulus *Ei* reduces gradually as strain accumulates, leading to a nonlinear τ-δ curve. In the failure stage, the τ-δ curve flattens out and the shear stress reaches the ultimate shear strength τp with a corresponding shear strain δp. In this stage, the shear stress is mainly contributed by the friction resistance at the failure surface of the soil sample. In sum, the

strain-hardening curve includes four mathematical features: through the origin, monotone increasing, convex to τ-axis, and infinite convergence.

**Figure 1.** Strain-hardening τ-δ curve.

#### 2.2.2. Falling τ-δ Behavior

In the direct shear test of seashore soft soil after adding Nm, the cohesive force was lost after failure and hence the shear stress decreased dramatically. The falling τ-δ curve after the elastic stage shows an evident softening behavior. As shown in Figure 2, the typical τ-δ curve can be divided into four stages. Stage 1 is the elastic stage (OA) which is similar to that of strain-hardening curve. In this stage, the shear stress increases with the gradient of initial elastic modulus until reaching the failure. The corresponding shear stress and strain at point A denote the failure displacement δp and shear strength τp, respectively. Stage 2 is the falling stage (AB), which evidently shows the falling of shear stress after the soil fails. This falling of shear stress is attributed to the loss of cohesion and the tangent modulus of the τ-δ curve gives a negative value. Stage 3 is the plastic stage (BC) wherein the friction resistance starts to dominate after the loss of cohesion. In this stage, the tangent modulus of the curve approximates the initial elastic modulus at the beginning which subsequently decreases due to the occurrence of plastic shear stress. Stage 4 is the residual shear stress stage (CD) where the tangent modulus approaches zero and the shear stress is equal to residual shear stress. It should be noted that the τ-δ falling curve can be modified by ignoring Stages 2 and 3 (AB and BC), then it returns to the strain-hardening behavior. However, the shear strength in the falling curve refers to the shear stress at the end of Stage 1 which is different from its counterpart in the strain-hardening curve.

**Figure 2.** Falling τ-δ curve.

#### 2.2.3. S-Type Falling τ-δ Behavior

Based on the τ-δ response of Nmcs in the scenario with high corrosion, the typical S-type falling curve is shown in Figure 3. As can be seen, the S-type falling curve consists of five stages. Stage 1 refers to the erosion softening stage (OA) where the surface of the sample is eroded by highly corrosive sulfuric acid and becomes relatively soft. Initially, the increment in the shear stress is relatively small as the displacement increases, giving rise to a relatively small initial modulus. As the shearing develops and enters the hard soil, which is less corroded, the tangent modulus tends to increase until stabilizing when accessing Stage 2, i.e., linear elastic stage (AB). The shear strength τp and corresponding displacement δp at failure occur at the end of Stage 2, i.e., point B. After reaching failure, the falling stage (BC), the frictional plastic stage (CD) and the residual shear stress stage (DE) emerge continuously. These three stages are similar to those in the above falling behavior. Thus, the S-type falling curve can be modified in a similar way as that for the above falling curve. However, the obtained modified curve is still unlike the strain-hardening curve which is convex to τ-axis; namely, an inflection point occurs on the curve, e.g., before this point, the curve is convex to δ-axis, while after this point, it is convex to τ-axis.

**Figure 3.** S-type Falling τ-δ curve.

#### *2.3. Mathematical Characteristics of* σ*-*δ *Behavior*

Based on the UCS (unconfined compression strength test) results, the stress–strain curve under uniaxial compression exhibits a strong softening and brittle failure behavior, as shown in Figure 4. As can be seen, the stress–strain curve is hump-shaped where the peak point of the curve gives the unconfined compressive strength σp corresponding to a strain of εp. This curve comprises three stages. In the hardening stage (OP), the stress initially increases linearly with strain; the gradient of which represents the initial elastic modulus *E*0. This gradient starts to decrease in the later phase of the hardening stage until arriving at the peak, i.e., point P where the brittle failure takes place and the tangent modulus equals to zero. After that the stress reduces monotonically with strain in the softening stage (PM) and remains unchanged when entering the residual stress stage (MN). In sum, the mathematical features of the curve include: through the origin, having extreme value point, and converging at residual stress.

**Figure 4.** Axial stress–strain curve.

#### **3. Established Mathematical Model**

The characteristics of modified falling τ-δ curve are almost consistent with those of strain-hardening τ-δ curve. Therefore, this study attempts to establish a simple, mathematical constitutive model which is applicable for modeling both strain-hardening and modified falling τ-δ behaviors of Nmcs.

#### *3.1. Conventional Shear Stress-Displacement (*τ*-*δ*) Models*

The conventional shear stress-displacement models have three types: hyperbolic model, exponential model and power function model.

#### 3.1.1. Hyperbolic Model

The most classical nonlinear model describing hardening curve is hyperbolic model, which is widely applied to the nonlinear modeling in various fields because of its simple expression, convenient simulation and easy determination of parameters. The hyperbolic model was proposed by Duncan and Chang [40] and its expression is

$$
\pi = \frac{\delta}{1/E\_0 + \delta/\tau\_\mathbf{p}} \tag{1}
$$

where τ is the shear stress (kPa), δ is the shear displacement (mm), *E*0 is the nominal elastic modulus (kPa/mm) and τp is the shear strength (kPa).

According to the τ-δ curves of shear test on the soil-structure contact surface, the hardening curve is rigid and plastic, and the hyperbolic model is difficult to meet this condition. In contrast, the strain in the τ-δ curve of Nmcs is mostly elastic before failure and only a small amount of plastic strain occurs after failure. In addition, the hyperbolic curve produces a large error in fitting the softening curve, which causes the deviation between the fitting results and the measured data due to its mathematical characteristics. Therefore, the hyperbolic model may be not suitable for modeling both hardening and softening behaviors.

#### 3.1.2. Exponential Model

The exponential model converges faster, and it is suitable for the τ-δ curves with elastoplastic strain. Hence, it is superior to the hyperbolic model for hardening curves. The exponential model was firstly proposed based on the one-dimensional consolidation theory of Terzaghi, and was mainly applied to describe the stress–strain curve of soil. The mathematical constitutive function is

$$
\pi = \tau\_{\mathbb{P}} \left( 1 - e^{-E\_0 \delta / \tau\_{\mathbb{P}}} \right). \tag{2}
$$

Cai et al. [41] investigated the mathematical defects of the exponential model using the half-value strength index. The results showed that the half-value strength index of both the exponential and the hyperbolic function is a fixed value which is only related to the peak strength and the initial elastic modulus. In this regard, the simulated stress–strain curve is only applicable for specific cases. In contrast, the half-value strength index of the power function is a parameter with a non-fixed value. The shape of its curve varies with the variation of the parameters, and hence it is widely applicable.

#### 3.1.3. Power Function Model

Due to the mathematical characteristics of the power function model, its simulation effect is remarkable in modeling plastic curves. In addition, the power function model of the nonlinear constitutive model of clay has the parameter of tangent modulus index. The expression of the power function model is

$$\tau = \tau\_{\rm P} \left\{ 1 - \left[ 1 + \frac{(\theta - 1)E\_0}{\tau\_{\rm P}} \delta \right]^{\frac{1}{1-\theta}} \right\} \tag{3}$$

where the value of θ is larger than 1; when θ = 2, the power function becomes the hyperbolic shear stress-displacement constitutive equation, so the hyperbolic function is only a special case of the power function. The first derivative of Equation (3) is given as

$$\frac{d\tau}{d\delta} = E\_0 \left[ 1 + \frac{(\theta - 1)E\_0}{\tau\_\text{P}} \delta \right]^{\frac{\theta}{1-\theta}}.\tag{4}$$

Since θ > 1, the first derivative of the power function is always greater than 0 in the domain of definition, and the curve increases monotonically. As the parameter θ changes, it is more applicable to the hardening curve and modified falling curve.

The second derivative of Equation (3) leads to

$$\frac{d^2\pi}{d\delta^2} = -\frac{E\_0^{-2}\theta}{\tau\_\mathcal{P}} \left[ 1 + \frac{(\theta - 1)E\_0}{\tau\_\mathcal{P}} \delta \right]^{\frac{2\theta - 1}{1 - \theta}}.\tag{5}$$

It can be found that the second derivative of power function is always less than zero, meeting the characteristic of hardening and modified falling curves, i.e., convex to τ-axis. However, the inflection point occurs on the S-type τ-δ curve under a highly corrosive environment. Therefore, the second derivative of power function cannot be equal to zero.

