Characteristic of Erosion Properties and Relationship With Geotechnical Properties for Red Riverbank Soil in Hanoi, Vietnam


 Soil erosion properties are the main factors affecting riverbank and river channel stability. In this paper, a modified water flume in the laboratory was conducted to evaluate the characteristic of erosion properties including the critical shear stress, the slope of the erosion curve, and erosion rate. The relationships between erosion properties and geotechnical properties as dry density, grain size distribution, shear strength, and soil suction were built. Results obtained from laboratory tests indicate (i) the clay content, cohesion force, residual suction has a great effect and linear correlation in the relationships with the critical shear stress and erosion rate. While the change in clay content leads to a markedly change in the erosion rate. The difference of 5 % clay content enough to build great effects on the erosion rate curve for the Silt soil group; (ii) the sand content has the greatest influence on the slope of the erosion curve (the initial slope and the erosion slope); (iii) the density also has a close relationship with the critical shear stress and the erosion slope, but not for a fine–sand mixture with clay content less than 10%. Based on obtained results and relationships found in this paper, the cohesion force and residual suction should be considered in process of soil riverbank improvement and riverbank undercutting erosion protections.

morphograph, flow hydrodynamic (Li, 2020;Roy 2020), and vegetable covering on the riverbank. The soil geotechnical properties as the effects of the grain size distribution, soil bulk density, and shear strength will be determined and discussed here in the relationships with the erosion properties.
The most meticulous and successful results of the relation between soil properties and the erosion rate were found in a series of studies and papers published by Briaud and his colleagues (Shafii et al. 2016;Briaud 2008;Briaud et al 1999Briaud et al , 2001aBriaud et al , 2001b. Based on 15 years of erosion testing experience using erosion function apparatus (EFA), a series erosion categories depending on the classification of soils or rocks was proposed (Briaud 2008). For practical use, these erosion categories are used to select tested and protected material. However, the structure and density of mixture soil were not mention in these erosion categories.
The grain size effects were also analysed in the variation of mud or fines content (silt and clay) in the mixture (Mitchener and Torfs 1996;Couper 2003;Ahmad et al. 2011;Jacobs et al. 2011;Benamar et al. 2012), in cohesive soils (Berlamont et al.1993;Jianfar 2014). In mixed soils, the clay content or silt content variation, defined as the weight of both silt and clay contents, is added to sand or vice versa. Results reported from earlier studies have demonstrated that adding fine content (mud/silt, clay) more drastically changes critical soil erosion than when adding sand to mud sediment (Mitchener and Torfs 1996;Panagiotopoulos et al. 1997;Van Ledden 2004). The addition of small percentages of mud by weight to sand leads the strongest effect on erosion resistance (Mitchener and Torfs 1996). The mode of erosion also changes from cohesion-less to cohesive behavior for low fine contents added to sand, with a transition occurring in the region of 3% to 15% mud by weight. Two sand-mud mixtures were conducted in (Panagiotopoulos et al. 1997): one regime for mud contents less than 30% (clay mineral content 10%) and another for contents greater than 30%. These two unimodal sands were mixed separately with various proportions of Combwich mud by dry weight of 5%, 10%, 20%, 30%, 40%, and 50%, which respectively correspond to 1.8, 3.6, 7.2, 10.8, 14.4, and 18% of clay mineral. The experimentally obtained results depend on the flow conditions and clay contents. Results concluded that the linear increase occurs only in steady conditions. Under oscillatory flow conditions, the threshold criterion used was not significant when the clay content was ≤11%. Otherwise, the mean critical shear stress increases dramatically when the clay content approaches 50%. Also assess the effect grain size content on the erosion properties, but there is no correlation between the critical shear stress and erosion slope found in (Kimiaghalamn et al. 2016) The effects of bulk density on erosion rates and critical shear stress of uniform size quartz particles from fine-grained (5 m diameter) to coarse grained (1,350 m diameter) sediments were assessed in (Jepsen et al. 1997;Roberts et al. 1998;Lick and McNeil 2001). The erosion rate was demonstrated as a unique function of bulk density and that it decreases as the bulk density decreases for compacted soil samples (Jepsen 1997). The critical shear stresses of finer particles were strongly dependent on the particle size and bulk density in fine soil. However, that were strongly dependent only on the particle size in larger particle soil (Jepsen et al. 1997;Roberts et al. 1998;Lick and McNeil 2001). The linear relation between the density and degree of compaction in the soil column with the soil erosion rate was also demonstrated in (Lick and McNeil 2001).
