Introduction

The pyroclastic soil deposits originating from the deposition of air-fall materials ejected into the atmosphere during volcanic eruptions, are commonly composed of various layers of granular soils with a predominantly loose fabric (Picarelli et al. 2006; Moon et al. 2016; Yamao et al. 2016). This gentle deposition results in a high soil porosity, which allows for special water retention and drainage characteristics. Coupled with their mineralogy, these characteristics make them attractive for agricultural and human development, as in the case of Campania, southern Italy. The volcanic activity in this area, particularly from the Somma-Vesuvius and Phleagrean Fields volcanic complexes, has contributed to mantle wide areas with layered deposits (Scrocca 2010; De Vita and Nappi 2013). While the pumice strata are mostly gravel-sized materials, the ashes are often well-graded silty sands. Along with a relatively high friction angle and permeability, these deposits are usually stable due to the action of soil matric suction under unsaturated conditions (Picarelli et al. 2020). Nonetheless, steep slopes covered with pyroclastic soils are often prone to landslides, where rapid movements frequently occur, causing catastrophic effects (Fiorillo et al. 2001; Cascini et al. 2008; Greco et al. 2021). The soil behavior at failure looks similar over a relatively wide area, with the sliding surface within the layers of ashes for many of the studied landslides, such as in 1998 in Sarno (Cascini et al. 2000; Bilotta et al. 2005), in 1999 in Cervinara (Olivares and Damiano 2007; Picarelli et al. 2020), and 2005 in Nocera (Revellino et al. 2013).

The matric suction contributes to the shear strength of unsaturated soils due to the negative water pressure in capillary pores exerting a compressive action, joining together the soil grains. This phenomenon tends to intensify as the soil dries out and diminishes as the soil approaches saturation. Hence, when the soil resting on sloping terrain becomes wet, e.g., during rainwater infiltration, rainfall-induced landslides can be triggered, and on the steepest slopes, failure may occur even under unsaturated conditions (Olivares and Damiano 2007; Marino et al. 2021; Damiano et al. 2023). Therefore, it is relevant to study the unsaturated properties of the soils in the area and, specifically, the link between the unsaturated soil shear strength and water retention.

Since Bishop’s effective stress theory was proposed (Bishop 1959), many studies have developed theoretical models to predict soil shear strength under unsaturated conditions. Owing to the partial occupation of pores by water, the suction partially contributes to the effective stress state of soils, and this contribution (i.e., suction stress) depends on the degree of saturation. In this respect, as originally proposed by Bishop, it is described through a coefficient, \(\chi\), highly non-linear and variable from 0 (dry soil) to 1 (saturated soil); thus, the suction stress can be defined as \({\sigma }^{s}=\chi s\), where \(s\) represents soil suction (Lu and Likos 2006). The quantification of \(\chi\) has encountered many difficulties regarding its theoretical basis, practical implications, and experimental determinations (Jennings and Burland 1962; Fredlund and Morgenstern 1977; Khalili et al. 2004; Lu and Likos 2006). Starting from the simple assumption that it can be assumed equal to the degree of saturation (Öberg and Sällfors 1997), several expressions have been proposed over time, where \(\chi\) is a function of either the degree of saturation or matric suction (e.g. Fredlund et al. 1996; Vanapalli et al. 1996; Khalili and Khabbaz 1998; Lu and Likos 2006). Further studies estimate \(\chi\) by considering that suction acts on the contact area between water and soil particles (Tuller et al. 1999). In this approach, the suction contribution to the stress state is now linked to the so-called wet area fraction (the ratio between the wet area of particles and their total external surface) rather than to the volume of water in pores. This micromechanical approach can lead to a better interpretation of the strength characteristics of unsaturated soils (Gray and Schrefler 2001; Greco and Gargano 2015; Chen et al. 2023).

Regardless the theoretical approach, the estimation of the unsaturated soil strength using Bishop’s theory is attractive because it relies on the well-established experimental determination of soil mechanical properties under saturated conditions (\({c}^{\prime}\) and \({\phi }^{\prime}\)) and of the soil water retention curve (SWRC) rather than on time-consuming and complex experimental procedures required for the direct determination of unsaturated soil shear strength. In fact, this latter approach implies the use of suction-controlled devices such as simple shear, direct shear or triaxial machines. By imposing suction values on a soil sample, these tests can simulate several field conditions allowing the measurement of the strain‒stress soil behavior for any given suction value. Basically, the unsaturated strength of the soil can be evaluated by subjecting the soil sample to critical loading conditions while maintaining a constant suction value, providing insights into the contribution of the imposed suction to the shear strength.