#### *3.2. Mathematical REP Model for* τ*-*δ *Behavior*

Based on the above conventional mathematical models, a new REP (reinforced exponential and power function) mathematical model for modeling the shear stress-displacement behavior of Nmcs under acid erosion environment is proposed in this study. This model combines exponential and power functions, which is expressed as

$$
\pi = a \Big[ 1 - e^{-b\delta} (1 + k\delta)^{-\lambda} \Big], \tag{6}
$$

where *a*, *b*, λ, and *k* are parameters to be determined, and *a* ≥ 0, *b* > 0, λ > 0, *k* > 0. When *k* = 0, Equation (6) degrades into exponential function.

Taking the limit and the first derivative of Equation (6) leads to

$$\begin{cases} \tau \big|\_{\delta=+\infty} = a \\ \frac{d\tau}{d\delta} = abe^{-b\delta} (1+k\delta)^{-\lambda} + a\lambda ke^{-b\delta} (1+k\delta)^{-\lambda-1} \end{cases} \tag{7}$$

τ =

The progressive limit of τ-δ curve is shear strength, i.e., τp. Hence,

$$a = \tau\_{\mathbb{P}}.\tag{8}$$

The first derivative of the new model with δ=0 is the initial modulus of elasticity, i.e., *E*0. Combining with Equation (8) gives

$$
\tau\_\mathsf{P} b + \tau\_\mathsf{P} \lambda k = E\_{0,\prime} \tag{9}
$$

where

$$b = \frac{E\_0}{\tau\_\mathbb{P}} - \lambda k.\tag{10}$$

 as

> (11)

According to Equation (10), (*E*0/τp − λ*k*) > 0 if *b* > 0. Basedontheabove,theREPmodelforthehardeningτ-δcurvecanbe

 − Use, the REP model for the hardening \(\tau\text{-}\delta\) curve can be expressed as
$$\tau = \tau\_{\rm P} \left[ 1 - e^{-\left(\mathbb{E}\_{0}/\tau\_{\rm P} - \lambda k\right)\delta} (1 + k\delta)^{-\lambda} \right].$$

In order to analyze whether REP model satisfies the mathematical characteristics of hardening curve, the zero point, the limit, the first derivative and the second derivative are discussed as below

$$\begin{cases} \pi|\_{\delta=0} = 0\\ \pi|\_{\delta=+\infty} = \pi\_{\mathsf{P}}\\ \frac{d\mathsf{T}}{d\delta} = E\_0 \big( \mathbb{E}\_0/\tau\_{\mathsf{P}} - \lambda k \big) e^{-(E\_0/\tau\_{\mathsf{P}} - \lambda k)\delta} (1+k\delta)^{-\lambda} + E\_0 \lambda k e^{-(E\_0/\tau\_{\mathsf{P}} - \lambda k)\delta} (1+k\delta)^{-\lambda-1} \\\ \frac{d^2\mathsf{T}}{d\delta^2} = -E\_0 \big( \mathbb{E}\_0/\tau\_{\mathsf{P}} - \lambda k \big)^2 e^{-(E\_0/\tau\_{\mathsf{P}} - \lambda k)\delta} (1+k\delta)^{-\lambda} \\\ -2E\_0 \big( E\_0/\tau\_{\mathsf{P}} - \lambda k \big) \lambda k e^{-(E\_0/\tau\_{\mathsf{P}} - \lambda k)\delta} (1+k\delta)^{-\lambda-1} - E\_0 \lambda (\lambda+1)k^2 (1+k\delta)^{-\lambda-1} \end{cases} \tag{12}$$

When δ = 0, the shear stress equals to 0 so the curve passes through the origin, satisfying the first characteristic of the hardening curve. The coefficients in the first-order derivative equation are all positive, and the first-order derivative is always greater than 0 in the domain of definition, which satisfies the characteristic of monotonic increase. When the displacement δ approaches infinity, shear stress gradually gets close to shear strength of τp. Therefore, the new model goes through the origin and has both upper and lower bounds. The coefficients of the second derivative equation are all negative, and the second derivative of the new model is always less than 0. Hence, the REP model is theoretically suitable for the hardening and modified falling curves.

#### *3.3. Mathematical Models for Stress-Displacement (*σ*-*δ*) Behavior*

Likewise, the conventional mathematical model for the constitutive relation of stress- displacement (σ-δ) behavior also has many types such as hyperbolic, exponential function, power function, piecewise function and quadratic function. As aforementioned, the power function model has a better fitting effect than hyperbolic and exponential functions, while the piecewise function has some defects, e.g., it is troublesome to fit and has many parameters. Therefore, in the study of models for stress-displacement (σ-δ) behavior, only power function, quadratic function, and the proposed REP function are discussed.

For the power function of σ-δ behavior, it can be easily modified from Equation (3), that is

$$
\sigma = \sigma\_{\rm P} \left\{ 1 - \left[ 1 + \frac{(\theta - 1)E\_0}{\sigma\_{\rm P}} \varepsilon \right]^{\frac{1}{1-\theta}} \right\} \tag{13}
$$

where ε is the strain (%), σ is the stress (kPa) and σp is the peak value of the stress–strain curve (UCS).

The quadratic model is able to simulate the stress–strain curve of compacted cement soil with an obvious peak value; its expression is

$$
\sigma = \sigma\_{\rm P} \left[ A \frac{\varepsilon}{\varepsilon\_{\rm P}} - B \left( \frac{\varepsilon}{\varepsilon\_{\rm P}} \right)^2 \right],
\tag{14}
$$

where σp and εp are the maximum stress and the corresponding strain, respectively. *A* and *B* are the fitting parameters to be determined.

When ε = 0, the stress of power and quadratic models is 0, which satisfies the characteristic of the stress–strain curve passing through the origin. As aforementioned, in the process of power function fitting, it is unable to converge in the failure stage, while the strong softening stress–strain curve will soften immediately after reaching the peak failure. Therefore, the convergence of the power function may be not timely, which may lead to a large deviation from the measured curve. Although the quadratic model is able to converge in time after the peak value; when the strain approaches infinity, the stress is also infinite, which theoretically does not meet the characteristics of infinite convergence of the stress–strain curve.

The expression of REP model for the σ-δ behavior is slightly di fferent from that for the τ-δ behavior, i.e., Equation (11)

$$
\sigma = a \Big[ 1 - e^{-h\varepsilon} (1 + k\varepsilon)^{-\lambda} \Big],
\tag{15}
$$

where *a*, *b*, λ*,* and *k* are parameters to be determined, and the value range of each parameter should be suitable for the hump curve. When ε = 0, the σ value of the REP model also equals to zero which satisfies the characteristic of passing through the origin.

The first and second derivatives of the stress–strain curve are as follows

$$\begin{cases} \frac{d\sigma}{d\delta} = ab\varepsilon^{-b\varepsilon}(1+k\varepsilon)^{-\lambda} + a\lambda k\varepsilon^{-b\varepsilon}(1+k\varepsilon)^{-\lambda-1} \\\frac{d^2\sigma}{d\delta^2} = -ab^2\varepsilon^{-(E\_0/\tau\_\mathbf{p}-\lambda k)\delta}(1+k\varepsilon)^{-\lambda} - 2ab\lambda k\varepsilon^{-b\varepsilon}(1+k\varepsilon)^{-\lambda-1} - a\lambda(\lambda+1)k^2(1+k\varepsilon)^{-\lambda-1} \end{cases} \tag{16}$$

It can be observed that the first and second derivatives of REP model are a ffected by the value of each parameter, and the positive and negative signs are uncertain which enables its adaptability to complex strain-softening curves. The specific value range of each parameter and the judgment of the positive and negative sign of the first derivative and the second derivative need further study.

#### *3.4. Application and Analysis*

⎪⎪⎪⎪⎪⎨

#### 3.4.1. Hardening τ-δ Behavior

Based on the measured data of direct shear test, comparisons of using hyperbolic, exponential and power function models as well as the proposed REP model are made. Two cases with 5% and 7% cement mixture ratio were examined. To determine the aforementioned model parameters, e.g., λ and *k*, four tests with vertical pressures of 100, 200, 300, and 400 kPa were carried out respectively. The comparison results for the cases under a vertical pressure of 400 kPa are shown in Figures 5 and 6.

**Figure 5.** τ-δ curve for mix ratio with 5% cement content.

**Figure 6.** τ-δ curve for mix ratio with 7% cement content.

As shown in Figure 5, on the whole, the four models have a good fitting effect, but the elastic stage of the measured curve is not smooth, and there is a prominent inflection point locally. In this stage, the four models have a large deviation from the measured value. The tangent modulus of the measured curve decreases gradually in the plastic stage, and the hyperbolic, exponential and power functions converge slowly, all of which appear below the curve while the fitting effect of REP model is very evident. When entering failure stage, both the hyperbolic and exponential fittings cannot converge to τp, and lie in the upper part of the measured curve with big difference. In contrast, the power function converges well, and the fitting effect is better than the hyperbolic and exponential functions, although the end of the curve still appears above the measured curve. The REP model also has a good convergence effect and the whole fitted failure stage is very close to that of the measured curve.

