Root characteristics of some grass species on the sea dikes in Viet Nam

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Communications on Hydraulic and Geotechnical Engineering 2012-03

ISSN 0169-6548

Root characteristics of some grass species

on the sea dikes in Viet Nam

Thinh Long, Thai Tho and Yen Binh dikes, 2009 to 2012

Report of measurements

Trung Lˆ

e Hai*

October, 2012

*

PhD student, Section of Hydraulic Engineering, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 3600 GA Delft, The Netherlands.

Tel. + 31 15 27 83348; Fax: +31 15 27 85124 e-mail: H.T.Le@tudelft.nl, trunglh@wru.vn

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Communications on Hydraulic and Geotechnical Engineering

2012-03

ISSN 0169-6548

The communications on Hydraulic an Geotechnical Engineering have been published by the De-partment of Hydraulic Engineering at the Faculty of Civil Engineering of Delft University of Technol-ogy. In the first years mainly research reports were published, in the later years the main focus was republishing Ph.D.-theses from this Department. The function of the paper version of the Communi-cations was to disseminate information mainly to other libraries and research institutes. (Note that not all Ph.D.-theses of the department were published in this series. For a full overview is referred to www.hydraulicengineering.tudelft.nl_{þ research þ dissertations).}

At this moment this series is mainly used to disseminate background information related to other publications (e.g. data reports with data underlying journal papers and Ph.D. theses). Recent issues of the Communications are only available in digital format. A notification will be sent to interested readers when new issues are released. For placement on the notification list, please send an e-mail to h.j.verhagen@tudelft.nl.

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Postal address for the Communications is: TU Delft, Faculty of Civil Engineering and Geosciences, department of Hydraulic Engineering, Stevinweg 1, 2628CN Delft, Netherlands. Permissions for republishing parts (figures, data), can be obtained from the responsible publisher, ir. H.J. Verhagen.

This publication has been produced in cooperation with the Water Resources University, Hanoi, Viet Nam.

The data presented in this report was mainly achieved through the project ”Technical Assistance for Sea Dike Research” supported by the Government of the Netherlands and the project ”Super Sea Dike with high safety level and environmental friendly” financed by the Viet Nam Ministry of Agriculture and Rural Development. Measurements were performed by the Faculty of Marine and Coastal Engineering, Water Resources University and the Plant Protection Research Institute Ha Noi, Viet Nam.

TU Delft, Section Hydraulic Engineering, Water Resources University Hanoi, Trung Lˆe Hai

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1 Introduction

1.1 Some grass species on sea dikes in the north of Viet Nam

Between 2009 and 2011, some grass-covered sea dikes were tested with the Wave Overtopping Simu-lator in the north of Viet Nam. To select suitable locations for testing, several field trips were made along the coastlines of Hai Phong, Thai Binh, Nam Dinh and Ninh Binh provinces. Slope speci-fications and grass species of sea and estuary dikes were quantitatively observed and investigated. Before 1991, all landward-side slopes were covered with grass, and about 98% was not gentler than 1/2 of inclination [Trung et al., 2012]. Recently, different protection measures have been applied, for example, grass cover within concrete frames and concrete block revetments. Bermuda, Carpet, Ray and Vetiver grass are popular species which are commonly found on the dike slopes. The Latin and Vietnamese names (commonly local names) of these grass are given in Table 1.

Table 1: Grass species on sea dikes in the north of Viet Nam.

English name

Latin name

Vietnamese name

Illustration

Bermuda grass

Cynodon dactylon

Co g`

a

Figure 1

Carpet grass

Axonopus compressus

Co khˆ

on

Figure 2

Ray grass

Hemarthria compressa

Co d`

ay

Figure 3

Vetiver grass

Vetiveria Zizanioides

Vetiver

Figure 4

Bermuda and Carpet grass has grown naturally and has been planted on slopes since the first dikes were built along rivers and coastline in the north of Viet Nam. Ray grass can be found on the riverside toe of many estuary dikes, for example dike route No. 7 in Thai Thuy distric, Thai Binh province. Recently, Vetiver grass was used in slope stability control in Viet Nam. Vetiver grass is used to entirely protect the slope part below the landward-side berm of the Dike Route number 1 in Do Son, Hai Phong. Vetiver grass is planted in combination with other grass species on slopes of river and sea dikes, for example Thai Tho dike in Thai Thuy, Thai Binh. Vetiver is also reclassified as Chrysopogon zizanioides. The four grass species are illustrated in Figures 1, 2, 3 and 4.

