Introduction

Riverbank retreat is globally an important issue that affects infrastructure and stream-side properties, in-stream habitats, and water quality (Daly et al. 2015). Excessive sediment from riverbank erosion is among the most common surface water pollutants that degrade water quality and destroy aquatic habitats (ASCE 1998; Wynn and Mostaghimi 2006; Midgley et al. 2012). Moreover, many studies have demonstrated that riverbank erosion contributes a large portion of the sediment yield in a drainage system, which reduces the drainage capacity of the river and thereby causes flooding (e.g., Simon 1989; Grissinger et al. 1991). Thus, riverbank retreat involves the overall ecosystem of the river and causes huge economic losses with damage to natural resources (ASCE 1998).

Riverbank retreat is the integrated product of three main processes: subaerial processes, fluvial erosion, and bank failure (Hooke 1979; Lawler 1992; Lawler et al. 1997; Couper and Maddock 2001; Rinaldi and Nardi 2013). Subaerial processes are climate-related phenomena that reduce soil strength, inducing direct erosion and making the bank more susceptible to fluvial erosion by, for example, desiccation cracking (Thorne 1982). Fluvial erosion is the removal of bank material by the action of the river’s hydraulic forces (Rinaldi and Nardi 2013), while the collapse of riverbanks due to slope instability is referred to as bank failure (Lawler 1995). Riverbank retreat is a cyclic process, initiated by the fluvial erosion of the river bed and/or toe, which creates a geotechnically unstable riverbank. This instability results in riverbank failure and deposition of failed materials at the bank toe. Subsequent floods remove that failed materials and the bank retreat cycle is repeated until the channel widens enough to reduce the boundary shear stresses to non-erosive levels (Thorne 1982).

The erosion rate of cohesive riverbank is commonly predicted using the excess shear stress equation (Partheniades 1965; Hanson 1990a, 1990b):

$$ \varepsilon ={k}_d{\left({\tau}_o-{\tau}_c\right)}^a $$
(1)

where ε is the rate of erosion (m/s), kd is the erodibility coefficient (m3/N.s), τo is the developed boundary shear stress (Pa), τc is the critical shear stress (Pa), and a is an empirical exponent, often in practice assumed to be unity (Hanson 1990a, 1990b; Hanson and Cook 2004). The riverbank erosion is initiated by non-negative excess shear stress (τo − τc). Once the erosion is initiated, kd defines the rate at which particles are detached from the riverbank (Daly et al. 2013).

In the excess shear stress equation, while τo is simply related to the flow rate of water (τo = γwRS, where γw is the unit weight of water, R is the local hydraulic radius calculated from the water depth, and S is the channel slope (Daly et al. 2015)), the soil erodibility parameters (τc and kd) are difficult to quantify (Grissinger 1982). There are many approaches for determining the erodibility parameters. Several studies have derived τc and kd for cohesive soils using various techniques such as flume tests (Hanson and Cook 1997), a laboratory hole erosion test (Briaud et al. 2001; Wan and Fell 2004), and a submerged jet test (Hanson and Cook 1997; Clark and Wynn 2007). Based on such experimental results, many studies have proposed simpler approaches to estimate τc from other soil properties: from clay content and liquid limit (Smerdon and Beasley 1961), silt-clay content (Julian and Torres 2006), and from unconfined compressive strength (Kamphius and Hell 1983). Once τc is determined, kd can be estimated from empirical formulae (e.g., Hanson and Simon 2001; Wynn 2004; Simon et al. 2011).

Alternatively, in situ measurement of the erodibility parameters can be done using the submerged jet device developed by Hanson (1990b). The jet test is preferred over the flume tests because it can be conducted directly on the intact riverbank material without sampling and sample preparation that would disturb the soil structure, as they do in the flume tests. Determination of τc and kd using the jet test results (i.e., jet pressure and scour depth created) has been proposed by many researchers, such as Hanson and Cook (1997, 2004) and Daly et al. (2013). A detailed description of the jet device and the testing methodology is presented elsewhere (Hanson and Cook 1997; Hanson and Simon 2001; Al-Madhhachi et al. 2013).