The relationship between soil erosion and other soil properties such as shear strength was also built in recent research (Kimiaghalam et al. 2016;Léonard and Richard 2004;Fattet et al. 2011;Boudreaux 2012). The shear strength was used as a key factor characteristic of the resistance properties to erosion in the mixture soil with vegetation in (Fattet et al. 2011;Boudreaux 2012). That research found that a significant positive linear relationship between mean weight diameter and soil cohesion but not with the internal angle of friction. Some empirical equations to determine the critical shear stress by the function of the shear strength and other properties were built and overviewed in (Kimiaghalam et al. 2016). That research also assessed some properties to the soil erosion but found the strongest correlation between the critical shear stress and cohesion force. The increase in cohesion force causes an increase in the critical shear stress. The correlation of the only total shear stress and the critical shear stress, and a function of two factors were built with a high coefficient of determination (R 2 = 0.93) in (Léonard and Richard 2004). That research also found that the relationship does not depend on soil texture, and found obviously in undisturbed soil rather than remound soil.
Although soil erosion is an important factor in the analysis of riverbank undercutting erosion, the determining process of soil erosion is still difficult. Moreover, the limitation in analyses of riverbank cantilever failure was at the quantification of the fluvial erosion rate because the determination of erosion coefficient remains complex, and varies from one site to another. There were varietal conclusions on the effects of soil geotechnical properties on the mixture soil. The critical shear stress and erosion curve need measuring locally (Patsinghasanee et al. 2017;Goharrokhi 2015). Moreover, those results mostly emphasized only the critical erosion shear stress, the soil erosion rate characteristics and the processing of soil erosion were limited. Analyzing riverbank stability requires not only the critical shear stress but also the soil erosion curve. Determined the soil erosion rate curve is required in the analysis of riverbank stability in the type of cantilever failure. This paper presents attempts to ascertain the characteristics of soil erosion properties using modified water flume model testing equipment in the laboratory. Determining the critical shear stress and erosion rate curve not only for finding the local soil erosion characteristic but also for assessing their effects on riverbank stability in further researches and analysis. Results of the present research conducted for analyses of riverbank and river channel stability suggest that when a river dyke is subjected to strong hydraulic flow such as river flow or run-off caused by heavy rainfall, soil erosion is likely to occur at the riverbank toe or near the riverbank zone, endangering them and leading to overhang-shaped damage. Eventually, the riverbank will fail. For clarification of this mechanism, however, analyses of riverbank stability with the accounting of soil erosion are required. Therefore, the authors must find a more accurate model that can accommodate precise numerical simulation.
The relationship between the soil erosion properties and the soil grain size, density, shear strength, and residual suction will be built and discussed. While the residual suction is soil suction when the riverbank changes from unsaturated to saturated by river water level increase. That value is presented in Figure 1, the suction at the end of the wetting process. By submerged under river water level and high flow shear stress, the soil may already erosion. However, in some clay soil with high cohesion, some air still exists in soil aggregate and the residual suction still exists. Moreover, this value indicates soil resistance properties under the attack of loading and shear stress. The relationship between residual suction and erosion properties gives engineers more options for properties for riverbank protection.

Soil materials
Field investigations were carried out along the riverbank of the Red River, which flows through Hanoi, Vietnam's national capital. The detailed investigated sites are the natural riverbank and have high erosion potential. Soil samples were gathered at these locations as presented in Figure 2.