As shown in Figure 6, the linearity of the measured curve in the elastic stage is not obvious while the hyperbolic, exponential, and power function curves are linear, deviating slightly from the measured curve. In the plastic deformation stage, the three functions appear below the measured curve, and the difference between the power function and the measured curve is the smallest. Similar to that observed in Figure 5, in the failure stage, the three models generally appear at the top of the curve. In contrast, the REP model is very close to the measured curve and shows an evidently favorable fitting effect.

Among the conventional models, the power function model is relatively superior in modeling τ-δ curves, particularly in the plastic stage where the computed results are closer to the measured curve and failure, and in the failure stage showing a faster convergence speed. Compared with the hyperbolic model, the exponential model has a better simulation effect. Moreover, the REP model shows superior fitting accuracy than the conventional mathematical models.

#### 3.4.2. Modified Falling τ-δ Behavior

After adding Nm, the τ-δ curve exhibits modified falling type. In the comparison of different mathematical models, two cases with Nm mixing ratios of 10% and 20% under a vertical pressure of 400kPa were selected. The results are shown in Figures 7 and 8.

**Figure 7.** τ-δ curve for mix ratio with 10% Nm content.

**Figure 8.** τ-δ curve for mix ratio with 20% Nm content.

As can be seen, the shape of the two measured curves is similar. Before failure, the modified curve is mostly elastic stage and there is no plastic transition stage showing significant linearity. In this stage, the conventional models produce non-linear curves, while the measured curve approximates a horizontal line in the failure stage. The curves of conventional models locate below the measured curve in the former part and above the measured curve in the later part. In the two stages, the conventional model intersects with the measured curve, exhibiting two "X" shapes. In general, the difference between conventional models and measured curve is relatively big while the REP model fits fairly well with the measured curve. Therefore, the proposed REP model has significant advantage in modeling the modified τ-δ curve. In contrast, it is easy for a double-"X" type discrepancy to appear in the conventional mathematical model simulation.

#### 3.4.3. Strong Softening σ-δ Behavior

To compare the performance of the power function and quadratic function models as well as the REP model, UCS experimental results for cases with 0 mol/L and 0.08 mol/L H2SO4 erosion were adopted, Figure 9. As can be seen, the power function model behaves the worst in the modeling of the hump-shaped σ-δ curve. For instance, it is convex at the rising stage of the curve, which is contrary to the characteristic of concave in the measured curve. In addition, it cannot simulate the softening behavior as the measured curve although it converges to an almost constant value in the end. The quadratic function model performs better than the power function model. It is able to simulate the softening behavior and give a peak stress value. However, the shape of the quadratic curve is convex in all stages, which di ffers with the shape of measured curves. Worse still, there exists a large discrepancy in the maximum stress value and its corresponding strain value between the results of quadratic model and the measured results. This may raise an adverse e ffect in predicting UCS results. In contrast, the results of proposed REP model agree incredibly well with the measured results. The REP model not only shows consistent shapes, but also predicts a fairly close maximum stress value and a corresponding strain value. This is of great engineering value in predicting the compressive strength.

**Figure 9.** Comparison of stress–strain curves: (**a**) pure water condition (0 mol/L H2SO4); (**b**) 0.08 mol/L H2SO4.

To further examine the performance of the REP model, a series of comparisons for cases with varying erosion concentrations (i.e., 0.00 mol/L, 0.02 mol/L, 0.04 mol/L, 0.06 mol/L and 0.08 mol/L) is conducted, Figure 10. As can be seen, in the stress rising stage, the REP model fits fairly well with measured results; in the reducing stage, slight discrepancy occurs for the cases with 0.00 mol/L and 0.02 mol/L erosion concentrations. This could be attributed to the scattered data of the measured results. In the final residual stage, the REP model deviates from the measured data when the convergent residual stress was relatively large, such as the cases in pure water (i.e., 0.00 mol/L) and 0.02 mol/L acid erosion environment. When the residual stress was relatively small in the environment with a high concentration of acid erosion, the REP model gives better performance in fitting. Therefore, it can be found that the REP model can adapt to the measured curve under di fferent acid erosion concentrations, with relatively high fitting accuracy. The fitting e ffect is more evident under a high concentration erosion environment. Table 1 provides the values of the four parameters in the REP model for these five cases.

**Figure 10.** Comparison of stress–strain curves of different H2SO4 erosion concentrations with REP model fittings.

**Table 1.** Four parameter values of REP model under different erosion concentrations.

In order to study the influence of erosion concentration on REP model parameters, an acid erosion factor was introduced

$$
\omega(\mathbf{x}, \mathbf{y}, z, a\_s) = \frac{\pi^2 \mathbf{x}}{2\pi y + 4za\_s},
\tag{17}
$$

where *x*, *y,* and *z* are the parameters to be determined; αs is the concentration of sulfuric acid solution.

In accordance with Table 1, substituting the acid erosion factor and acid erosion concentration αs into the four parameters of REP model leads to

$$\begin{cases} a = 8q \tan[\omega\_d(a\_s) + 1.84c] - 1.84c \\ b = -0.45c - 2.18q \cos[\omega\_b(a\_s) + 2.18q] \\ k = 0.11 \tan[\omega\_k(a\_s) + 0.16] - 0.16 \\ \lambda = -2.2c - a\_s - 2.1c \sin[\omega\_\lambda(a\_s) + 2.2c] \end{cases} \tag{18}$$

where *c* and ϕ are the cohesion and internal friction angle of silty clay in the experiment, respectively. Hence, the acid erosion factors of the four parameters can be obtained

$$\begin{cases} \boldsymbol{\omega}\_{\rm{h}}(\boldsymbol{a}\_{\rm{s}}) = \boldsymbol{\omega}(-7.96\boldsymbol{\varphi}, 0.881, 1.84\boldsymbol{c}, \boldsymbol{a}\_{\rm{s}})\\ \boldsymbol{\omega}\_{\rm{b}}(\boldsymbol{a}\_{\rm{s}}) = \boldsymbol{\omega}(2.18217\boldsymbol{\varphi}, -0.100816, 0.44586\boldsymbol{c}, \boldsymbol{a}\_{\rm{s}})\\ \boldsymbol{\omega}\_{\rm{k}}(\boldsymbol{a}\_{\rm{s}}) = \boldsymbol{\omega}(0.1111, -6.592\boldsymbol{\varphi}\times 10^{-6}, 0.158, \boldsymbol{a}\_{\rm{s}})\\ \boldsymbol{\omega}\_{\rm{h}}(\boldsymbol{a}\_{\rm{s}}) = \boldsymbol{\omega}(2.095\boldsymbol{c}, 2.1927\boldsymbol{c}, -105.507\boldsymbol{c}, \boldsymbol{a}\_{\rm{s}}) \end{cases} \tag{19}$$

Combining with Equations (15) and (19), the damage model of sulfuric acid erosion can be expressed as

$$\sigma = a\_{[\omega\_k(a\_\delta), a\_\delta]} \left[ 1 - e^{-b\_{[\omega\_k(a\_\delta), a\_\delta]} \ell} \left( 1 + k\_{[\omega\_k(a\_\delta), a\_\delta]} \varepsilon \right)^{-\lambda\_{[\omega\_\lambda(a\_\delta), a\_\delta]}} \right]. \tag{20}$$

As shown in Equation (20), the damage model only contains parameters of sulfuric acid concentration (α*s*), cohesion (*c*) and internal friction angle ( ϕ), making the new model more suitable for acid erosion environment.

#### **4. Mathematical CEL Model for Modified S-Type Falling** τ**-**δ **Behavior**

As discussed above, the REP model has fairly good fitting e ffect which can be used for di fferent types of stress–strain curves. However, for the S-type curve which has inflection points, it is time-consuming to calculate the zero point of the second derivative equation of REP model and determine the position of inflection points. To solve this, the REP is therefore simplified and a new CEL (coupled exponential and linear) model is put forth.

#### *4.1. Mathematical CEL Model*

The CEL model is actually a coupled exponential and linear function model. Setting λ = −1, Equation (6) can be simplified as

$$
\pi = a \Big[ 1 - e^{-h\delta} (1 + k\delta) \Big],
\tag{21}
$$

where α ≥ 0, *b* > 0 and *k* > 0; *k* is defined as the inflection factor.