Recently, Daly et al. (2015) evaluated the erodibility parameters of the Barren Fork Creek in eastern Oklahoma, USA, by calibration of a process-based riverbank retreat model. Streambank geography, bank soil properties, stream hydrograph, and initial erodibility parameters obtained from the jet test were used as inputs to the process-based riverbank erosion model (i.e., the Bank Stability and Toe Erosion Model, BSTEM), developed by the National Sedimentation Laboratory in Oxford, MS. The computed streambank was compared with the actual streambank retreat obtained from aerial imagery. The initial erodibility parameters were then adjusted until the computed streambank retreat was similar to the observed streambank retreat. The erodibility parameters obtained in this manner accounted for fluvial erosion and bank failure, along with several other field factors such as curvature-driven and turbulence-driven secondary flows and spatial and temporal changes of bank materials due to cyclical wetting and drying.

As a part of the U-Tapao River erosion study and protection project, the objective of this study was to analyze riverbank retreat of six representative composite riverbanks along the U-Tapao River in southern Thailand. The field survey was conducted to determine geometry of the riverbanks. In situ and laboratory measurements were performed to assess the riverbank soil geotechnical and erodibility parameters. Aerial imagery analysis was conducted to determine the actual bank retreats. The Bank Stability and Toe Erosion Model (BSTEM) was used to compute the riverbank retreats. The computed results were verified and validated using measured riverbank retreats from aerial imagery analysis.

Description of the study area

The study area is located in the U-Tapao River watershed, in the southern part of Thailand (Fig. 1). The U-Tapao River watershed covers 2392 km2 from the southern Thai-Malaysian border to the Songkhla Lake. This is the most important watershed of southern Thailand and is home to over 700,000 residents. Hat Yai city, the main city in the watershed, is a local center of economy, industry, and tourism in this region. The U-Tapao River, the main river in the watershed, is about 112 km long. It originates in the southern mountainous areas, flows northward through the center of the watershed, and drains into the Songkhla Lake. The average annual rainfall of the watershed is about 1524 mm due to the tropical monsoon climate in this region. Heavy rains in the months from October to December often cause great erosion and frequent failures of the riverbanks.

Fig. 1
figure 1

U-Tapao River watershed and the study site locations

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U-Tapao riverbanks along the midstream area of the watershed are reportedly experiencing high bank retreat problems and were selected as the study area. In this area, the U-Tapao River is about 20 to 40 m wide and 5 to 10 m deep. A picture of the U-Tapao River composite bank in the study area (Fig. 2) shows a typically steep bank face. The typical composite riverbanks in the study area consist mainly of two layers. The top layer (hereafter called “upper bank”) is low plasticity cohesive soil with thickness ranging from about 1.0 to 1.5 m. The underlying layer (hereafter called “lower bank”) is either cohesive or granular soil, which normally ranges in thickness from about 3.0 to 6.0 m. Field observation indicates toe erosion at the lower banks continuously leads to bank failure and retreat. In this study, six sites were selected at locations along the midstream area of the U-Tapao River and are designated as UT1 to UT6, as shown in Fig. 1 and Table 1. The distance from UT1 to UT6 is about 14 km. Pictures of the U-Tapao River bank sites are shown in Fig. 3. Around these sites, the typical land use is as para rubber plantations that have bank retreat problems according to local authorities and land owners. At each site, a representative cross section and a detailed bank stratigraphy were prepared using field survey data.

Fig. 2
figure 2

An U-Tapao River composite bank showing the typical layers. Upper bank with low plasticity cohesive soil (a) and lower bank with cohesive or granular soil (b)

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Table 1 Soil properties at the six study sites
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Fig. 3
figure 3

Pictures of U-Tapao River banks showing composite and cohesive riverbanks with steep bank faces