Soil materials collected along the surface of the banks of the Red River include both undisturbed and disturbed soil samples. Water contents and bulk density were measured directly in the field using a steel container and steel ring according to the ASTM standard (ASTM D 2216 and ASTM D 2937-00, respectively). Soil samples were used to assess the soil grain size, erosion, suction, shear strength, and hydraulic conductivity for simulation in the laboratory according to natural water contents, bulk density, and the predetermined dry density. The detail for these geotechnical properties were descripted in previous project (Toan 2014). This paper specifically examines description of the characteristics of soil erosion properties and build the relationships with these geotechnical properties. Soils of nine types, which are representative soils for samples from the banks of the Red River, can be arranged into three groups: the Clay group, Silt I group, and Silt II group (Table 1).
-The Clay group includes soils of three types, Cl 01, Cl 02, and Cl 03, with high clay contents and the low sand contents with less than 2% in this group. Sample Cl 03 has the lowest clay content of 36.0%; Cl 02 and Cl 01 have respective clay contents of 42.4% and 70.0%. The silt soils were classified into two groups: Silt I and Silt II.
-Silt I has silt grain content of about 70%, with clay contents decreasing from 25.0% for Silt I-01 to 19.4% for Silt I-02, and to 15% to Silt I-03 corresponding to an increase of sand contents.
-Silt II group has the same clay content at 10%, with sand content increasing by 20.3%, 25.5%, and 36.6%, respectively, for Silt II-01, Silt II-02, and Silt II-03. Table 1 and Figure 3 show the physical soil properties and grain size distribution curves of samples collected along the banks of the Red River in Hanoi, Vietnam.

Soil erosion test method
Soil bank erosion by water flow stress was simulated and interpolated based on soil movement. The concept of determining soil erosion in an open pipe is simulated using the erosion function apparatus invented (Briaud et al 1999(Briaud et al , 2001a(Briaud et al , 2001bBriaud 2008). The equipment includes an open rectangular pipe with 2 m length, 0.2 m width, and 0.1 m height. Figure 5, 6, 7 show the configuration and photographs of the soil test apparatus. Water flowing in the pipe is supplied from a water tank. Opening a water valve at the bottom of the water tank controls the water velocity, which is measured during the test. The water pipe slope and the water tank height can also be changed to control the water velocity. A cylindrical mould with the diameter 7.6 cm is attached to the bottom of the test pipe is used to compact the soil sample. The protrusion of soil in this mould can be manipulated using hand controls ( Figure 6). During the test, the time necessary to erode at a certain soil height by water flow in a simulated opening channel is measured. The ratio of the eroded height (mm) to the elapsed time (hr) is defined as the soil erosion rate (mm/hr).
The soil sample was mounted into the sample cylinder with predetermined water contents and dry density.
Before the test, the core soil is made to protrude at intervals of 1 mm (Figure 7). The open the water valve at a predetermined velocity (m/s). To ascertain the critical shear stress, the first test water velocity is set sufficiently small that one can see that soil is starting to erode. Record the time it takes to erode 1 mm or h (mm) soil core. This is the duration of time t (hr) it takes to erode the soil of height h (mm). The test results are given as the relation between the soil erosion rate and the water velocity or shear stress ( Figure   8).

Determining erosional rate and shear stress
The results of this analysis represent the relationship between erosion rate and shear stress, in which the erosion rate and shear stress are calculated using the following equations. The soil erosion rate ( ) is the ratio of the height of the eroded soil ( h) to the elapsed time ( t) (Briaud et al 1999(Briaud et al , 2001a(Briaud et al , 2001bBriaud 2008;Julien 2002;Mobley 2009).