With reference to the wide area of Campania (Italy) mantled with air-fall pyroclastic deposits, the aim of this study is to investigate the possibility of setting up a unique model for the preliminary assessment of landslide hazard in the study area. Hence, similarities and differences in the hydraulic and geomechanical characteristics of various layers of pyroclastic ashes from different sites based on experimental evidence are studied, and the ability of some existing models to predict unsaturated shear strength from soil water retention curves is assessed. To this end, investigations were conducted on various ash layers where sliding surface has been identified in past landslide events, as well as on the ashes in contact with the bedrock, responsible for water leakage from the soil cover, an aspect rarely investigated in previous research. Thus, novel experimental data and data from previous studies were collected, where both the water retention curve, and the unsaturated shear strength were determined.

Materials and methods

Study area

The study area includes the carbonate massifs of the Partenio, Avella and Sarno mountains, which belong to the Campanian sector of the Southern Apennines (Italy). This area is characterized by diffuse accumulation of air-fall pyroclastic deposits from nearby volcanic areas. Like other volcanic areas around the world (Stern 2004; Stern et al. 2006), it originated in a subduction zone, in this case within the Adriatic microplate, forming the Campanian volcanic arc (Di Bucci et al. 2010). The volcanic complexes, mainly represented by Ischia, Somma-Vesuvius, and the Phlaegrean Fields, are known for being the origin of the most catastrophic eruptions in Europe, particularly attributable to the last two mentioned volcanoes. Specifically, various eruptions dating back between 3,500 and 35,000 years B.P. contributed to the origin of the soil deposits in the area (Rolandi et al. 2003). These deposits often overlap the Apennine carbonate platforms throughout the region (Scrocca 2010), with thickness decreasing as the distance from the source grows and as the slope inclination increases (Del Soldato et al. 2018). Figure 1 shows the area and the sites analyzed in the present study: Cervinara and San Martino Valle Caudina, two sites a few kilometers apart; Monteforte Irpino, all located in the Avella-Partenio mountains; and Pizzo d’Alvano, belonging to the Sarno mountains. These sites are scientifically relevant because they host some of the most catastrophic landslides in recent decades within Campania (Cascini et al. 2008; Fiorillo et al. 2013; Comegna et al. 2018).

Fig. 1
figure 1

Study area with indications of the sites where some destructive landslides occurred in recent decades near the Campanian volcanic arc

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The studied slopes are located between 300 and 800 m above sea level, with inclinations ranging from 30° to 50°. The typical soil profiles are shown in Fig. 2a-c. As depicted in Fig. 2d-e, the stratigraphic sequence of the soil deposits exhibits several common features: a relatively thin soil deposit (which is always mantling a fractured carbonate bedrock) consisting of coarse-grained loose pyroclastic soils with alternating layers of pumice and ash. As shown in Figs. 2d and 2e, differences in deposit layers are observed because, owing to the distance and direction from the eruptive center, the deposits from some of the eruptions are not found at all sites. However, a common feature at all the sites is that at the base of the layered profile, near the contact with the underlying limestone bedrock, a layer of altered volcanic ash is observed Cascini et al. 2000).

Fig. 2
figure 2

Slope profiles at the study sites in (a) Pizzo d’Alvano (Bilotta et al. 2005), (b) Monteforte (Nicotera et al. 2015), and (c) Cervinara (Damiano et al. 2012) villages and typical soil cover stratigraphic sequences (not to scale) for (d) Pizzo d’Alvano and Monteforte and (e) Cervinara

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Several studies highlighted the volcanic ashes interbedded between the pumice layers (layer 3 and layer 5 in Fig. 2d and layer 3 in Fig. 2e) as those where the sliding surface of landslides developed (Cascini et al. 2000; Santo et al. 2018; Comegna et al. 2018). In fact, the interbedded ashes are the weakest layer within the stratigraphical sequence, as they present a smaller effective friction angle compared to pumices, and, differently from the underlying altered ashes, usually exhibit null effective cohesion. For this reason, special attention has been given to the ashes of these layers, and a specific analysis has been conducted on the ashes from layer 3 in San Martino Valle Caudina. However, the occurrence of any hypothesized failure mechanism (i.e., pore pressure buildup at the base of the soil profile (Olivares and Damiano 2007; Damiano and Olivares 2010; Reder et al. 2017), water exfiltration from the bedrock (Cascini et al. 2008), or the formation of capillary barriers at the upper boundary of the pumice layers (Mancarella et al. 2012) might be controlled by rainwater infiltration and drainage processes at the soil–bedrock interface to deeper systems (Marino et al. 2021). In this context, the altered ashes in contact with the fractured bedrock (see layer 7 in Fig. 2d and layer 5 in Fig. 2e) may play a crucial role in water exchange with underlying aquifers. Such a layer has not often been considered in the studies carried out thus far. Consequently, several other analyses, specifically for ashes in contact with the bedrock, were conducted in this study.