Taking the limit of Equation (21) gives

$$\left. \tau \right|\_{\delta = +\infty} = a \left[ 1 - e^{-b\delta} (1 + k\delta) \right] \Big|\_{\delta = +\infty} = a(1 - 0) = a. \tag{22}$$

Since the S-type curve eventually converge to the shear strength τp so

$$a = \tau\_{\mathbb{P}}.\tag{23}$$

Taking the first derivative of Equation (21) leads to

$$\frac{d\pi}{d\delta} = abe^{-b\delta}(1+k\delta) - ake^{-b\delta}.\tag{24}$$

If δ = 0, then

$$
\frac{d\pi}{d\delta}|\_{\delta=0} = a(b-k). \tag{25}
$$

The first derivative of the new model is the initial elastic modulus when the displacement is 0, i.e., δ = 0. Combining with Equation (23) gives

$$
\pi\_\mathbb{P}(b-k) = E\_0. \tag{26}
$$

Hence, the parameter b can be derived

$$b = \frac{E\_0}{\tau\_\mathrm{P}} + k\_\mathrm{\prime} \tag{27}$$

and the CEL model can be expressed as

$$
\pi = E\_0 \left[ 1 - \varepsilon^{-(\frac{F\_0}{\mathbf{r}\_\mathbf{P}} + k)\delta} (1 + k\delta) \right]. \tag{28}
$$

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

In order to explore whether the CEL model satisfies the mathematical characteristics of the S-type curve, its zero point, limit, first derivative, and second derivative are discussed

$$\begin{cases} \tau \Big|\_{\delta=0} = E\_0[1 - 1 \cdot (1 - 0)] = 0\\ \tau \Big|\_{\delta \to +\infty} = \tau\_\mathrm{P} \\ \frac{d\tau}{d\delta} = \tau\_\mathrm{P} \Big|\_{\tau\_\mathrm{P}} + k \Big| e^{-(\frac{E\_0}{\tau\_\mathrm{P}} + k)\delta} \quad (1 + k\delta) - \tau\_\mathrm{p} k e^{-(\frac{E\_0}{\tau\_\mathrm{P}} + k)\delta} \\ \frac{d^2 \tau}{d\delta^2} = -\tau\_\mathrm{P} \Big| \frac{E\_0}{\tau\_\mathrm{P}} + k \Big|^2 e^{-(\frac{E\_0}{\tau\_\mathrm{P}} + k)\delta} \quad (1 + k\delta) + 2\tau\_\mathrm{P} \Big| \frac{E\_0}{\tau\_\mathrm{P}} + k \Big| e^{-(\frac{E\_0}{\tau\_\mathrm{P}} + k)\delta} \end{cases} \tag{29}$$

According to Equation (29), the CEL model goes through the origin and converges to τp at infinity. Combining the similar items in the first derivative of Equation (29) gives

$$\frac{d\tau}{d\delta} = \left(E\_0 + E\_0 k \delta + \tau\_\mathrm{p} k^2 \delta\right) e^{-\left(\frac{E\_0}{\tau\_\mathrm{p}} + k\right)\delta} > 0. \tag{30}$$

Hence, the first derivative of CEL model is always greater than 0 in the domain of definition, and the curve increases monotonically.

The displacement at zero point of the second derivative of Equation (29) is obtained by

$$\delta\_{\mathbb{C}} = \frac{\tau\_{\mathbb{P}}k - E\_0}{\tau\_{\mathbb{P}}k^2 + E\_0k}. \tag{31}$$

To analyse the concavity of CEL model at zero point of second derivative, the relations are

$$\begin{cases} \frac{d^2 \tau}{d\delta^2} > 0, \left(\delta < \frac{\tau\_{\rm P}k - E\_0}{\tau\_{\rm P}k^2 + E\_0k}\right) \\\ d^2 \tau < 0, \left(\delta > \frac{\tau\_{\rm P}k - E\_0}{\tau\_{\rm P}k^2 + E\_0k}\right) \end{cases} \tag{32}$$

When δ < δc, τ" > 0 and the curve is convex to the δ-axis; when δ > δc, τ" < 0 and the curve is convex to the τ-axis.

#### *4.2. Application and Analysis*

Comparisons of hyperbolic, exponential and power function models and the above CEL model are carried out based on the experimental results of two cases with 0.09 mol/L H2SO4 erosion under vertical pressures of 300 kPa and 400 kPa, respectively. The results are shown in Figures 11 and 12.

**Figure 11.** τ*-*δ curve under 300 kPa vertical pressure.

**Figure 12.** τ-δ curve under 400 kPa vertical pressure.

As can be seen, the curves of conventional models are well banded which are above the measured curve before the inflection point and below the measured curve after the inflection curve. In contrast, the fitting effect of CEL model is obviously better than that of the other conventional models. It is basically consistent with the measure curve in the S-shaped range and converges faster and closer to τp than the other models in the failure stage. However, at the initial stage, the CEL curve is slightly lower than the measure curve, while in the failure stage, the difference between the CEL curve and the measured curve is relatively evident.


**6. Clio's new challenges**

In Greek mythology, Zeus joins Mnemosyne to celebrate his victory against Cronus. From this union, nine Muses are born, among them Clio. Titan Mnemosyne is, from Greek theogony, the feature of memory; Zeus, of authority, of power; while Cronus, of time. Can we say, even without a careful reading, that memory combined with power is capable of defeating time? Perhaps it is rushed to assert. But it is important to say that Clio, or the allegorical feature of history, emerges from this union.

I use this brief digression to refer to the Brazilian Law 14038, of August 17, 2020, for innovating the legal system. This law met a demand for years, to regulate the profession of and the historian.

There is an apparent irony in this legal instrument: it was signed by the current President of the Republic, who, in his awkward statements, claims that these professionals who practice shamelessness, drug addicts and cultivators of substances prohibited by law, are unnecessary for Brazilian science (practice, the abrupt and radical cut in the transfer of resources to the colleges and institutes of History of Brazil, present in Federal Universities), among other absurdities. However, it should be noted that the President totally vetoed the bill, and the veto was overturned by the National Congress.

The law lists as historians and historians (article 3) those who hold a diploma in higher education in history, issued by a regular educational institution; holders of a higher education diploma in history, issued by a foreign institution and revalidated in Brazil, in accordance with the law; holders of a master's or doctoral degree in history, issued by a regular educational institution or by a foreign institution and revalidated in Brazil, in accordance with the law; holders of a master's or doctoral degree obtained in a postgraduate program recognized by the Coordination for the Improvement of Higher Education Personnel – CAPES with a line of research dedicated to History; professionals with degrees in other areas who have proven to have been historians for more than 5 (five) years, as of the enactment of this Law.

In other words, there is a wide spectrum of professionals who can work in the area. I do not think it is a market reserve or epistemological preciousness. It is about enabling professionals to have legal and professional security to exercise the teaching of History in primary and secondary schools; organize information for publications, exhibitions and events on history topics; plan, organize, implement and direct historical research services; advising, organizing, implementing and directing historical information and documentation services; advise actions aimed at the evaluation and selection of documents for preservation purposes; prepare opinions, reports, plans, projects, reports and works on historical themes, as dictated in article 4.

However, I believe that the greatest challenge will be, and has already been, to meet the requirements of Articles 5 to 7, as they deal with professional registration and legal qualification for the exercise of the profession. The Brazilian National Association of History is an institution dedicated to supporting teaching and research in the field of History, since the 1960s, as well as the defense of the free exercise of the activities of History professionals. Establishing itself as a class entity based on legislation that, at first sight, evokes the need for an organization along the lines of the Brazilian Bar Association and the Federal Council of Medicine, mutatis mutandis, is the great obstacle put.

To emerge from the dismissal of a titanic authority, to resist persecution during the civil-military dictatorship, to overcome obscurantism and negationism and to bring the current president to his knees before the overthrow of the veto, we have already done so, and we continue to struggle. Now we have to trim the inside edges and promote our craft to the level of its conspicuous relevance.

### **7. Conclusion**

"God bless America"! This is the phrase that 10 out of 10 Americans cry out countless times a day, at least among conservatives. However, what will save Americans, like the entire world population, will be vaccines and supplies, in addition to oxygen. China and Russia, with their respective Coronavac and

Sputnik V, are giving us a hint of hope that everything will start to change, at least in countries where necropolitics is not the government regime. Even with the anti-diplomatic attacks carried out by the Brazilian government and its appendices, as ministers and the presidential clan, the countries that once called themselves communists and governed from their Politburos (central committees of the Communist Party), are being the breather for way out of this terrible crisis. This stalker ideology of Bolsonaro has caused the country thousands of deaths. As Millôr Fernandes would say, "I am suspicious of any idealist who profits from his ideal."