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Background

Empirical relationships for determining erodibility parameters

There are several approaches to determine soil erodibility parameters. The parameters can be simply estimated from empirical relationships using soil index properties, as proposed by several researchers. Estimates of τc can be obtained from empirical equations using plasticity index, dispersion ratio, mean particle size, and percent clay (Smerdon and Beasley 1961), silt-clay content (Julian and Torres 2006), unconfined compressive and vane shear strength (Kamphius and Hell 1983), and dispersion ratio, activity, and soil pH (Thoman and Niezgoda 2008). Based on flume testing results, Smerdon and Beasley (1961) developed empirical relationships of τc to various soil index properties, as shown in Eqs. 2–4.

$$ {\tau}_c=3.54\times {10}^{-28.1{D}_{50}} $$
(2)
$$ {\tau}_c=0.493\times {10}^{0.0182{P}_c} $$
(3)
$$ {\tau}_c=0.16{(PI)}^{0.84} $$
(4)

where τc is the critical shear stress (Pa), D50 is the median particle size of soil (mm), Pc is the percentage of clay content (i.e., content of soil particles less than 0.002 mm in size), and PI is the soil plasticity index.

Julian and Torres (2006) established an empirical equation to estimate τc from the percentage of silt-clay (SC):

$$ {\tau}_c=0.1+0.1779(SC)+0.0028{(SC)}^2-2.34\times {10}^{-5}\times {(SC)}^3 $$
(5)

Unlike τc, empirical estimates of kd from the soil properties are not available (Hanson and Temple 2002). However, kd can be given empirical estimates from known τc. Such empirical relations between kd and τc have been developed based on submerged jet test results and are often power laws (Hanson and Simon 2001; Wynn 2004; Thoman and Niezgoda 2008). Using the Blaisdell solution (Blaisdell et al. 1981), Simon et al. (2010) concluded from jet test results that kd is related to τc as shown in Eq. 6. Daly et al. (2013) developed a scour depth solution method to fit the jet test results and proposed the relationship in Eq. 7.

$$ {k}_d=1.62{\tau}_c^{-0.838} $$
(6)
$$ {k}_d=157{\tau}_c^{-1.620} $$
(7)

where kd is the erodibility coefficient (cm3/N.s) and τc is the critical shear stress (Pa). The discrepancy between the various empirical models indicates that, while the type of model might have wide applicability, each model fit is restricted to a specific context of soil samples.

Submerged jet test

For cohesive soils, the soil erodibility parameters can be experimentally determined using an in situ submerged jet device. Designed by Hanson (1990b), the device distributes a circular jet through the nozzle at a uniform velocity, to produce shear stresses in the bank material. Consequently, the scours or the eroded depths generated are measured, and their time profiles are used to determine the erodibility parameters. Hanson and Cook (1997) developed an analytical procedure to estimate τc by fitting a hyperbolic logarithm equation proposed by Blaisdell et al. (1981) to the scour depth vs time data, while kd was estimated by fitting the scour data to the excess shear stress equation (Eq. 1). Daly et al. (2013) stated that the conventional Blaisdell solution method is too conservative, so they developed an alternative approach, the so-called scour depth solution method.

The jet test device has been used numerous times to determine the erodibility of cohesive soils (Hanson et al. 1999; Langendoen et al. 2000; Hanson and Simon 2001; Semmens and Osterkamp 2001; Simon and Thomas 2002; Thoman and Niezgoda 2008; Karmaker and Dutta 2011). Results from most of these studies indicate large variations in τc and kd. After conducting 83 jet tests on stream beds of highly erodible loess in the Midwest of USA, Hanson and Simon (2001) found that τc ranges from 0.0 to 400 Pa and kd ranges from 0.001 to 3.75 cm3/N.s. Thoman and Niezgoda (2008) investigated the channel stability of the Power River Basin in Wyoming. They determined erodibility parameters of the cohesive banks using jet tests and found the range for 0.11 to 15.35 Pa for τc and from 0.27 to 2.38 cm3/N.s for kd. Karmaker and Dutta (2011) studied the erodibility parameters of many sites along the Brahmaputra in India and reported the ranges from 0.1 to 100 Pa for τc and from 0.519 to 11.28 cm3/(N.s) for kd.