The shear stress from the water flow can be calculated using the Moody chart in which ( ) is the shear stress (N/m 2 or Pa), (ρ) is the density of water, (V) is the average water velocity, and (f) is a friction coefficient. Theoretically, (f) is obtained from the Moody diagram using the relative roughness (roughness height/conduit diameter) and the Reynolds number (R e ), which is calculated as: For R e > 3000: when Re < 105, the equation above can be approximated as presented below.
Where the Reynolds number (Re) is determined by Eq. 5: is the hydraulic diameter of the pipe and (ν) is the kinematic viscosity of water. The hydraulic diameter is calculated as: The open pipe is assumed to be smooth; (a) represents the width, and (b) represents the height of water flow in the open pipe. For turbulent flow in smooth conduits, the following approximations of the friction coefficient and the Reynolds number dependence can be used.
Finally, the results are presented by the erosion curve as shown in Figure 8, is relationship between the soil erosion rate and the water flow shear stress. In the curve relating soil erosion rates and water stress, the critical shear stress ( c  ) is defined as the stress value at which soil begins to erode, at which the soil erosion rate as 0.1 mm/hour (Shafii et al. 2016).

Results and discussion
In this paper, nine types of soil with difference of grain size content was selected and all these soils were tested at the dry density of 15.0 kN/m 3 . Only four soils as Silt II-03, Silt I-03, Silt I-01, and Cl-03 were carried out at more density of 13.5 and 16.5 kN/m 3 .
Results of tests conducted to ascertain the soil erosion behavior under typical water velocities and the water shear stresses for soils at the dry density of 15.0 kN/m 3 are presented in Figure 9. In the low flow velocity and shear stress (less than 0.2 m/s and 5 Pa), it is difficult to see clarify the deference erosion rate at deference soil. However, almost the silty soil (group Silt I and Silt II) were eroded. In this stage, there is a important factor required to determine as the critical shear stress, which the soil was start eroded. By recording during the erosion testing and drawing the initial stage of the relationship of the flow shear stress and erosion rate the critical shear stress were pointed out.
The critical shear stresses for Silt I and Silt II groups are small, they are nearly equal among all soils of these groups, 0.7-1.5 Pa. Especially, the critical shear stress is the same, about 1 Pa in group Silt II. Critical shear stresses for the Clay group are higher and are quite different for each soil, at 5.55-7.81 Pa.
Besides the critical shear stress, other properties of soil erosion will be extracted. These include the initial slope (K i ) which is the slope of the erosion curve at the initial stage with the water flow shear stress less than 5 Pa, and the erosion slope (K) which is the slope of the erosion curve with the flow shear stress higher than 5 Pa, see in Table 2.
The initial slope of soil is lower than the erosion slope in almost all soils. That means the erosion rate increase slowly when the shear stress is low, then increases quickly when shear stresses higher than 5 Pa.
The relationship of these properties with the soil grain size content (sand/silt/clay content, the mean grain size diameter D 50 , the grain size slope); soil density, shear strength (cohesion force and internal friction angle), and the residual suction. Table 2 and Figure 10 to Figure 21 present the erosion properties and some geotechnical properties, and these relationship graphs, the characteristics of these relationships will be discussed following.

The effects of grain size on erosion properties
The effects of grain size on the soil erosion properties are assessed based on the relationship of the soil grain size content (sand, silt, and clay content), of the mean grain size D 50 , and of the grain size curve slope on the critical shear stress and on the erosion slope as shown in Figure 10 to Figure 15, respectively. The results of the coefficient of determination (R 2 ) in Figure 10 shows that the critical shear stress has a strong correlation with the clay content with R 2 = 0.91, but a quite weak correlation with the sand and silt content (R 2 = 0.57 and 0.49 for with silt and sand content, respectively). Contrary to the critical shear stress, the correlation of the initial erosion and erosion slope with sand content is stronger with sand content than clay and silt content. Figure 11 shows only the relationship between the slope of erosion curve and sand content, with the R 2 = 0.89 and 0.76, while that value with clay and silt content are not shown here but very small.