Experimental investigations of the pyroclastic ashes of Campania

The present research collected a series of previous experimental investigations and contributed additional data on the pyroclastic soils under investigation, focusing on the ashy layers (see Fig. 2d-e). Specifically, the analyzed materials were the ashes interbedded between pumice strata in layer 3 in Cervinara (referred to as AC3, from Olivares et al. 2019); in layer 3 in San Martino Valle Caudina (ASM3, new experimental data); layers 3 and 5 in Pizzo d’Alvano (AS3 and AS5, from Olivares et al. 2019 and Bilotta et al. 2005); and layer 3 in Monteforte (AM3, from Sorbino and Nicotera 2013). Additionally, the altered ashes in contact with the bedrock are highlighted in Cervinara (BC5, new experimental data) and in Monteforte (BM7, from Papa 2007).

Index properties and shear strength under saturated conditions

Numerous studies have reported the properties of pyroclastic soils in the study area. Concerning the grain size distribution, findings from Cervinara indicate that the AC3 volcanic ash corresponds to a silty-sand material (Olivares et al. 2019). In the case of Pizzo d’Alvano, the ashes AS3 and AS5 presented relatively well-graded compositions and were classified into two primary groups: coarser silty-sand ashes (AS3) and finer silty-sand ashes (AS5) (Bilotta et al. 2005; Olivares et al. 2019). Monterforte ashes AM3 also exhibit relatively well-graded characteristics and have been classified as a silty-sand material (Nicotera et al. 2015). Other index properties, such as porosity (\(n\)) and specific gravity (\({\text{G}}_{\text{s}}\)), are reported in Table 1.

Table 1 Physical and mechanical characteristics of the studied ashes in Cervinara: AC3 (Olivares et al. 2019), BC5 (this study), S.M. Valle Caudina: ASM3(this study), Pizzo d’Alvano: AS3 (Olivares et al. 2019), AS5 (Bilotta et al. 2005) and Monteforte: AM3 (Sorbino and Nicotera 2013), BM7 (Papa 2007)
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Regarding the mechanical characteristics of the materials, most studies have reported the resistance of interbedded ashes in saturated conditions by estimating the effective friction angle (\(\phi ^{\prime}\)) and effective cohesion (\(c^{\prime}\)) on both undisturbed and reconstituted samples via conventional direct shear (Bilotta et al. 2005) and triaxial tests (Pirone et al. 2015; Nicotera et al. 2015; Picarelli et al. 2020).

The soils from different layers in Cervinara-S.M. Valle Caudina were investigated in this study. Specifically, standard tests on specific gravity, grain size distribution, and Atterberg limits were performed on samples of altered ashes BC5 sampled from the site with coordinates 41°0′29.50″N and 14°38′35.37″E. The same procedures were conducted for ASM3 ashes sampled from the site with coordinates 41° 0′52.43″N and 14°39′40.19″E. The obtained values are reported in Table 1.

Hydraulic characteristic curves

The water retention properties of pyroclastic soils in Campania were estimated in all cases by measuring the soil suction and water content under equilibrium conditions through different experimental devices. Nicotera et al. (2015) investigated the water retention properties of AM3 ashes and proposed a quick procedure by applying wetting and drying cycles to undisturbed soil samples under atmospheric conditions, measuring suction at two different points and weighing the sample at any equalization step. The same procedure was applied to investigate the water retention behavior of the BM7 ashes (Papa 2007). Sorbino and Nicotera (2013) reported some results about the investigation of the water retention properties of AS5 ashes. These data were obtained by using a suction-controlled oedometer with a vertical net stress ranging between 20 and 100 kPa combined with drying/wetting cycles in the volume extractor apparatus. Olivares et al. (2019) investigated the water retention behavior of AS3 and AC3 ashes by applying progressive suction increments using a suction-controlled triaxial apparatus within a suction range between 5 and 80 kPa with a mean net stress ranging between 50 and 270 kPa. The same procedure was applied to the ASM3 ashes with a mean net stress of 50 kPa. In contrast, the water retention of the BC5 altered ashes was investigated using a Richards plate apparatus within a suction range between 5 and 85 kPa.