Process-based riverbank retreat model

A process-based riverbank retreat model has been used to compute the bank retreat and to study factors affecting bank stability and erosion (Wilson et al. 2007; Cancienne et al. 2008; Midgley et al. 2012; Daly et al. 2015). It consists of two main processes which are the bank erosion and the bank failure. The bank erosion includes both bank and bank toe erosions by hydrological processes (e.g., rainfall, river hydrograph, groundwater oscillations) that lead to bank profile changes over time (Rinaldi and Nardi 2013). The bank failure process involves reduction of the resisting forces in the bank soil mass by several factors, such as toe erosion and shear strength decrease due to wetting of soil, until the resisting forces are exceeded by the bank self-weight. The most common process-based riverbank retreat model is the Bank Stability and Toe Erosion Model (BSTEM) developed by the National Sedimentation Laboratory in Oxford, MS, USA (Simon et al. 2000). The current version of BSTEM (Dynamic Version 5.4) has bank stability and toe erosion modules, and the capacity to model a continuous hydrograph by sequentially applying the various model components for a stream depth defined by the hydrograph, redrawing the bank profile, and then moving to the next step of hydrograph (Daly et al. 2015).

Daly et al. (2015) used BSTEM to determine erodibility parameters of composite streambanks by calibrating the parameters to fit two temporal streambank retreat data sets from aerial imagery. They stated that spatial and temporal changes occur in the fluvial resistance of bank materials due to wetting/drying cycles. In addition, the deeper and faster flows at the outsides of river bends exert elevated shear stresses on the streambank. Therefore, τc and kd can change considerably over time due to the wetting/drying cycles and the subaerial processes. They suggested that a “lumped” adjustment factor (α, dimensionless) should be used to modify Eq. 1, to account for the simplified hydraulics in BSTEM as well as for potential changes in erodibility, as shown in Eq. 8. This adjustment factor has been utilized in long-term analyses of repeating bank retreats in several prior studies (Langeodoen and Simon 2008; Lai et al. 2012; Nardi et al. 2013; Daly et al. 2015).

$$ \varepsilon ={k}_d\left({\alpha \tau}_o-{\tau}_c\right)=\alpha {k}_d\left({\tau}_o-\frac{\tau_c}{\alpha}\right) $$
(8)

where ε is the rate of erosion (m/s), kd is the erodibility coefficient (m3/N.s), τo is the developed boundary shear stress (Pa), τc is the critical shear stress (Pa), and α is a “lumped” adjustment factor.

Methodology

In situ measurements with a submerged jet test device

In situ measurements of soil erodibility parameters were performed using a submerged jet test device during January to February 2015. The jet test device and the testing procedures complied with ASTM D5852. A total of 24 jet test runs were conducted at the six selected sites described previously. Duplicate jet test runs were conducted on both upper and lower banks at each site (four tests per site). Each test was conducted for 50 min, with scour depth and pressure differential readings taken at 5-min intervals. The τc and kd were estimated from the scour and shear stress data obtained, using the scour depth solution method developed by Daly et al. (2013).

Soil testing

At each site, both disturbed and undisturbed soil samples were collected. The disturbed samples were air-dried prior to conducting index property tests. The median particle diameter (D50) and the mass fraction passing sieve no. 200 (i.e., sieve size of 0.75 μm) were determined according to the soil particle size distribution test (ASTM D6913). Plastic limit, liquid limit, and plasticity index of each soil sample were determined following ASTM D4318. Hydrometer analysis (ASTM D422) was conducted to determine the silt-clay content (SC). For the undisturbed samples, the multi-stage direct shear (MSDS) test was performed according to ASTM D3080 to determine the shear strength parameters, namely the effective cohesion (c') and the effective internal friction angle (ϕ').