And not only have these countries given logistical support to Brazil. India and Venezuela have served Brazil with oxygen and inputs, even though the government of our country insists on conspiracy theories and replicates Trumpist silliness here, despite the orange president of the USA having left through the back doors of the White House. Therefore, God bless Bolívar and Raja. Or that Buddha protects us.

One of the president's sons told us: "it happens in the USA, it happens in Brazil". It referred to the terrorist attacks by white supremacists on that country's Congress. However, I hope that the inept Brazilian congressman is right, as American democratic institutions have survived the chaos of the past four years. May your father be prevented here and that democracy has oxygen to resist.

The polymath and polemic Millôr Fernandes, a great critic of Brazilian party politics, once shouted: "Brazil is the United States where I live". The ironic power of this great genius united the equation between the bovarism pointed out by Lima Barreto and denounced by Nelson Rodrigues, so present in the Bolsonaro clan. The president, if Millôr could define it (in fact he did it prophetically), would do it this way: "every ruler is composed of 3% of Lincoln and 97% of Pinochet".

It fits like a glove for the president, although there is, in Millôr himself, a bit of bovarismo. Let us be Latin Americans (the Brazilian lacks that!) And replace Lincoln with Allende. The old conservative waves that plague some parts of the world, and sweep Brazil, with neo-fascist agendas and unfounded alibis that "justify" the necropolitics, have made Brazil a perennial obituary. "When an ideology is very old, it comes to live in Brazil," stated Millôr.

Countless are the legal causes for Bolsonaro's impeachment. Even with the facts described above, the mayor, Rodrigo Maia, insists on saying that there is no political inclination for the impediment. What does the congressman expect? Die his? I use Millôr as a true argument of authority: "a politician is a subject who convinces everyone to do something that he has no conviction about"!

As there is still no political viability for Impeachment? I like those who defend human rights and who practice and promote inclusion and emancipation policies. They are invariably in the field on the left. But there is this other left, which is nothing more than a group of conservatives in Jacobean allegories.

"Idleness is the mother of all vices", taught Millôr! In addition to Temer's decoration, Mourão has also cleaned up presidential dejection. And point. His only contribution is to give euphemisms to the captain's profanity fenestrated by the Armed Forces.

The work of legal professionals, who specialize in Cultural Heritage, is perhaps an answer to this crisis that UNESCO, IPHAN and other preservation and protection agencies are experiencing in Brazil. The action of ICOMOS (the acronym in English, International Council for Monuments and Sites) is at the forefront of this, since it has a specific committee to deal with the relationship between Law and Heritage. But it is necessary to reinforce this committee. You need to make it robust.

Thus, this brief text also serves as a call for interested parties to allow ICOMOS to be an effective vehicle for the preservation of Brazilian heritage.

*Cultural Heritage and the Crisis of Democracy DOI: http://dx.doi.org/10.5772/intechopen.97575*


**2. Materials and Methods**

Nowadays, architects propose solutions not found before and they use technological novelties to create innovative building concepts. It is the first of the architects' roles: creating innovative building concepts which make use of technological achievements and presenting them in attractive visualizations and films used to promote the idea of sustainable smart cities.

Of course, only a few architects become famous innovators and visionaries. Despite this, a lot of emphasis is put on the development of creativity in the education process of architects at the Silesian University of Technology in Gliwice (Poland) [46]. As an example, we can provide a study conducted by the author of the article with second-cycle students at the Faculty of Architecture. The topic was formulated as follows: "How will seniors be participating in the life of a future smart city (in the perspective of 10 years) and what amenities will it be offering them?" It combined two very important issues, i.e., the problem of designing a friendly space for seniors and the problem of a smart city.

The layout of the research work is presented in Figure 1. It shows the duality of the research approach, which has been also demonstrated in the structure of the article, i.e., the "gray path" (on the left) presents the pilot study with the participation of students, and the "blue" path (on the right) presents the expert research documented by the author's own publications, which are listed in the bibliography. Both sources combine to obtain the synthesis of knowledge.

**Figure 1.** Layout of research procedures used in the article. It refers to the indicative level and illustrates the author's pursuit of the synthesis of knowledge and holistic approach to the investigated problem, i.e., "the role of the architect in creating the image of a sustainable smart city friendly to seniors" (author's own study).

The study was conducted in two groups of 12 students, which were then divided into teams of 4. In total, 24 students divided into 6 teams took part in the study. It should be noted that the first group had in-depth knowledge of the needs of the elderly, acquired during the previous research studies. This research concerned a different topic and was conducted under the guidance of Anna Szewczenko [47], associated professor an expert in the field of architectural solutions friendly to seniors. In the course of the study, the group developed, among others, "personae" or characteristics of fictitious people of senior age, who were given names, their health condition was described, scenarios of their functioning and spending free time was conceived, including passions and interests, as well as their social roles, fears and worries. The "personae" characterized in this way were used in the further part of the study described here. The second group of students had only general knowledge in the field of senior related issues.

The scientific objective of the research was to find out the vision of future architects about the life of seniors in a smart city of the future in the perspective of 10 years, and to collect inspiring, innovative ideas. The study had also a didactic goal—stimulating students' creativity, familiarizing them with brainstorming techniques and sensitizing future architects to the problems of older people in cities of the future. The study was conducted using brainstorming, which is an important element of the design thinking method. According to the definition of Willemien Visser: "Design Thinking refers to design-specific cognitive activities that designers apply during the process of designing" [48]. Items explaining design thinking principles are presented in the following publications:

• Brown, T. "Change by Design. How Design Thinking Transforms Organizations and Inspires Innovation" [49],

Examples involving the application of Design Thinking in the discipline of architecture and urban planning, are presented in the following articles:

The brainstorming was carried out with a classic division into two stages (as shown in Table 1):

The collection of ideas for each of the partial topics took five minutes. Ideas were written on post-it notes and stuck on boards assigned to each team.

During the brainstorming the students were to imagine that in 10 years, cities would change, becoming smart cities. There was an auxiliary research question related to this was: "What facilities for seniors represented by the three "personae" should be found in the smart city in the future?" It was clearly emphasized that the smart city had evolved since the creation of that concept—from smart city 1.0 focused on technology to human smart city 4.0 focused on people [56]. Importantly, the problem was to be considered by the students from the architect's perspective.

The diagram of the research methodology (Figure 2) and Table 1 presents the scenario of the research below.

**Table 1.** Research scenario with the participation of students of the Faculty of Architecture of the Silesian University of Technology involving the following research problem: "How will seniors be participating in the life of a future smart city (in the perspective of 10 years) and what amenities will it be offering them?".

**Table 1.** *Cont.*

**Figure 2.** Diagram of the research methodology presents the design thinking method step by step (red path). Additional explanations are presented on left and right side. On the right (grey path) you can see how research activities have been realized on indicative level, and on the right (blue path)—how it should be conducted on investigative level, when the full design thinking methodology in cooperation with sociologist and psychologist should be applied.


**9. Conclusion**

The research of published data suggests that there is a lack of proper knowledge on emergency dental first-aid among the parents, care givers, school authority and general public. In most of the countries worldwide, no attempt has been made by the government or other dental organizations to educate people on the management of dental trauma. TDI's are an important general and public health issue and public awareness of its importance should be bolstered to enable equitable access for injury care. Greater emphasis on prevention and the significance of emergency care for dental injuries will reduce the financial burden of the individual and improve the quality of life [6].

Research conducted to assess the treatment and management of TDI's have shown that the treatments provided at emergency care units are often inadequate and patients remain unsatisfied with care provided. The International Association of Dental Traumatology (IADT) has given a comprehensive guidelines management of TDI's, which can be accessed via Internet (www.iadt-dentaltrauma.org) [38]. The IADT recently developed a core outcome set (COS) for traumatic dental injuries (TDI) in children and adults, these guidelines should be followed and, even in extreme situations, replantation of teeth should always be considered [39]. Interactive website has been introduced for clinicians (Dental Trauma Guide, www. dentaltraumaguide.org) which can be used by dentist and health care workers either via computer or smart phone during a trauma situation [40]. Mobile phone based free App was introduced by IADT (IADT ToothSOS Mobile App) to help user to take care of a dental trauma at the scene of an accident.