That means the soil with high sand content, the slope of erosion curve at both the initial stage and highshear stress, and the erosion rate obtained higher. Figure 12 and 14 indicate the relationships of the critical shear stress with mean grain size (D 50 ) and the grain size curve slope. Figure 13 and 15 are the relationships of the erosion curve slope with the D 50 , and the grain size curve slope. In these relationships, the initial slope and the mean grain size D 50 has a quite strong correlation with R 2 =0.86; other relationships have medium correlation to very weak correlation, with R 2 of 0.60 to 0.02. (Figure 12 to Figure 15). The results on the relationship of the critical shear stress and the erosion curve slope in this research have the same trend as results in most previous research (Shafii et al. 2016;Panagiotopoulos et al. 1997). Especially, it can see that the clay content had a great effect on the critical shear stress when the soil has clay content higher than 11% and cause dramatically with the clay content reach up 50% as concluded in (Panagiotopoulos et al. 1997). However, the coefficient of determination in (Kimiaghalam et al. 2016) shown that there was no strong correlation between the grain size properties and erosion properties. In that research, the erosion rate was carried out with different densities and clay content, which may be as the reason causing the deference trend of results. To comparing the erosion rate, the erosion rate has to be carried out in the sample physical density. Moreover, the sandclay mixture structure also needs concern as shown in Barman et al. 2019).
It can find a close relation exists between the erosion rate and the soil grain size when the shear stress increase higher than 5 Pa as shown Figure 9. Silt I and Silt II groups have sand content increasing the intervals of 5% from Silt I-01 to Silt II-03 (the highest sand content is 36.6%). Therefore, Silt II-03 has the highest erosion rate among the Silt groups. The four soils of Silt I-01, Silt I-02, Silt I-03, and Silt II-01 have clay contents that decrease in the interval of about 5% in each soil sample (decrease from 25% to 10%), corresponding to a sand content increase from 4% to 20% (see Table 1). Soil erosion curves of those four soils are markedly different, an especially marked difference is observed for soil with water velocity higher than 0.4 m/s (the shear stress is higher than 10 Pa). The change of erosion rate of Silt I (or four these soil as Silt I-01, Silt I-02, Silt I-03 and Silt II-01) with gradually decreasing 5% of clay and responding to increase of sand content, is more strongly affected than in Silt II group in which change of silt and sand contents was found. The increasing of the erosion rate of a soil is presented by the initial slope and erosion slope as shown Figure 11). The soil with higher sand content has higher the slope that means the erosion rate increase quickly when the flow shear stress increases.
In the of clay group including Cl 01, Cl 02, and Cl 03, with clay contents of 36.0%, 42.4%, and 70.0%, respectively, and with sand contents less than 2%, the erosion rate of this soil group is the lowest. The Cl 03 and Silt I-01 (36% and 25% clay contents, respectively) have nearly the same erosion value, whereas the erosion rates of Cl 01 and Cl 02 are very small, and therefore might be negligible compared to the erosion rates of Silt I and Silt II soils. This result demonstrates that clay soil with clay contents higher than 40% might be affected non-significantly in terms of stability against water flow shear stress, which agrees with results reported from earlier studies (Panagiotopoulos 1997;Van Ledden 2004). Figure 16 shows the relationship of the critical shear stress and the erosion slope with the soil strength (the cohesion force, the internal friction angle, and residual suction). Base on that result, a strong correlation can be seen in the relationship between cohesion force and residual suction. The coefficient of determination R 2 higher than 0.9 in both these relationships, but only about 0.5 in the relationship with friction angle. With the high cohesion force and the residual suction, the critical shear stress has a higher value. In general, of shear strength properties, the high shear strength normally found in the cohesion soil.