Aerial imagery analysis

Aerial imagery analysis was conducted to determine the actual bank retreat over time. Aerial images with 0.5-m resolution representing the years 2002, 2010, and 2016 (Fig. 4) were obtained from the Royal Thai Survey Department for the analysis. All the aerial images were geo-referenced with the World Geodetic System 1984 (WGS-84) using ArcGIS10. For each site, the bank edges were digitized along the field-determined reach length. Retreat was determined to have occurred when the digitized bank in the next image appeared to be farther away from the river centerline of year 2002. For example, the 2002 river centerline shown as a light line in Fig. 4 acted as a reference line, and three digitized bank locations were then overlaid onto the 2016 image. A series of transects were created from the centerline to the bank locations, and the corresponding transect lengths were measured. The bank retreat at each transect was computed by subtracting the current transect length from the previous one. A single bank retreat number for each site was computed by averaging the bank retreats across all transects along the reach length. In this study, the bank retreat for 2010, designated by R2010 (m) was defined as the bank retreat from comparing years 2002 and 2010. Correspondingly, R2016 (m) denotes the bank retreat from comparing 2010 and 2016. The total bank retreat (RT) denotes the sum of R2010 and R2016.

Fig. 4
figure 4

Aerial photograph of U-Tapao River for bank retreat determination by analysis of aerial imagery

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Riverbank retreat analysis

In this study, a bank retreat analysis for the U-Tapao River was conducted using BSTEM (Dynamic Version 5.4) according to the procedure developed by Daly et al. (2015). The BSTEM input data include river cross section, shear strength parameters, erodibility parameters, and river hydrograph. A representative cross section obtained from field survey was used as the bank geometry. The shear strength parameters (c' and ϕ') were obtained from the multi-stage direct shear test described previously. The τc and kd were obtained from the jet tests and were used as initial erodibility parameters. River hydrographs and rating curves for the period from 2002 to 2016, by two nearby available stations (X44 and X90 stations in Fig. 1) of the Royal irrigation department, provided the hydraulic loading at the bank faces. A specific hydrograph for each site was generated via back water curve analysis using boundary conditions such as upstream water discharge, downstream water level, and downstream bed level from both control stations. All generated hydrographs had the same pattern. A representative hydrograph from site UT6 is shown in Fig. 5.

Fig. 5
figure 5

A hydrograph of the site UT6 used in BSTEM analysis

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Bank retreat results from the BSTEM runs (BSTEM R2010) were compared with the aerial R2010 obtained from aerial imagery analysis. When BSTEM R2010 did not equal the aerial R2010, this indicated that the initially used erodibility parameters did not represent the field conditions hydrologically and geotechnically. The initial τc and kd were then adjusted using the lumped calibration factor (α) described in Eq. 8, and BSTEM R2010 was recomputed. This was iterated until the difference between BSTEM and aerial R2010 was less than 0.5 m (which is the resolution of the aerial images) and the lumped τc and kd were obtained. To verify that these lumped τc and kd values were good for modeling the bank retreat, another set of BSTEM runs was conducted using the 2010 to 2016 hydrographs, and the corresponding BSTEM R2016 values were computed. The BSTEM R2016 model predictions were then compared to observed R2016 from aerial imagery analysis, to validate the models using lumped τc and kd values.

Results and discussion

Soil testing results

The laboratory test results are shown in Table 1. Thickness of the upper bank ranged from 1.0 to 1.5 m. The upper bank soil was classified as either low plasticity silt (ML) or as low plasticity clay (CL), with D50 values from 0.007 to 0.065 mm, SC values from 48.9 to 86.0%, Pc values from 6.93 to 35.0%, and PI values from 6.90 to 14.7%. Despite being classified as silty or clayey soils, these fine-grained soils with low plasticity exhibit properties between cohesive and non-cohesive soils, and the properties are not exclusively dependent on particle mass and interparticle electrochemical interactions (Grissiniger et al. 1981). Regarding the lower banks, as shown in Table 1, their thickness varied from 2.8 to 6.2 m. Both fine- and coarse-grained soil types were found. They fell into a wide range of soil types, including silty sand (SM), low plasticity silt (ML), low plasticity clay (CL), and high plasticity clay (CH). Fine-grained soil (i.e., ML, CL, and CH) was found in the sites UT1, UT3, UT5, and UT6, while coarse-grained soil (i.e., SM) was found in the sites UT2 and UT4. Shear strength parameters of the upper and lower bank soil (Table 1) were obtained using multi-stage direct shear tests. Effective cohesion (c') ranged from 3.12 to 17.05 (from 1.26 to 18.27) kPa and the effective internal friction angle (ϕ') ranged from 22.61 to 31.30 (from 23.97 to 33.74) ° for the upper (lower) bank soils.