Dental injuries cause both periodontal and pulpal complications. The delay in dental consultation for TDI's increases the amount of complications that develop later during the maintenance. Time lapse between the TDI's and the date of dental consultation is a decisive element in the therapeutic choice and influences the prognosis [5]. The parents and individuals should be educated to consult a dentist immediately after trauma and take prompt treatment for the TDI's to reduce the complications that develop at the later date.

There is need for refinement of dental curriculum for the management of TDI's in terms of design, content, teaching methodology and long term maintenance for better prognosis of the patients with dental trauma [41].

The prevalence of TDI's in Europe and many other continents is one in five school going children and if untreated they affect the quality of life of children. The environment of the school and action taken towards management of TDI's is very crucial. Schools with supportive social and physical environment have fewer occurrences of TDI's. Schools should adopt health and safety policies, improvements in the physical environment and closer supervision of children while playing will reduce the occurrence of TDI's [42]. School teachers and physical instructors should be educated about emergency management of TDI's and consult child specialist and dentist at the earliest to lessen post traumatic complications. Studies have pointed out that health promotion policies, safe environment at the schools, correction of predisposing risk factors of TDI's and use of protective intraoral and extra oral devices while physical activity will lessen the financial burden caused by TDI's [43]. Conducting health educational programs to improve the level of general knowledge about prevention and managing TDI's at the schools is necessary [44].

Parents, Education authorities, and children involved with sports and recreation activities should be educated about the risk factors involved and management of TDI's. Screening programs to identify children with high anatomic (incisal over jet and inadequate lip coverage) and behavioral risk for occurrence of traumatic injury and necessary corrective measures (preventive orthodontic treatment and use

*Short and Long Term Oral Hygiene Maintenance Protocols for Traumatic Dental Injuries DOI: http://dx.doi.org/10.5772/intechopen.96043*

of Mouth guards) will help reduce the occurrence of injury among children [45]. Mounting posters, leaflets at public places along with media campaigns using television, social networking sites and internet will educate people for managing avulsed permanent teeth [1]. The teachers and school management should be educated about TDIs and emergency care and referral to dentist as schools with good physical structures and promote health activities had lesser prevalence of TDIs [46, 47].

The dentist treating TDIs must involve other specialists including Oral Radiologist, Pediatrician, Paedodontist, Endodontist, Periodontist, Prosthodontist, Orthodontist and Oral maxillofacial Surgeon. Dentist must capture good quality photographs of the TDIs and lesions and can use them to discuss the treatment protocol with specialists. Studies have proved that photographic assessment method of dental trauma was valid and reliable as compared to the oral clinical examination [48].

Dentist must be aware of different types of TDIs and its immediate treatments [49]. Dentist should educate good oral hygiene maintenance techniques to the patients suffering from TDIs. During the healing and splinting of teeth, oral hygiene cleaning with interdental brushes will help the patients.

Complications even with the best of treatment guidelines followed occur occasionally and pulp necrosis is the most observed complication [12]. Dentist must refer the patient to other specialists whenever deemed necessary. Combined efforts of different specialists will improve the prognosis of the teeth and soft tissues.


**1. Introduction**

Drug delivery systems grounded on hydrogels (HGs) are interesting because of their high biocompatibility and biodegradability. These properties are especially relevant for materials used for biomedical engineering applications, an example of which may be drug delivery or tissue engineering [1–3]. HGs are water-swollen polymeric networks containing chemical or physical cross-links able to absorb large quantities of water or biological fluids [4]. HGs have a variety of structures, architectures, sizes (from centimetres to sub-nanometres), and functions, and together with other properties, these variables determine HG use for drug delivery [1–3,5].

HGs can be prepared from one polymer (homo-polymeric HG), two or more polymers (multi-polymeric HG); they may also contain other nanostructures/nanoparticles in a polymeric network [6–9]. These polymeric networks can be chemically and physically modified imparting new and unusual properties [9–11]. Chemical structures, compositions, biodegradability, biological functions and di fferent physicochemical properties (e.g., mechanical, rheological, spectral, thermosensitive, pH stability) can be modified [2,6,9,12]. These variations influence the performances of HGs and a ffect loading and releasing properties for drugs [7,9,11–15].

HGs can be used to form microparticles, nanoparticles, micelles and films [15,16]. For HG particles, the particle size (macro, micro and nano) determines the route by which HGs can be delivered into the human body [17–21]. For micro- or nano-sized HGs, the e ffects of various physical and chemical factors on drug release should be considered [15,21]. Therefore, drug immobilization in a polymer matrix should be considered in the context of controlled release at target sites. Various in vivo and in vitro drug application techniques have been developed with various therapeutic properties [12,22–24], including antifungal [25–27], antibacterial [28–32], antitumor [33–36], anti-inflammatory [37,38], immunomodulatory [39–41], anti-glycemic [42], antioxidant [32,37,43], tissue repair and regeneration [14,16,44].

The objective of this review is to explore the potential use of HG particles in drug delivery systems with respect to their size (macro, micro and nano). This review also attempts to identify the e ffects of HG particle size and physicochemical properties on biological performance and medical applications. Finally, novel drug delivery methods for enhancing treatments are discussed.

#### **2. Types of Hydrogels**

A gel is a liquid treated with gelling substances, including natural polymers (e.g., agar, alginates, and dextran), semi-synthetic polymers (cellulose derivatives) or synthetic polymers (acrylic and methacrylic acid derivatives) [45]. Lipophilic gels (oleogels) are obtained using oil as the dispersing phase. Hydrophilic gels (hydrogels) are obtained using water as the dispersing phase [46–48]. Due to their similarity to living human tissues, HGs with controlled drug release are widely used in pharmaceuticals. By modifying their compositions and physicochemical properties (e.g., to impart hydrophilic or hydrophobic character), HGs can be used as drug carriers for external or internal use [49].

HGs are classified using di fferent criteria [50]. The simplest criterion is origin, i.e., natural or synthetic [50,51]. Natural HGs are biocompatible, biodegradable [1] and support cell activity. However, natural HGs have low mechanical strength and large inter-batch variety. Proteins such as collagen or polysaccharides (e.g., chitosan, dextran, and alginate) are examples of natural HGs [52–55]. Synthetic HG polymers are prepared from polymerizable monomers, including vinyl acetate, acrylamide, ethylene glycol and lactic acid (made from plants, mostly from corn and sugarcane) [56–59]. Synthetic HGs can be precisely controlled and tailored to achieve desired properties. However, synthetic HGs typically lack bioactivity and have low biodegradability. Hybrid HGs consist of chemically, functionally and morphologically di fferent units [60–65]. Biologically active proteins, peptides, nano/microstructures are constituent parts of hybrid HGs and are connected with each other by physical or chemical forces [60–66]. Because of their construction, hybrid HGs derive their bioactivity from natural materials; furthermore, the easy control over physical and chemical properties of hybrid HGs are due to synthetic material properties [66].

#### *2.1. Physical and Chemical Hydrogels*

HGs can be classified into two groups based on the type of interactions involved in the creation of the network structure. The first group includes chemical solids [47,51,67,68], wherein HGs form three-dimensional (3D) networks with polymer chains are connected by permanent covalent bonds via cross-linking reactions [69]. Characteristic features of chemical HGs include their ability to swell resulting from interactions among the polymer network, water and the density of connections between polymer chains. Chemical HGs are not homogeneous due to the hydrophobic aggregation of cross-linking agents and high cross-link-density clusters [60].

The second group includes physical (reversible) HGs [51,67,68]. These HGs have chains connected by weak hydrogen bonds, ionic bonds and dipolar or hydrophobic interactions excluding those that dissolve before use [68]. These forces result in non-homogeneous HGs [60]. Examples of physical HG are solutions of agar, gelatine, and polyvinyl alcohol [70,71].

These two types of HGs encompass a wide variety of macromolecular structures formed from cross-linked and entangled linear homopolymers and linear, block or graft copolymers [72–74]. The HG networks can be stabilized by reactions of monovalent and polyvalent ions, multiple monovalent ions or complexes containing hydrogen bonds. The properties and applications of these HGs are closely related to cross-linking density, which determines swelling behaviour and the combined properties of solid and liquid phases [51,68,75].

#### *2.2. Conventional and Stimuli-Responsive Hydrogels*

HGs are also classified as conventional and stimuli-responsive. Conventional HGs comprise loosely connected hydrophilic, mostly non-ionic polymers with significant degrees of swelling in water without dissolution [76]. Stimuli-responsive HGs respond to various factors, such as small changes in temperature, ionic strength, pH, electric field, mechanical stress, light and selected substances (Figure 1a) [49,51,77–80]. Stimuli-responsive HGs can be tailored to react to various types of stimuli in the body, including ionic strength, pH and temperature, to act as potential drug carriers [49,51,77].