The interpretation of the soil hydraulic properties, depicting the relationship between the degree of saturation (\({S}_{r}\)) and soil suction (\(s\)) in the studied ashes, was performed here using the van Genuchten–Mualem model (van Genuchten 1980), shown in Eqs. (1) and (2). The optimal model parameters were found by minimizing the root mean square error (RMSE) between the experimental data and the model estimations.

$${S}_{e}=\frac{\theta -{\theta }_{r}}{{\theta }_{s}-{\theta }_{r}}=\frac{1}{{\left[1+{\left({\alpha }_{VG}s\right)}^{{n}_{VG}}\right]}^{{m}_{VG}}}$$
(1)
$$k={K}_{sat}{S}_{e}^{l}{\left[1-{\left(1-{S}_{e}^{1-{m}_{VG}}\right)}^{{m}_{VG}}\right]}^{2}$$
(2)

On one hand, in Eq. (1), \({S}_{e}\) is the effective degree of saturation; \(\theta\) is the soil volumetric water content; \({\theta }_{s}\) is the volumetric water content at saturation; \({\theta }_{r}\) is the residual volumetric water content; \(s\) is the soil suction; \({n}_{VG}\) and \({\alpha }_{VG}\) are van Genuchten’s model shape parameters, with \({n}_{VG}\) related to the slope of the curve in the transition zone between the near-saturation conditions and dry residual conditions; and \({\alpha }_{VG}\) being an index of the air entry value of the soil. The parameter \({m}_{VG}\) was assumed to be \({m}_{VG}=1-1/{n}_{VG}\). On the other hand, in Eq. (2), \(k\) is the hydraulic conductivity, \({K}_{sat}\) is the hydraulic conductivity under saturated conditions, and \(l\) is a fitting parameter optimized here according to the experimental data.

The optimal parameters of the van Genuchten – Mualem model were estimated in two stages: firstly, the best fitting parameters of Eq. (1) \({\alpha }_{VG}\), \({n}_{VG}\) and \({m}_{VG}\), were found; secondly, by keeping \({\alpha }_{VG}\), \({n}_{VG}\) and \({m}_{VG}\) fixed to the obtained values, and searching on the value of \(l\) by fitting Eq. (2) to the hydraulic conductivity experimental data. The obtained RMSE for the two curves are given in Table 2 for all the studied soils.

Suction stress contribution to the shear strength

Soil suction contributes to the shear strength of unsaturated soils through suction stress \({\sigma }^{s}=\chi s\). This mechanism can be interpreted based on Bishop’s effective stress theory (1959) with the Mohr–Coulomb formulation:

$${\uptau }_{lim}={c}^{\prime}+\left(\sigma -{u}_{a}\right)\text{tan}\phi^ {\prime}+\chi s\text{tan}\phi^ {\prime}$$
(3)

Alternatively, following the two independent stress variables approach (Fredlund and Rahardjo 1993), the shear strength can be expressed as

$${\uptau }_{lim}={c}^{\prime}+\left(\sigma -{u}_{a}\right)\text{tan}\phi ^{\prime}+s\text{tan}{\phi }_{b}$$
(4)

In Eq. (4), \({\phi }_{b}\) is the angle of shearing resistance due to the contribution of suction, which can be interpreted as \(\text{tan}{\phi }_{b}=\chi \text{tan}\phi ^{\prime}\); thus, in any case, knowledge of \(\chi\) is required to estimate the unsaturated shear strength when no direct measurements are available.

The shear resistance of AC3 and AS3 under unsaturated conditions was experimentally evaluated on undisturbed specimens via a suction-controlled triaxial apparatus. This approach aimed to determine the critical state of the soil within a suction range of 5 kPa to 80 kPa under varying confining pressures from 50 to 270 kPa (Olivares et al. 2019). A similar triaxial testing technique was used for AM3, in which the suction was controlled from 6 to 20 kPa (Nicotera et al. 2015). Additionally, AS3 was studied using a procedure involving the testing of unsaturated soil specimens on a conventional direct shear apparatus, retrieving the degree of saturation at the end of the test, and estimating the corresponding soil suction (ranging between 0 and 50 kPa) from the SWRC of the materials (Bilotta et al. 2005). From all the experimental tests, the suction stress was estimated from the critical state conditions. On one hand, for triaxial tests, the following equation was derived from the critical state line:

$${\sigma }^{s}=\frac{\text{q}-c^{\prime}\text{N}}{\text{M}}-\overline{\text{p} }$$
(5)