Erodibility parameters from jet tests and empirical formulae

The jet test results are presented in Table 2. It was found that τc of the riverbanks at the selected sites varied in a comparatively narrow range, by about an order of magnitude. The data in Table 2 indicate that the upper bank soil was slightly more erosion resistant than the lower bank soil. The τc ranged from 7.12 to 20.93 Pa with a median of 10.99 Pa in the upper bank, while it ranged from 1.43 to 16.88 Pa with a median of 8.525 Pa in the lower bank. The kd value ranged from 1.74 to 14.29 cm3/N.s with a median of 3.76 cm3/N.s. in the upper and from 3.67 to 19.55 cm3/N.s with a median of 9.67 cm3/N.s in the lower bank.

Table 2 Jet test results and estimates of erodibility parameters using empirical formulae
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The τc and kd data in Table 2 were plotted to assess the relationship of τc and kd (Fig. 6). Additionally, erodibility categories as proposed by Hanson and Simon (2001) are also shown in Fig. 6. It was found that the riverbank soil mostly fell in the category “very erodible.” Only the CL soil from sites UT4 and UT6 had sufficient erosion resistance to be considered “erodible.” As demonstrated by Simon et al. (2010) in Eq. 6 and Daly et al. (2013) in Eq. 7, τc and kd are inversely related and tend to be related by a power law. In this current study, the relationship of τc and kd was fit by the solid line in Fig. 6:

Fig. 6
figure 6

Relationship of the critical shear stress and the erodibility coefficient, as obtained from the jet tests

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$$ {k}_d=19.54{\tau}_c^{-0.547} $$
(9)

where kd is the erodibility coefficient (cm3/N.s) and τc is the critical shear stress (Pa). It is also seen in Fig. 6 that the relationship between τc and kd obtained in this study has similar trend as that in Daly et al. (2013), whereas the fit in Simon et al. (2010) tends to underestimate the kd in our data. This may be due to the fact that Simon et al. (2010) used the Blaisdell solution method to estimate τc and kd, while Daly et al. (2013) and the present study use the scour depth solution method. In the Blaisdell solution, the measured scour time data may give unreliable estimates of both τc and kd (Simon et al. 2010).

The estimated erodibility parameters are tabulated in Table 2. The τc was measured in situ with the jet test and estimated using the median particle size (D50) and Eq. 2, using percentage of clay content (Pc) and Eq. 3, and using plasticity index (PI) and Eq. 4. The median values were 10.99, 0.37, 0.93, and 1.04 Pa, in the same order. The τc values estimated using D50, Pc, and PI were as much as two orders of magnitude below the experimental τc from the jet test. This indicates that estimates of τc from the formula by Smerdon and Beasley (1961) can be very poor. Estimates using the silt-clay content (SC, Eq. 5) following Julian and Torres (2006) were better. Comparing the estimates for an individual site and for its upper and lower banks, the measured jet test τc values were relatively similar to those estimated from SC. For example, for UT4 (Table 2), the τc from jet test for the upper (lower) bank was 16.47 (2.68) Pa, while the corresponding estimate was 16.67 (2.99) Pa. Also, Karmaker and Dutta (2011) reported that their best estimates of τc were based on SC. They stated that the submerged jet test method provides a better estimate of the τc under field conditions, while the SC-based estimate may be used as an alternative method of estimation.

The kd from jet tests and corresponding estimates are given in Table 2. Estimates of kd were based on Eq. 6 (Simon et al. 2010), Eq. 7 (Daly et al. 2013), and Eq. 9 (this study), using only the estimates of τc based on SC content (Eq. 5). The median kd values were 6.51, 0.18, 2.21, and 4.62 cm3/N.s, from the jet test and from Eqs. 6, 7, and 9, in this order. The data in Table 2 indicate that Eq. 9 provided the best estimates of kd, while Eq. 7 was better than Eq. 6. As previously mentioned, use of the scour depth solution method in Eqs. 7 and 9 resulted in better estimates of kd than the Blaisdell solution method with Eq. 6.