Figure 1: Bermuda grass on Thinh Long and Thai Tho sea dikes.

1.2 Soil samples

Hollow cylinders made of steel were used to take soil samples including roots on dike slopes of Thinh Long, Thai Tho and Yen Binh. There are three different diameters of these cylinders 3 cm, 5 cm and 10 cm (e.g., see Figure 5). The cylinder lengths could vary from 40 to 80 cm depending on grass species and soil types. The cylinder is hammered perpendicularly into the dike slope to a depth of at

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Figure 2: Carpet grass on Thinh Long and Thai Tho sea dikes.

Figure 3: Ray grass on the Thinh Long and Thai Tho sea dikes.

least 30 to 35 cm. The surrounding soil is dug and removed away before lifting the cylinder to keep the soil sample inside intact. Later on, the soil sample is pushed out of the cylinder by a simple piece of equipment. Depended on the characteristics of interest, the soil sample is remained as a whole or slided into shorter parts. Attached soil particles/ aggregates are cleaned and removed with water sprays to obtain roots for further measurements.

1.3 Report contents

The data obtained from a number of grass investigations at Thinh Long, Thai Tho and Yen Binh dikes are integrated and presented in this report. Parts of the data were already given in other reports of the project ”Technical Assistance for Sea Dike Research” and ”Super Sea Dike with high safety level and environmental friendly” as Trung [2011] and Tuan [2012]. After the introduction, section 2 determines the number and corresponding diameters of roots which are classified into four levels 1, 2, 3 and 4. Distribution of root over increasing depth including volume, weight and number are

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Figure 4: Vetiver grass on the Do Son and Thai Tho sea dikes.

(a) Steel pipe with diameter of 3 cm (b) Taking soil sample with hollow steel pipes

Figure 5: Hollow steel pipes used to take soil sample on dike slope.

examined in section 3. Root density of Bermuda, Carpet, Ray and Vetiver grass are estimated in section 4. Tests of pulling root to determine tensile stress is presented in section 5. Shear strength of root permeated soils characterised by cohesion are measured at different depths under the slope surface and are given in section 6. Based on findings achieved in previous parts, root permeated soil material is modelled in section 7 by establishing a relationship between total root tensile strength and grass turf cohesion. The last section summarises the main facts and figures about grass roots and shows a procedure examining several parameters related to the shear strength of a root permeated soil.

2 Root diameter

In the present research, roots are classified into four levels as depicted in Figure 6. Level 1 is the main root from which other roots develop. Root diameter is measured by an outside micrometer (Panme) with thimble graduation of 0.01 mm as illustrated in Figure 7.

At the Thinh Long dike, three samples were taken for each species, Bermuda and Ray grass (from now on grass at the Thinh Long dike is denoted as TL). Two samples were taken for each species, Bermuda, Ray, Carpet and Vetiver grass at the Thai Thuy dike (denoted as TT). Grass on the Thinh Long and Thai Thuy dike was about four and five years old, respectively, when being investigated. All samples were 30 cm long and 10 cm in diameter. Number of the four levels in each sample were counted and a diameter value was averaged out for each level. Measurement and calculation results are plotted in Figure 8 and 9, in which the horizontal axis gives the percentage while the vertical axis gives the value of the corresponding root diameter. In general, roots of the level 4 are about up to 80

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Figure 6: Root level 1,2,3 and 4.

(a) Outside micrometer (b) Roots extracted from a soil sample

Figure 7: Outside micrometer for measuring root diameter and roots extracted from a

cylin-der soil sample.

% of the total number of roots in a sample. Average diameter of the level 4 roots varies between 0.1 and 0.2 mm. Roots of level 1, 2 and 3 contribute more or less 20 % of the total number of roots.