In Eq. (5) \(\text{q}\) and \(\overline{\text{p} }\) are the deviatoric stress and the mean net stress, respectively; \(\text{N}=6\text{cos}\phi^ {\prime}/\left(3-\text{sin}\phi^ {\prime}\right)\) and \(\text{M}=6\text{sin}\phi ^{\prime}/\left(3-\text{sin}\phi^ {\prime}\right)\), with \(c^{\prime}\) and \(\phi^ {\prime}\) the effective cohesion and shear strength angle, respectively. On the other hand, \({\sigma }^{s}\) for direct shear tests was interpreted, as could be seen in Eq. (6), from the Mohr–Coulomb criterion, where \(\tau\) and \({\sigma }=\left(\sigma -{u}_{a}\right)\) are the shear stress and net vertical stress, respectively.

$${\sigma }^{s}= \frac{\tau -c}{\text{tan}\phi ^{\prime} }-{\sigma }$$
(6)

Estimation of the suction stress from the water retention curve

As stated hereinbefore, estimating Bishop’s effective stress parameter from the water retention curve eliminates the need for direct measurements of unsaturated soil shear strength. Hence, in this study, the parameter \(\chi\) was estimated with four different models, which predictions were compared with experimental shear strength data from the ashy soils of the study area.

First, the empirical approach proposed by Khalili and Khabbaz (1998) was used, which links the parameter \(\chi\) to the ratio between soil suction and soil suction at the air entry value (\({s}_{aev}\)) as \(\chi ={\left(s/{s}_{aev}\right)}^{b}\). The exponent \(b\) is a fitting parameter, which was originally proposed as -0.55 by the authors of the model, and was fitted here with the experimental data of each investigated soil.

Furthermore, several analytical models have been used considering two approaches, denoted here as the pore water volume approach and the wet area approach. The pore water volume approach proposed by Lu and Likos (2006) assumes that \(\chi ={S}_{e}\), so that the suction stress can be obtained directly from the water retention parameters of van Genuchten’s model (Lu et al. 2010):

$${\sigma }^{s}=-\frac{{S}_{e}}{{\alpha }_{VG}}{\left({S}_{e}^{\frac{{n}_{VG}}{1-{n}_{VG}}}-1\right)}^{{n}_{VG}^{-1}}$$
(7)

According to the wet area approach, \(\chi ={\alpha }_{w}\) is assumed, where \({\alpha }_{w}\) is the wet area fraction, i.e., the ratio between the area of soil particles in contact with pore water and the total external surface area of the soil grains. The dependence of the wet area fraction on \({S}_{e}\) was evaluated with two models. The first one, proposed by Greco and Gargano (2015), assumes the following:

$${\alpha }_{w}=\left\{\begin{array}{c}{\alpha }_{0}C+\left(1-C\right)\left[{\alpha }_{0}-\frac{\frac{{\gamma }_{w}\left({\theta }_{s}-{\theta }_{r}\right)}{{T}_{w}\text{cos}{\theta }_{c}}{\int }_{{s}_{0}}^{s}\frac{\kappa }{\alpha }s\frac{d{S}_{e}}{ds}ds}{{A}_{0}+\frac{{\gamma }_{w}\left({\theta }_{s}-{\theta }_{r}\right)}{{T}_{w}\text{cos}{\theta }_{c}}{\int }_{{s}_{0}}^{0}\frac{\kappa }{\alpha }s\frac{d{S}_{e}}{ds}ds}\right], s<{s}_{0}\\ {\alpha }_{w}={\alpha }_{0}, s\ge {s}_{0}\end{array}\right.$$
(8)

In Eq. (8), \({s}_{0}\) is the soil suction above which adsorption becomes the dominant process of water retention in the soil pores, a parameter to be determined based on experimental data; \({\alpha }_{0}\) is the constant wet area fraction associated with adsorbed water, estimated as \({\alpha }_{0}={\left({\theta }_{r}/{\theta }_{s}\right)}^{2/3}\) considering an isotropic distribution of the residual water content in the pore space; \({A}_{0}\) is the wet area corresponding to \({\alpha }_{0}\); \(C\) is a function of soil suction, introduced to smooth the discontinuity when \(s\to {s}_{0}\), which has no influence on the results presented here; \({\gamma }_{w}\), \({T}_{w}\) and \({\theta }_{c}\) are the unit weight of water, water surface tension and soil‒water interface contact angle, respectively; and \(\kappa /\alpha\) is a pore shape geometric factor, here assumed constant and equal to 1.