Aerial imagery analysis results

The results from analysis of aerial images representing 2002, 2010, and 2016 (Table 3) indicate that bank retreat took place at every site. The R2010 (bank retreat from 2002 to 2010) ranged from 3.04 m (site UT6) to 11.76 m (site UT5) with an average retreat of 8.33 m, while the R2016 (bank retreat from 2010 to 2016) ranged from 1.87 m (site UT1) to 20.06 m (site UT5) with an average of 8.88 m. The RT (bank retreat from 2002 to 2016) ranged from 7.52 m (site UT6) to 31.83 m (site UT5) with an average of 17.21 m. The retreats observed for the sites UT2 to UT4 were closely similar (Table 3). This is reasonable as these sites are located close to each other (about 1.4 km apart), so their soil properties and hydraulic loadings are expected to not differ by much.

Table 3 Aerial imagery analysis results
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The least 7.52-m RT was found at the site UT6, which might be caused by several factors. The lower bank soil of this site was high plasticity clay (CH) with high effective cohesion, resulting in low bank failure potential and correspondingly low bank retreat. In addition, the site UT6 is located in the downstream area close to the Songkhla Lake, so a less steep channel slope is expected. This reduced slope would result in reduced boundary shear stress and, in turn, would reduce the fluvial erosion potential. At the other extreme, the highest bank retreat was found at the site UT5 with R2010, R2016, and RT being 11.76, 20.06, and 31.83 m, respectively. The R2010 does not differ much from that of the other sites, but R2016 does. Aerial images of this site clearly show that during 2002 to 2010, retreat occurred but the bank remained straight. However, river bank concave in shape is observed in the 2016 aerial image. Concave banks generally cause both curvature-driven and turbulence-driven secondary flows that alter the flow fields and the morphology of the banks (Camporeale et al. 2007; Papanicolaou et al. 2007). These secondary flows are here considered to be the major cause of high R2016 of this site. The reason for the emergence of the concave shape at this site is not known. However, it is believed that soil heterogeneity in the river banks combined with the complexity of subaerial and hydrogeological processes to cause this.

At the site UT1, R2010, R2016, and RT were 10.08, 1.87, and 11.96 m, respectively. R2016 was much less than R2010 or retreats at the other sites (Table 3). Course change of the U-Tapao River was the cause of the low R2016 observed at this site. It is believed that a big flood in 2010 changed the course of the river, as observed in the aerial images, so that the site UT1 became located on the inside of a bend. Bank accretion and formation of point bars are usually found at the insides of bends (Motta et al. 2012).

Riverbank retreat analysis results

The bank retreats (R2010) from BSTEM runs using the τc and kd values from the jet tests were 0.0 m (no retreat) at the sites UT1, UT5, and UT6. In contrast, the R2010 values at sites UT2 to UT4 were very large exceeding 100 m. These simulation results differed dramatically from the observed R2010 values, measured from aerial images (Table 3). The incorrect R2010 estimates from BSTEM runs were caused by several factors. Among these were the spatial and temporal changes of fluvial resistance of the bank materials, due to wetting/drying cycles. Fluvial resistance is typically measured at a specific time, but due to the wetting/drying cycles and the subaerial processes, the observed τc and kd can change considerably over time (Daly et al. 2015). Furthermore, the bank retreat can progress inland over a long time period so that it encounters spatial changes of the bank materials, and this affects the τc and kd as well.