Similar investigation of root diameter was conducted for one year old Bermuda and Carpet grass on the Yen Binh dike. The hollow steel cylinders deployed here were 5 cm in diameter. Roots were extracted from soil, classified into four levels and counted. Obtained results are presented in Figure 10. The level 4 roots with an average diameter of 0.2 mm contribute about 70 to 80 % of the total number of roots. From 20 to 30 % of roots belongs to level 1, 2 and 3.

As can be seen in the above figures, root diameter dr [mm] can be expressed as function of its

associated percentage P er [%]:

dr= ad· P erbd (1)

The fitted curves of the diameter-percentage relationship of the studied grass species are drawn in corresponding figures. Coefficients (a and b) and goodness of fit statistics of these curves are given in Table 2. In which, SSE is the sum of squares due to error and Adj R-sq is the adjusted R-square are used to help determine the best fit. The SSE statistic is the least-squares error of the fit; the closer to zero the SSE is the better a fit is.

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0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (a) Bermuda 0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (b) Ray

Figure 8: Root diameter distribution, four year old Bermuda and Ray grass on Thinh Long

(TL) sea dike.

0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (a) Bermuda 0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (b) Carpet 0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (c) Ray 0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (d) Vetiver

Figure 9: Root diameter distribution, five year old Bermuda, Carpet and Ray grass and six

month old Vetiver grass on Thai Tho (TT) sea dike.

3 Distribution of root in depth

3.1 Distribution of root volume in depth

A soil sample was divided into three short parts, the first from 0 to 10 cm under the slope surface, the second from 10 to 20 cm and the third from 20 to 30 cm (10 cm long each). The root volume in

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0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (a) Bermuda 0 50 100 0 0.5 1 1.5 Percentage [%] Root diameter [mm] measurement d r = a*Per b (b) Carpet

Figure 10: Root diameter distribution of one year old Bermuda and Carpet grass, Yen Binh

(YB) dike.

Table 2: Coefficients of fitted curves of the relationship between root diameter and percentage,

d

r

= a

d

· P er

bd

.

Grass

a

d

b

d

SSE

Adj R-sq

Bermuda TL

0.686 -0.286

1.055

0.702 Ray TL

0.667 -0.299

0.252

0.810 Carpet TT

1.053 -0.416

0.127

0.731 Bermuda TT

0.992 -0.565

0.110

0.765 Ray TT

1.942 -0.552

0.158

0.902 Vetiver TT

1.459 -0.203

1.731 -0.089

Bermuda YB

1.795 -0.520

0.027

0.952 Carpet YB

3.534 -0.852

0.032

0.965

each 10-cm-long part was measured. Percentage of root volume is defined as the ratio of root volume Vr in each 10-cm-long part to the total root volume in 30-cm-long sample as follow:

%Vr=

Vr

P Vr

· 100% (2)

The ratio of root volume, Vr, to sample volume including soil and root, Vs, is calculated as:

RV R = Vr Vs

· 100% (3)

in which, sample volume including soil and grass root is Vs = π · r2· h [ml or cm3] with h, the

height and r, the radius of the sample of interest.

Percentage of root volumes and RVR are considered to represent at the middle of each part, i.e., at depth of 5 cm for the first part, at 15 cm for the second part and at 25 cm for the third part. Figure 11, 12 and 13 illustrate distributions of root volume and RVR in depth of different grass species on Thinh Long, Thai Tho and Yen Binh dike.

It can be seen that, the root volume decreases gradually in depth. The first 10 cm under the slope surface consists of about 50 to 90 % of the root volume. Abour 10 to 40 % of the root volume is concentrated in the second layer from 10 to 20 cm under the surface. Deeper than 20 cm, there is less than 10 % of roots being present. Most of the samples have less than 6 % of root in total volume of

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0 50 100 0 10 20 30 Volume percentage [%] Depth [cm] 0 5 10 0 10 20 30

Root Volume Ratio [%]

Depth [cm]

Bermuda Ray

Figure 11: Distribution of root volume percentage (left) and RVR (right) in depth of Bermuda

and Ray grass on Thinh Long dike.

Depth [cm]

Bermuda Carpet Ray Vetiver

Figure 12: Distribution of root volume percentage (left) and RVR (right) in depth of four

grass species on Thai Tho dike.