The wet area fraction was also evaluated using the equation proposed by Chen et al. (2023):

$${\alpha }_{w}={e}^{\eta \left(1-\frac{1}{{S}_{r}}\right)}$$
(9)

In Eq. (9), \({S}_{r}=\theta /n\) is the degree of saturation of the soil, and \(\eta\) is a material constant parameter determined from the experimental data.

For both, the empirical and wet area approaches, the additional calibration parameter was estimated by minimizing the RMSE with the corresponding experimental data.

Results

Index properties of the studied pyroclastic ashes

Figure 3 shows the grain size distributions for each soil. The shaded areas represent the grain size spectra of each soil type according to previous investigations (Bilotta et al. 2005; Damiano et al. 2012; Nicotera et al. 2015; Olivares et al. 2019), while the lines represent the samples specifically tested in the present study.

Fig. 3
figure 3

Particle size distributions of the ashes studied in (a) Cervinara-S.M. Valle Caudina, (b) Pizzo d’Alvano and (c) Monteforte

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The grain size distributions indicate that the interbedded volcanic ashes AC3, ASM3, AS3, AS5 and AM3 consist mostly of silty sands. In contrast, the altered ashes BC5 and BM7, which are in contact with the bedrock, have a significantly larger fine fraction, especially for the sample BC5 tested in the present study. This, in turn, suggests that the ash layer in contact with the bedrock may have widely variable properties even at the same site, probably related to a different degree of alteration or weathering. In fact, the depositional history at each site is different, as the materials ejected during the various eruptions did not always reach all the sites (Rolandi et al. 2003). This affects not only the stratigraphic sequences, presenting different layers and thickness, but also the exposition of the deposits to weathering agents, that may explain the observed variability. However, further investigations are needed to shed more light on this aspect.

Hydraulic characteristic curves of the ashes

Figure 4 shows the experimental data of the water retention of all the studied soils, in addition to the best-fitting van Genuchten water retention curves (Eq. (1)); the parameters of which are reported in Table 2. In the same table, the air-entry suction values (\({s}_{aev}\)), estimated from the shape of the water retention curves, are also reported.

Fig. 4
figure 4

Experimental data on water retention and their interpretation through the van Genuchten model (VG) of BC5 (this study) and AC3 (Olivares et al. 2019) in Cervinara; ASM3 in S.M. Valle Caudina (this study); AM3 (Nicotera et al. 2015) and BM7 (Papa 2007) in Monteforte; and AS3 (Olivares et al. 2019) and AS5 (Sorbino and Nicotera 2013) in Sarno

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Table 2 Soil hydraulic characteristic curve parameters of the van Genuchten–Mualem model, the air-entry value of the suction stress model from Khalili and Khabbaz (1998), \({s}_{aev}\), and the wet area fraction at the residual water content of the suction stress model from Greco and Gargano (2015), \({\alpha }_{0}\), for the studied pyroclastic ashes. The Root Mean Squared Error on \({S}_{r}\) of the Van Genuchten model (VG RMSE) and on \(k\) of the Van Genuchten – Mualem model (Mualem RMSE) are also reported
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The water retention properties show that the interbedded ashes exhibit relatively low air entry values (depicted by \(1.0 \text{kPa}\le {\alpha }_{VG}^{-1}\le 8.0 \text{kPa}\) and \(0.45 \text{kPa}\le {s}_{aev}\le 3.80 \text{kPa}\)), along with \(1.18 \le {n}_{VG}\le 1.36\). Even if in contact with the bedrock, the ashes BM7 look similar to the interbedded ashes, with \({\alpha }_{VG}^{-1}=10.0\) kPa, \({n}_{VG}=1.25\) and \({s}_{aev}=5.0\) kPa. In contrast, the altered ashes BC5 exhibit \({\alpha }_{VG}^{-1}=50 \text{kPa}\) with \({n}_{VG}=1.07\) and \({s}_{aev}=24.0\) kPa.

Figure 5 shows the results of the experimental estimation of the saturated and unsaturated hydraulic conductivity (k) for the interbedded ashes AC3 (Olivares et al. 2019), ASM3 (this study), AS3 (Olivares et al. 2019) and AS5 (Bilotta et al. 2005), as well as for the altered ashes BC5 (this study) and BM7 (Papa 2007). The points represent the experimental data, while the dotted lines are the van Genuchten–Mualem hydraulic conductivity curves (Eq. (2)) fitting each data series.