To improve the computed bank retreat results, the τc and kd values were adjusted iteratively using trial lumped adjustment factors (α) in a series of BSTEM runs, until the computed R2010 were optimally close to the values measured from aerial imagery. The α, adjusted τc and kd, and computed R2010 values are tabulated in Table 4. It was found that α values approximately from 0.3 to 3.0 were sufficient to adjust the τc and kd so that the computed R2010 were in good agreement with the measured ones. For sites UT1 and UT3, use of equal α values for upper and lower banks provided good R2010 results. However, for sites UT2 and UT4 to UT6, it was found that the R2010 were caused only by erosion of the lower banks. Thus, for these sites, the calibration of α was conducted solely on the lower banks while the α values of the upper banks were kept as unity. The computed R2010 obtained from BSTEM runs for all sites considered were fairly similar to the observed values, as shown in Fig. 7: the points in the scatter plot fall close to the diagonal line with identical values. The computed and measured R2010 differed in terms of the root mean square (RMS) error by as low as 0.69 m (Table 4), showing that BSTEM with adjusted erodibility parameters can be used to accurately fit our data, modeling the appropriate failure mechanisms of fluvial toe erosion leading to bank undercutting and sloughing of upper cohesive layers, as commonly observed in composite riverbank studies (Rinaldi et al. 2008).

Table 4 Bank retreat analysis results compared to BSTEM simulation runs with adjusted erodibility parameters
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Fig. 7
figure 7

Comparison of bank retreat measured from aerial imagery to bank retreat computed with BSTEM

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Bank retreats (R2016) calculated using BSTEM with the adjusted τc and kd values, and another set of hydrographs from 2010 to 2016 are tabulated in Table 4. The R2016 values calculated using BSTEM compared well with the corresponding R2016 values measured from aerial imagery, for all sites except the site UT1. For the sites UT2 to UT6, the absolute difference between measured and computed R2016 ranged from 0.81 to 2.40 m with an average of 1.49 m. This indicates that the erodibility parameters obtained using the lumped adjustment factor could be effectively used to predict the bank retreat. The τc and kd obtained using this technique are better than those obtained from empirical formulae or the jet tests, because these parameters already account for the “lumped” subaerial process, fluvial erosion, and slope failure.

For the site UT1, however, the computed R2016 overestimated the R2016 considerably, by + 9.94 m (Table 4). As mentioned previously, the river course change observed at site UT1 was the probable reason to this overestimate. The R2016 computed using the adjusted erodibility parameters to model R2010 (the course change of the river had not yet occurred) should show about similar rate of retreat as R2010, given that the hydrograph between these two periods was not much different. However, due to the river course change, turning this site to the inner bend bank, the actual retreat reduced or even reversed to bank accretion. The measured R2016 at this site that was much less than predicted using BSTEM is entirely reasonable on this basis.

Conclusions

Steep riverbanks of the U-Tapao River in southern Thailand consisted of two layers. The thickness of upper and lower banks varied from 1.0 to 1.5 m and 3.0 to 6.2 m, respectively. Toe erosion at the lower banks was observed to continuously lead to bank failure. Laboratory test results showed that the riverbank soils along the U-Tapao River consisted of silty sand, low plasticity silt, low plasticity clay, and high plasticity clay. The erodibility parameters from the jet tests indicated that the soils can be classified as erodible to very erodible which were very susceptible to erosion. In addition, the lower bank soils were found to be more erodible than the upper ones. Aerial imagery analysis results revealed that the observed bank retreat from 2002 to 2016 ranged from 7.52 to 31.83 m with an average of 17.21 m. Process-based riverbank retreat analysis which incorporates the erosion of the riverbank soil through excess shear stress equation and the riverbank failure through slope stability equation was conducted using the Bank Stability and Toe Erosion Model (BSTEM) to compute long-term riverbank retreat. The computed retreats were verified with the observed ones. Initial BSTEM runs using the erodibility parameters obtained either from the jet test or the empirical formula over the period from 2002 to 2010 did not provide good predictions of bank retreat. However, good agreement of the retreats was achieved by adjusting the erodibility parameters iteratively, using the lumped adjustment factor. The adjusted critical shear stress and erodibility coefficient of the erodible riverbank soils ranged from 4.41 to 20.93 Pa and 2.23 to 39.99 cm3/N.s. These adjusted erodibility parameters are believed to account for local subaerial processes, fluvial erosion, and slope failures that cause the bank retreat. Another set of BSTEM runs using adjusted erodibility parameters was further validated against later observations, over the period from 2010 to 2016, and appeared to provide reasonably good predictions of river bank retreat.