Depth [cm]

Bermuda Carpet

Figure 13: Distribution of root volume percentage (left) and RVR (right) in depth of Bermuda

and Carpet grass on Yen Binh dike.

the first 10 cm under the slope surface ( i.e., RVR smaller than 6 %). In the next 10 cm, root volume ratios are less than 2 %. Under 20 cm, soil contents of less than 1 % of roots.

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3.2 Distribution of root weight in depth

Ten soil samples were taken randomly for Bermuda grass and Carpet grass, five each, on the Yen Binh dike. The hollow steel cylinders are 5 cm in diameter and at least 40 cm long. Soil samples were cut into slices of 5 cm long as shown in Figure 14. For every single 5-cm-long slice, roots were extracted from soil and cleaned with water spray. The amount of roots in each slice was weighted after being dry to a stable weight, i.e., the scale gave a stable (constant) value in gram, for example. A Scientech SA 210 Model scale with resolution of 0.0001 gram was deployed in weight measurement (Figure 15).

(a) Samples of 5 cm long (b) Roots are extracted from soil by water spray

Figure 14: Soil sample is divided into 5-cm-long slices and roots are cleaned by water spray.

(a) Roots ready for weighting (b) Scientech scale SA 210 Model

Figure 15: Dry roots ready for weighting with a Scientech scale SA 210 model.

The root weight in a 5-cm-long slice is compared to the total root weight in the entire soil sample which is at least 30 cm long as follow:

%wr=

wr

P wr

· 100% (4)

Performing this calculation for all slices of ten soil samples produces ten distributions of root weight over depth which are graphically depicted in Figure 16. In the first 10 cm under the slope surface, more than 60 to 90 % of the total root weight is concentrated. Less than 10 % of the roots can be found below 20 cm of depth.

3.3 Distribution of root number in depth

At the Yen Binh dike (denoted as YB), number of root distribution in depth were determined manually for Bermuda and Carpet grass of one year old. A hollow steel cylinder with diameter of 3 cm was

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0 50 100 0

10

20

30

Root weight percentage [%]

Depth [cm] Bermuda (a) Bermuda 0 50 100 0 10 20 30

Root weight percentage [%]

Depth [cm]

Carpet

(b) Carpet

Figure 16: Distribution of root weight percentage in depth of Bermuda and Carpet grass at

Yen Binh dike.

used to take samples of grass turf with a depth of at least 30 cm, for example Figure 5. Each sample was divided into shorter parts which were 3 cm long each. The number of roots nr was counted and

recorded with corresponding depth di of each part. About 12 samples of Bermuda grass and Carpet

grass were taken giving two distributions of roots in depth as shown in Figure 17.

0 50 100 0 10 20 30 Number of roots Depth [cm] Bermuda V. poor Poor Average Good

(a) Bermuda 0 50 100 0 10 20 30 Number of roots Depth [cm] Carpet V. poor Poor Average Good

(b) Carpet

Figure 17: Distribution in depth of the numbers of roots in a 3-cm-diameter cylinder of

Bermuda and Carpet grass at Yen Binh dike.

Percentage of root number in each 3-cm-long part to total number in the entire sample which is usually 30 cm long is calculated as follow:

%nr=

nr

P nr

· 100% (5)

Calculation results are made for Bermuda and Carpet grass and plotted in Figure 18. Despite the diameter and level, about 20 to 60 % of root numbers is concentrated in the first 3 cm under the slope surface. The first 9 cm consists of about more than 50 to 90 % of the root number. Abour 10 to 40 % of the root volume is concentrated in the layer from 9 to 21 cm deep. Deeper than 21 cm, there is less than 10 % of roots being present. In comparison with root volume, number of roots is distributed in depth with a similar pattern.

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0 50 100 0 10 20 30 Percentage of roots Depth [cm] Bermuda (a) Bermuda 0 50 100 0 10 20 30 Percentage of roots Depth [cm] Carpet (b) Carpet

Figure 18: Distribution of root number percentage in depth of Bermuda and Carpet grass at

Yen Binh dike.