Fig. 5
figure 5

Hydraulic conductivity of the pyroclastic ashes in contact with the bedrock in Cervinara (BC5, this study) and in Monteforte (BM7, from Papa 2007) and the interbedded pyroclastic ashes in Cervinara (AC3, from Olivares et al. 2019), in S.M. Valle Caudina (ASM3, this study), and in Sarno (AS3 and AS5, from Olivares et al. 2019 and Bilotta et al. 2005 respectively). The dotted lines represent the van Genuchten–Mualem hydraulic conductivity curves fitting each data series

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Under saturated conditions (\(s=0 \text{kPa}\)), the altered ashes in contact with bedrock BC5 and BM7 had the lowest hydraulic conductivities among the investigated soils, characterized by great variability ranging in an order of magnitude of approximately 10–7 m/s. However, again under saturated conditions, the interbedded ashes exhibit significantly greater hydraulic conductivities with lower variability, ranging between 1.5∙10–6 m/s and 5.0∙10–6 m/s. Conversely, under unsaturated conditions, the hydraulic conductivities of altered ashes BC5 and BM7 exhibit very different trends: the hydraulic conductivities of the BC5 ashes decrease to values between 5∙10–8 m/s and \({10}^{-7}\) m/s in the suction range between 40 and 90 kPa, while those of the BM7 ashes decrease to values between 1∙10–9 m/s and 4∙10–9 m/s. In contrast, in the same suction range, the conductivity of all the interbedded ashes is less than 3∙10–8 m/s, dropping even up to 10–9 m/s, as for AS5. Interestingly, the unsaturated behavior of these ashes (AS5) results in a hydraulic conductivity greater than that of the other interbedded ashes when \(s<10\) kPa but decreases to the smallest values, even smaller than 10–9 m/s, at the highest investigated suction.

Suction stress contribution to the shear strength of the ashes

Figure 6 shows the experimental data relating \({\sigma }^{s}\) and \(s\) in the studied interbedded ashes AC3, AS3, AS5 and AM3 retrieved from the results of the laboratory tests, as indicated in Section 2.2.3. Specifically, Fig. 6a shows the results of Cervinara ashes AC3 tested within a soil suction ranging between 5 and 80 kPa. Figure 6b shows the results for Pizzo d’Alvano ashes AS3 from experimental tests covering soil suctions ranging from 7 to 40 kPa. Figure 6c shows the results of the experimental tests carried out on AS5 with a suction ranging from 10 to 50 kPa. Finally, Fig. 6d shows the experimental data from tests carried out on Monteforte ashes AM3 within a suction range from 6 to 20 kPa. Moreover, Fig. 6 also shows the different tested models fitting the experimental data. The best-fitting parameter values for the applied models as well as the RMSEs for each case, are given in Table 3.

Fig. 6
figure 6

Experimental data relating soil suction and suction stress contribution to shear strength and different model relationships for (a) Cervinara ashes AC3 (Olivares et al. 2019), (b) Pizzo d’Alvano ashes AS3 (Olivares et al. 2019) and (c) AS5 (Bilotta et al. 2005), and (d) Monteforte ashes AM3 (Nicotera et al. 2015)

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Table 3 Model parameters and Root Mean Squared Error (RMSE) estimated for different models fitting the experimental data of interbedded pyroclastic ashes
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Discussion

The ash soils belonging to different layers of the pyroclastic deposits found in different landslide-prone areas of the Partenio and Sarno mountains in Campania, southern Italy, have been analyzed from different points of view: grain size distribution, hydraulic characteristic curves, and suction stress contribution to the shear strength under unsaturated conditions. The analysis of the grain size distribution reveals that the interbedded ashes are silty sands with limited variability. Conversely, the altered ashes in contact with the bedrock, often described as clayey altered ashes (Fiorillo et al. 2001; Bilotta et al. 2005; Pirone et al. 2015; Nicotera et al. 2015), show greater variability, ranging from coarse-grained materials to fine clayey limes. The hydraulic behavior of the studied soils confirms this frame. The interbedded ashes from the different study sites exhibited relatively similar hydraulic characteristics. Instead, the altered ashes in one case exhibited typical coarse-grained soil behavior with low unsaturated conductivities, and in another case, they exhibited typical fine-grained soil behavior with relatively high unsaturated conductivities.