The relationships of shear strength, soil suction on the critical shear stress
That trend is also found in this research. Combining with the effects of clay content, it can seem that the soil has a high clay content, having high cohesion force, and then found the high critical shear stress. The cohesion force also had the most effects on the critical shear stress than other geotechnical properties found in (Kimiaghalam 2016). the erosion curve becomes divergence responding to density. After that point, the erosion rate increasing quickly and has a higher value in the soil has the low density. The erosion properties at deference densities are calculated from erosion curves and presented in Table 3. When the dry density is low (at 13.5 kN/m 3 ), the critical shear stress is small and nearly constant with changing grain size in the silt group. At a high dry density (16.5 kN/m 3 ), the critical shear stress increases concomitantly with increasing clay contents. Figure 27 shows the relationship of density and the initial slope of the erosion curve. For all soils, the slope of the erosion curve decreases when the soil density increase. And the soil with high sand content has a higher slope, the slope of the erosion curve decrease from Silt II-03; Silt I-03; Silt I-01; Cl 03, respectively.
These results show that the erosion rate will increase quickly in the soil has low density and high sand content

Characteristics of the soil surface during erosion
Different behaviors of silt soils and clay soils are recognizable from images of soil particle movement during soil erosion tests conducted in the laboratory (Figure 28 and 29). For this study, the silt soil groups (Silt I and II) are considered non-cohesive. Particularly, no cohesion exists between the soil particles for Silt II group soils. Each soil particle is independent of the soil particle. Therefore, each particle is removed separately by water flow from the soil-water interface. Figure 28 (left) shows a surface of Silt II-03 after completion of 1-mm erosion. The surface is quite smooth. Most soil particles in the protruding soil core were easily swept away by the water. Silt I-03, which has a higher fines content (70% silt and 15% clay), also has a smoothly eroded surface, although it is less smooth than that of Silt II-03, which has a lower fines content (53.4% silt and 10% clay). A notable difference is apparent in the images of the Clay group's erosion ( Figure 29). Because of the high cohesiveness between soil particles, which tend to bind together (aggregate) to form large aggregate particles, the soil is more difficult to move. At the high water velocity, the soil was removed in aggregate particles, rather more markedly than in individual particles, as in noncohesive soil. Finally, the surface erosion of the clays is not smooth, as presented in Figure 29. As the discussion in Barman et al. 2019), the soil has a clay content of about 10%, the network caging between clay and sand was not possible, enhancing the erosion process. When the clay increases up to 25-30%, the mode of erosion changes from particles-by-particles to chunk-by-chunk. The influence of ejection and sweep decreases, increasing the soil erosion rate in the soil has high clay content.

Conclusions
This paper focus to evaluate the erosion properties of soil collected from the banks of the Red River, and assess the influences of geotechnical properties as grain size, density, shear strength, and residual suction.
In general, the soil erosion rate decreases concomitantly with increasing clay content, dry density, and shear strength, whereas the critical shear stress increases concomitantly respectively. Some specific conclusions were obtained from the test results as following: The change of clay content has a strong effect both on the critical shear stress and the erosion curve. In the mixture soil, the difference of 5 % clay content enough to build great effects on the erosion rate curve. The erosion rate of the soil with high clay content (more than 40 %) is very low and might be affected nonsignificantly by the change of grain size content. The change of sand content has a strong effect on the erosion rate and slope of the erosion curve. The soil with higher sand content has a higher slope and the soil erosion rate increase quickly.
The density has a close relationship with the critical shear stress and erosion slope. The soil with higher density has higher critical shear stress; The erosion rate increase quickly in the soil has a low density and high sand content.
Both the cohesion force and soil suction have a strong effect and have a linear correlation with the critical shear stress. The relationship of the critical shear stress with the friction angle and the shear strength with the slope of erosion curves is a medium or weak correlation.
Base on the result in this research, the clay content, and dry density is a first important factor need considered. These properties have greatly affected other properties, including the shear strength, suction, and the critical shear strength mention in this paper. Here also suggest use shear strength and residual suction as the major factors controlling the resistance soil properties and erosion.