**Figure 1.** (**a**) Types of stimuli causing HG swelling. (**b**) Schematic illustration of a thermo-reactive HG formation loaded with a drug that uses temperature as a stimulus.


*2.2. Enzymatic Treatment of Bee Pollen*

Bee pollen samples (composed of more than 92% *Brassica campestris* pollen according to palynological counting) were collected from the beekeeping base of the Institute of Apicultural Research (IAR), Chinese Academy of Agricultural Sciences (CAAS). The sample was lyophilized after grinding into powder, and then sterilized by irradiation at 7 kGy. Cellulase, pectinase and papain were used for enzymatically treating bee pollen as described in our previous study [15]. In brief, 10 mL of Millipore water and 5 g of bee pollen powder were combined and vortexed for 5 min. For two kinds of enzyme-treated bee pollen (2E-BP) groups, 3000 U cellulase and 3000 U pectinase were added into the sample. For three kinds of enzyme-treated bee pollen (3E-BP) groups, 3000 U cellulase, 3000 U pectinase and 3000 U papain were added into the sample. All samples were adjusted to pH 4.0 with vitamin C solution, and then incubated at 45 ◦C for 24 h. A vacuum

freeze dryer was used for sample lyophilization, and samples were stored at −80 ◦C for further study.


*3.1. Analysis of the Reaction Time Variable*

To establish a relationship between the reaction time variable and the designed taskload of each exercise, it was decided that a combined graph should be created. The same graph shows the designed taskload profile, which is different for each of the exercises, and superimposed on it are the reaction time values for each of the six participants.

A representation of the four exercises can be seen in Figure 3. Each participant is represented by a different geometric shape and colour, as can be seen in the legend that appears under the four plots.

**Figure 3.** Combined representation of the designed taskload profile of the different exercises together with the reaction time values for the six participants. The first row of graphs presents the two simplest exercises, with Exercise 1 on the left and Exercise 2 on the right. The second row presents the data from Exercise 3 on the left and Exercise 4 on the right.

Each of the exercises has been associated with a different colour to facilitate the interpretation of the plots. The taskload profiles of Exercise 1 appear in magenta, those of Exercise 2 in green, those of Exercise 3 in orange, and finally those of Exercise 4 in purple. To correctly interpret Figure 3, the following aspects should be considered.

• The x-axis of the four graphs represents the time elapsed since the start of the simulation. All exercises lasted 45 min.

As can be seen in the figure above, the taskload distribution profile for each exercise is different. In the exercise design process, the starting point was a specific shape of designed taskload and a total reference taskload score. Specifically:

Table 1 shows a summary of the design characteristics of each of the exercises to compare their design values. The second column presents the total taskload value for each of the exercises. The next two columns present the maximum value of the designed taskload and the minute of simulation at which this value was expected to be reached.

Taking all the above into account, the obtained values for reaction time and the designed taskload for each of the exercises were represented in a combined graph.

The initial hypothesis was that reaction time would increase as the taskload faced by the ATCO increased. Given that the situation in the sector is more complex, it would be expected that the controller would take longer to assess the workload.

However, such a correlation was not observed in any of the four exercises. Contrary to what might be expected, the highest reaction time values appear at the beginning of Exercise 1. The explanation for these values is not that the situation in the sector was more complex, but that the participants were not yet familiar with the platform, the radar screen, or the additional windows.

Some isolated cases that confirm the initial hypothesis are the values of Participants 3, 5, and 6 in Exercises 1, 2, and 4, where the reaction time values increase at times with high taskload values. However, in general, the expected generalised relationship is not observed. Based on the analysis conducted, it was considered that, in the case of the registered data from participants, reaction time was not a significant variable in the study, and it was decided to discard it.


**3. Control System**

The main stator winding set of the DOL DWIM is directly connected to the grid and it is tasked with handling the main power flow toward the mechanical load. Differently, the additional stator winding set is supplied by a floating power inverter, which enables a current vector control according to Figure 3. Low-cost devices are used to measure the AC quantities in both windings. An analysis of the different blocks composing the control system is presented in the following.

**Figure 3.** Block diagram of the proposed direct online (DOL) DWIM control solution.


**Abstract**

Red blood cells (RBCs) moving in circulation are continuously exposed to the reactive oxygen species (ROS) that are circulating within the vascular system of body. The objective of the study is to determine the erythrocyte zeta potential and its morphological changes caused by oxidative stress in hypertensive patients in relation to the risk of development of cardiovascular disease (myocardial infarction). In this retrospective study, we investigated 186 samples, which include hypertension patients (n = 64), myocardial infarction patients (n = 52), treated myocardial infarction patients (n = 20), and normal healthy volunteers (n = 50). Morphological and electrochemical characteristics of RBCs in patients were analyzed using scanning electron microscopy and zeta potential study. These parameters were also statistically analyzed applying one way ANNOVA (Tukey's comparison) using Graph Pad. Statistical analyses of data showed that Hypertensive (ZP-16.06 mV) and cardiac patients (ZP-9.94 mV) RBCs possessed significantly reduced zeta potential relative to that of RBCs from healthy individuals (ZP-23.39 mV) (P-value <0.0001). Microscopic imaging of Hypertensive RBCs revealed increased anisocytes and poikilocytes. These parameters were found exacerbated in patients suffering from Myocardial infarction. Hence, it can be concluded that ZP can be used as an effective diagnostic tool for detection of hypertension associated cardiovascular disorder risk.

**Keywords:** red blood cells (RBCs), zeta potential, erythrocyte fragility, lipid peroxidation, hypertension, myocardial infarction


**3.11 Dissocializing**

In connection with socialization, there are two types of socialization processes: re-socialization and dissocialization. Dissocialization entails leaving a particular status and role and, as a result, abandoning the rules and behaviors associated with that status and function. It entails both physical and social seclusions. Separation of environments or people who have met their interaction demands and gives them support statuses to get rid of previously taught habits of behavior and interaction. Individual members of the so-called whole institutions, such as the army, monastery, prison, and so on, who are especially susceptible to this, whereas resocialization is a process of learning new roles, while abandoning previous roles [23].  The term "socialization" is used in this context to describe the process of transforming people who have engaged in antisocial behavior [33].

The aims of re-socialization is to learn new roles offered by the society as if professionalization, the professional reconversion, or rehabilitation of those who have committed deviant or delinquent roles and norms of life accepted by society [34]. Resocialization occurs in tandem with dissocialization and entails the orientation of learning and social control, as well as the uptake and expression of individual behaviors that are congruent with the new integrator system's board of values and attitudes. It is important to note that the efficiency of resocialization is determined not only by individual receptivity, but also by the new agent of socialization's level of social control and the degree to which previously gratifying elements are removed [1, 35]. These two processes of socialization, that is, de-socialization and re-socialization are not only concurrently happens, but interdependent [24].


**5. Discussion**

As mentioned above, *OCR* can not only directly reduce the thermal pore water pressure (Equation (6)), but it can also change the magnitude of the thermal pore water pressure by affecting the value of *Λ* (Equations (10) and (11)). However, the effect of *OCR* on *Λ* is often ignored in existing calculation methods [9,26], which may be the main reason for overestimating the thermal pore water pressure of highly overconsolidated soil. To quantitatively analyze the effect of *Λ* on the thermal pore water pressure, two cases are given here, namely, Case 1: the predicted results without considering the variation of *Λ* (*Λ* = 6.5), and their comparison with the experimental results; and Case 2: the predicted results considering the variation of *Λ* (*Λ* = 5.4, 5.0, and 3.8), and their comparison with the experimental results. The effect of *Λ* on the thermal pore water pressure is analyzed by comparing the coincidence between experimental results and predicted results. Figure 4a,b show the comparison of experimental results and predicted results for the two cases.

**Figure 4.** Comparison between experimental results and predicted results of (**a**) Case 1; (**b**) Case 2.

From Figure 4a, it can be observed that the predicted results without considering the variation of *Λ* will seriously overestimate the thermal pore water pressure. For clays with *OCR* equal to 10 and 30, the coefficients of determination (*R*2) of predicted results are both 0. When the change in temperature is 35 ◦C, the difference between the experimental results and predicted results reaches 61.5% for the clay with *OCR* equal to 10, and the difference reaches 127.2% for the clay with *OCR* equal to 30. However, from Figure 4b, it can be found that the coincidence between the predicted results considering the variation of *Λ* and experimental results was greatly improved. Especially, when *OCR* is equal to 30, the accuracy of the predicted results was improved by 92.7%, which means that the variation of *Λ* with *OCR* cannot be ignored when predicting the thermal pore water pressure inside the highly overconsolidated clay.