3.4 Root Number Ratio

The previously presented measurements reveal that the distributions of three parameters, number, volume and weight of grass roots over depth are principally identical. At an arbitrary depth, the volume and weight of roots are proportional to the number of roots despite of level and size. About 60 to 90 % of root amount (number, volume and weight) presents in the top soil layer of 10 cm thick. There is less than 10 % of roots under the depth of 20 cm. The first parameter, number of roots, can be simply determined by manually counting on site, directly after taking samples. The volume and weight of roots are measured at laboratory with request for typical apparatus. Further steps in processing and measuring root samples might cause uncertainties. Therefore, value of root numbers is recommended to be the parameter representing the distribution of roots in depth. Reubens et al. [2007] introduced three parameters, size, branching pattern and number of roots per soil area or volume to characterise root architecure.

A new parameter is proposed as the ratio of number of roots at a certain depth nrto the number

of roots nr0 at a reference depth d0:

RN R = nr nr0

(6) The reference depth is the representative depth of the first slice extracted from an entire soil sample. For example, a cylinder with length of 30 cm and diameter of 3 cm at Yen Binh dike are cut into 10 slices of 3 cm long each. The reference depth d0 is taken at 1.5 cm under the slope surface.

Root Ratio Ratio (RN R) is calculated for data of Bermuda and Carpet grass at Yen Binh dike and plotted in Figure19.

As can be seen in Figure17, the Root Number Ratio decreases over depth with an exponential function:

RN R = eaR·(d−d0) ₍₇₎

in which, d is the depth, d0 = 1.5 cm is the reference depth and a is the shape parameter. At the

reference depth d0, RN R equals 1. The shape parameter and statistics of RN R curves of one year

old Bermuda and Carpet grass at Yen Binh dike are given in Table 3.

4 Grass root density

After measuring the volume, a number of root samples were dried to humidity of 14∼15 % with temperature of 700C to determine dry root density. As root samples were divided into separate slices with regard to depth, weight could be measured for each slice individually or for an entire cylinder soil sample containing a number of slices. Density of roots in a slice is defined as ratio of root weight mri to corresponding root volume Vri:

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0 0.5 1 0

10

20

30

Root Number Ratio

Depth [cm] Bermuda RNR=e−a(d−1.5) (a) Bermuda 0 0.5 1 0 10 20 30

Root Number Ratio

Depth [cm]

Carpet

RNR=e−a(d−1.5)

(b) Carpet

Figure 19: Distribution of Root Number Ratio in depth of Bermuda and Carpet grass at Yen

Binh dike.

Table 3: Coefficients of fitted curves of the relationship between depth d and Root Number

Ratio, RN R = e

aR·(d−d0)

_.

Grass

a

R

d

0

[cm]

SSE

Adj R-sq

Bermuda YB

0.1177

1.5 2.3771

0.6432

Carpet YB

0.1507

1.5 1.9072

0.7537

γri= mri Vri [g/cm3] (8)

Besides, density of roots can be also calculated from the total weightP mri and volumeP Vri of

roots extracted from the entire sample: γr=

P mri

P Vri

[g/cm3] (9)

Dry root density of four species, Bermuda, Carpet, Vetiver and Ray grass on Thinh Long, Thai Tho and Yen Binh dikes are given Table 4. For every grass species, two values of dry density are given with regard to how it is calculated for separate slices or entire cylinder soil samples, respectively.

Values of root density given in Table 4 are plotted in Figure 20 showing a great consistency in obtained results. Discrepancies between two ways of calculation are visually considerable, from 10 to 30 % for most cases and even more than 100 % for Ray grass on Thai Thuy dike. Besides, root density of the same grass species varies from one dike to dike. For example, Bermuda root density calculated for samples is 2.666 g/cm3 _{at Thinh Long, 0.972 at Thai Tho and 0.797 at Yen Binh. It can be also}

seen that, dry density of Carpet grass at Thai Thuy and Yen Binh dike are most comparable, 0.512 and 0.567 g/cm3_{, respectively. Dry density of grass root can be found in work of Sprangers [1999];}

and recently Young [2005] presented a value of 300 kg/m3 _{using a root diameter of 0.13 mm.}

5 Root tensile stress

For each grass species, a number of samples were taken to determine the tensile strength of roots. The whole root system was carefully extracted from a soil sample and cleaned with water sprays. Use wet paper to wrap these roots, and pack into plastic bag to maintain a certain moisture. The root samples were kept at a temperature of 5 to 7oC. Every single root was pulled by a digital force gauge as shown in Figure 21. The value of pull force which breaks the root Fp was documented with the

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Table 4: Dry root density of four grass species calculated w.r.t separate ’slices’ or entire

’samples’ of soil.