The analysis of the evolution of the suction stress along with the suction level, carried out for the interbedded ashes from three different sites, showed a rapid increase in suction stress in the range \(0.0 \text{kPa}\le s\le 10.0 \text{kPa}\) in all the cases. Such an increase always occurs in a suction range containing the air entry value of the materials. Interpreting the experimental results with the empirical model proposed by Khalili and Khabbaz (1998), the fitting parameter b varies in a relatively narrow range between -0.34 and -0.42, except for the AS5 ashes from Pizzo d’Alvano, for which the parameter results equal -0.22. This anomalous behavior of this soil, likely related to the larger fine fraction compared to the other interbedded ashes (see Fig. 3), also arises from the adoption of different models. For instance, analyzing the results with models based on wet area theory, the parameter \(\eta\) of the model proposed by Chen et al. (2023) ranges between 1.18 and 1.45 for all the analyzed soils, while for AS5, the value is 0.91. With the model proposed by Greco and Gargano (2015), the suction value \({s}_{0}\), corresponding to the transition from capillary to adsorbed water, lies in the narrow range between 62 and 65 kPa for all the studied soils, while the AS5 ashes exhibit a slightly larger value of approximately 69 kPa.

Regarding the capability of the tested models to predict the contribution of suction to soil shear strength, it is worth to note that slope inclination angle affects the degree of saturation of the soil at failure. In fact, slopes with inclination angle higher than the effective friction angle of the soil will fail in unsaturated conditions, while slope rupture will occur at saturation for smaller inclinations (Olivares and Damiano 2007). In this respect, the model of Lu et al. (2010), which does not require the assignment of any additional parameter, works reasonably well for soils near saturation only; however, this model rapidly deviates as the soil becomes dry, tending to overestimate the suction stress contribution. All the other tested models provide good predictions of the shear strength far from saturation, but they require a further parameter to be estimated. In this respect, the model of Greco and Gargano (2015) seems preferable for the studied pyroclastic ashes, as the best-fitting values of \({s}_{0}\) are very close to each other, thus allowing setting up a reliable model of unsaturated soil shear strength even in the absence of experimental data (i.e., by assuming \({s}_{0}\cong 65\) kPa).

Moreover, the transition between adsorption and capillarity (which occurs at high suction values) may impact the unsaturated shear strength in the materials under investigation. Therefore, further research that provides experimental evidence on this matter is should be addressed, especially for applications where the assessment of soil strength in dry conditions is required.

Conclusions

This study collected data from three sites in a wide but geologically uniform landslide-prone area in Campania, southern Italy, where relatively thin layered pyroclastic deposits cover a karstic limestone bedrock; the Partenio and Sarno Mountains. The gathered data focus on index properties, hydraulic properties, and suction stress contribution to the shear strength of the soil. In this respect, the analyses show that the interbedded ashes of the same layer from different study sites, where failure surfaces of observed landslides usually occur, exhibit relatively uniform behavior from hydraulic and mechanical points of view in both saturated and unsaturated conditions.

The analysis with different models, carried out to assess how suction contributes to the shear strength of interbedded ashes under unsaturated conditions, confirms this picture. In this respect, it is worth noting that the model by Lu et al. (2010) is a useful tool for estimating shear strength near saturation directly from the water retention curve of the soil, as further calibration parameters are not needed. However, it deviates from the experimental data as the soil becomes dry, overestimating the suction contribution to soil strength. Conversely, the models based on the wet area fraction fit well with the data under dry conditions, but they require the calibration of an additional parameter based on experimental observations of unsaturated shear strength. In this respect, the model by Greco and Gargano (2015) seems more attractive, as the additional parameter of this model is practically constant for all the studied pyroclastic soils, thus allowing the first assessment of unsaturated soil shear strength in the absence of direct measurements.

Regarding the altered ashes in contact with the bedrock, empirical evidence shows significant variability of their hydraulic properties, likely owing to the different degree of alteration. Indeed, in some sites they resemble the coarse-grained interbedded ashes, in others they exhibit high air entry values, such as fine-grained soils. Nonetheless, the saturated hydraulic conductivity of the altered ashes is significantly lower than that of the interbedded ashes in any case under analysis. Further research is necessary to better understand the implications of the variability in the hydraulic properties of altered ashes in landslide-prone areas. In fact, these ashes, in contact with the bedrock, control the leakage from the soil cover to deeper hydraulic systems through the soil–bedrock interface, in turn affecting the conditions that may lead to landslide triggering.

In conclusion, the results from this study show the importance of the correct modelling of the suction stress contribution to unsaturated soil shear strength, especially in soils resting on high slope inclinations, where slope failure may develop in unsaturated conditions. In that sense, it is feasible the use of a single model for early assessments of the suction stress contribution to soil shear strength for the entire study area, using only the water retention parameters in absence of specific experimental data.