*4.2. CO2 Exposure*

ATII and A549 cells were exposed to 40 (normocapnia, Ctrl) or 120 mmHg (hypercapnia, CO2) CO2 conditions unless otherwise indicated. Normocapnia and hypercapnia media solutions were prepared freshly with DMEM or DMEM/F12, Ham's F12, and MOPS base to obtain a final pH of 7.4 at 40 (5%) or 120 mmHg (15%) of CO2 while maintaining 21% O2 balanced with N2 and were kept overnight in the humidified C-chamber (BioSpherix Ltd., Parish, NY, USA), as described previously [24]. Levels of CO2 in the chamber were controlled by an RO-CO2 carbon dioxide controller (BioSpherix Ltd., NY, USA). Before experiments media pH, pCO2 and pO2 levels were measured using a Rapid-lab blood gas analyzer (Siemens, Erlangen, Germany).

#### *4.3. Western Blot Analysis*

Protein concentrations were determined by using the Bradford assay after lysing the cells. Equal protein concentrations were resolved in 7%–10% polyacrylamide gels and transferred to a nitrocellulose membrane using a semidry apparatus from Bio-Rad (Hercules, Berkeley, CA, USA). Membranes were blocked for one hour in 5% fat-free milk and were subsequently incubated with primary antibodies overnight at 4 ◦C. For some experiments, loading control was performed by staining of the nitrocellulose membranes with Coomassie brilliant blue 250 (Sigma Aldrich, St. Louis, MO, USA). Densitometric analyses were performed by using the Image J software (NIH, Bethesda, MD, USA).

#### *4.4. Cell Surface Biotinylation*

After hypercapnia exposure, PM surface proteins were labeled for 20 min by using 1 mg/mL EZ-Link-NHS-SS-biotin (Pierce Biotechnology, Waltham, MA, USA). Proteins were pulled down with streptavidin-agarose beads (Pierce Biotechnology, Waltham, MA, USA) and analyzed by SDS-PAGE and immunoblotting, as described previously [14].


**Rice Leaf Blast Classification Method Based on Fused Features and OneȬDimensional Deep Convolutional Neural Network**

**Shuai Feng 1, Yingli Cao 1,2, Tongyu Xu 1,2,\*, Fenghua Yu 1,2, Dongxue Zhao 1 and Guosheng Zhang 1**

This paper developed seven one-dimensional deep convolutional neural network (DCNN) models to determine the best classification features and classification models for the five disease classes of leaf blast in order to improve the accuracy of grading the disease. It first pre-processed the hyperspectral imaging data to extract rice leaf samples of five disease classes, and the number of samples was increased by data-augmentation methods; then, spectral feature wavelengths, vegetation indices, and texture features were obtained based on the amplified sample data, which were used to construct CNN-based models. Finally, the proposed models were compared and analyzed with the Inception V3, ZF-Net, TextCNN, and bidirectional gated recurrent unit (BiGRU); support vector machine (SVM); and extreme learning machine (ELM) models in order to determine the best classification features and classification models for different disease classes of leaf blast. The experimental results also showed that the DCNN models provided better classification capability for disease classification than the Inception V3, ZF-Net, TextCNN, BiGRU, SVM, and ELM classification models. The SPA + TFs-DCNN achieved the best classification accuracy with an overall accuracy (OA) and Kappa of 98.58% and 98.22%, respectively. In terms of the classification of the specific different disease classes, the F1-scores for diseases of classes 0, 1, and 2 were all 100%, while the F1-scores for diseases of classes 4 and 5 were 96.48% and 96.68%, respectively. This study provides a new method for the identification and classification of rice leaf blast and a research basis for assessing the extent of the disease in the field.

remotesensingȬ13Ȭ04587Ȭv2


**1.5 The experience in using glucocorticoids in PDT patients**

This study was the first study which was carried out in the Institute of Physiology and Pathology of Hearing World Hearing Center and will be continued with different groups of patients and different implants and algorithms of glucocorticoid administration. The aim of the study was to evaluate different regimes of administration of glucocorticoids: dexamethasone and dexamethasone/prednisone to *partial deafness* treatment (PDT) patients who underwent cochlear implantation on the hearing preservation. Implant used in the study was the MED-EL implant with an electrode length of 28 mm (Flex 28). The impact of administrated glucocorticoids on hearing was measured in six different periods:

Forty-six patients were enrolled to the trial and then divided randomly into three subgroups. Patients from the first subgroup underwent intravenous steroid therapy (**Figure 1**). According to the scheme, 30 min before implantation, dexamethasone at the dose of 0.1 mg/kg body mass was administrated intravenously to patients from the first subgroup. For the next 3 consecutive days in every 12 h, dexamethasone was administrated intravenously at the same dose to each patient.

Patients from the second subgroup underwent prolonged (combined) steroid therapy: oral and intravenous. Three days prior to the surgery, prednisone was administrated orally at a dose of 1 mg/kg body mass/day. Then, 30 min before the cochlear implantation surgery, dexamethasone was administrated intravenously at a dose of 0.1 mg/kg body mass. For the next 3 consecutive days in every 12 h, dexamethasone was administrated intravenously (the same as in the first subgroup). For the next 3 days, prednisone was administrated orally at the dose of 1 mg/kg body mass/day. After this period, the dose of prednisone was reduced (10 mg per every

**163**

preservation.

*Role of Glucocorticoids in Hearing Preservation in Partial Deafness Treatment*

day) till complete reduction of dose, due to reducing the risk of adverse effects. The algorithm of administration of glucocorticoids to patients form the second sub-

The third subgroup was a control group and underwent standard cochlear

Only 2.6% of the chemically unchanged dose is eliminated via kidneys.

medical products: dexamethasone and prednisone.

**and exclusion criteria**

According to the protocol of this study, two different algorithms of administration with two different glucocorticoids were proposed in the study. Although both substances belong to the same pharmacological group, both of them have different pharmacokinetics and pharmacodynamic properties. Dexamethasone is a synthetic glucocorticoid (*molecular weight 392.46 g/mol*) with anti-inflammatory, anti-allergic, and immunomodulating activity. In common practice dexamethasone is administrated *intravenously* or off-label, e.g., *transtympanic injections*. After *intravenous* administration the mean time to peak concentration (Cmax) is between 10 and 30 min, and the half-life (t1/2) is from 2.2 to 3.8 h. Transport proteins are responsible for transport and distribution of dexamethasone in blood. Dexamethasone is mainly metabolized by the liver and eliminated with the bile.

Prednisone is a synthetic glucocorticoid (derivative of cortisone) and classified according to the *Anatomical Therapeutic Chemical (ATC) Classification System* as H02 AB 07. Prednisone is *prodrug* which converts into *active metabolite—prednisolone* (higher anti-inflammatory activity). According to characteristic of medical product and literature data, bioavailability of prednisone administrated orally is between 70 and 90%. The mean time to peak concentration (Cmax) is between 1 and 2 h. Half-life (t1/2) is between 3.4 and 3.8 h in plasma and 18–36 h in tissue. Binding prednisone with plasma proteins is between 70 and 73% (binding prednisolone (active metabolite) to the plasma proteins is higher (90–95%)). Similar to dexamethasone, prednisone is metabolized mainly by the liver and eliminated with the bile. Pharmacodynamic and pharmacokinetic data were based on characteristics of

**1.7 Methodology of the study: primary and secondary outcomes and inclusion**

The primary outcome variables were mean values of hearing thresholds averaged across all 11 frequencies (125–8000 Hz). The secondary outcome variable was hearing preservation (HP). Hearing preservation (HP) was calculated by comparing hearing thresholds in the 1-year postoperative period with the preoperative hearing thresholds, according to the hearing preservation (HP) formula (below) and converted to three levels: minimal, partial, and complete hearing

*DOI: http://dx.doi.org/10.5772/intechopen.88863*

*Scheme of steroid administration in the second subgroup of patients.*

group is presented below (**Figure 2**).

**1.6 Administrated glucocorticoids**

implantation procedure [18].

**Figure 2.**

#### **Figure 1.**

*Scheme of steroid administration in the first subgroup of patients.*

*Role of Glucocorticoids in Hearing Preservation in Partial Deafness Treatment DOI: http://dx.doi.org/10.5772/intechopen.88863*

**Figure 2.** *Scheme of steroid administration in the second subgroup of patients.*

day) till complete reduction of dose, due to reducing the risk of adverse effects. The algorithm of administration of glucocorticoids to patients form the second subgroup is presented below (**Figure 2**).

The third subgroup was a control group and underwent standard cochlear implantation procedure [18].