Dike

wrt

Dry root density γ

r

[g/cm

3

]

Bermuda grass

Carpet grass

Ray grass

Vetiver grass

Thinh Long

sample

0.266

0.437 slice

0.296

0.377 Thai Tho

sample

0.972

0.512

0.604

0.753 slice

0.894

0.582

1.292

0.538 Yen Binh

sample

0.797

0.567 slice

0.657

0.567 Figure 20: Dry root density of Bermuda, Ray, Carpet and Vetiver grass. Calculations are

made for separate ’slices’ of entire samples of soil.

corresponding root diameter at breaking point db. Large part of the studied roots were 0.1 to 0.6 mm

in diameter and classified level 1 and 2.

The tensile stress τrof a grass root is defined as the ratio of the pull force Fp to its cross-section

area ar:

τr=

Fp

ar

(10) where the root cross-section area is derived from the root diameter at breaking point db as ar=

(pi/4) · d2

b. The relationship between root diameter and tensile stress of grass species at three dikes

are plotted in Figure 22, 23 and 24. Where, root diameter is given in [mm], and tensile stress is measured in [106N/m2] or [MPa]. In general, root tensile stress is below 500 [106N/m2]. Few roots of Bermuda and Vetiver grass at Thinh Long and Thai Tho dikes have tensile stress above 500 [106N/m2]. Comparison between Figure 22 and 24 indicates that roots of the one year old Bermuda and Carpet grass at Yen Binh are weaker than those of the five year old grass at Thai Tho.

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(a) Root is stretched (b) A broken root after testing

Figure 21: Root is stretched by a digital force gauge.

0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (a) Bermuda 0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (b) Ray

Figure 22: Root tensile strength of Bermuda and Ray grass at Thinh Long dike.

τr= aτ· dbbτ (11)

in which, db is the root diameter at breaking point, aτ and bτ are coefficients. These coefficients

and other statistics of various fitted curves are given in Table 5. The inverse relationship that tensile stress decreases with increasing root diameter has been proposed in previous works, for example Pollen and Simon [2005], Fan and Chen [2010].

The mean and standard deviation of root tensile strength are given in Table 6 for different grass species at Thinh Long, Thai Tho and Yen Binh. All measured data can be found in the Appendix, section E. For root samples taken from Yen Binh dike, the average diameter was determined before the root was being pulled. Root tensile strength was also derived from the average diameter. Figure 25 compares the root diameter before and after breaking of Bermuda and Carpet grass of Yen Binh dike. It can be seen that the diameters of the intact roots are slightly smaller than those of the broken roots.

6 Shear strength of root permeated soil

Similar to other measurements, cylinder soil samples were cut into shorter parts, for example, 15 cm for Thinh Long samples, 10 cm for Thai Tho and 7 cm for Yen Binh. Undrained unconsolidated (direct) shear tests were performed for these parts to determine the shear strength of soil. In fact, each sample part was sliced into three pieces for the direct shear test to determine value of cohesion c and angle of internal friction ϕ at its representative depth (middle of the sample part). For example,

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0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (a) Bermuda 0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (b) Carpet 0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (c) Ray 0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (d) Vetiver

Figure 23: Root tensile strength of Bermuda, Carpet, Ray and Vetiver grass at Thai Tho

dike.

0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (a) Bermuda 0 0.5 1 1.5 0 100 200 300 400 500 Root diameter [mm] Tensile strength [10 6 N/m 2 ] measurement t r = a*dr b (b) Carpet

Figure 24: Root tensile strength of Bermuda and Carpet grass at Yen Binh dike.

a layer from 0 to 10 cm is characterised by c and ϕ at the depth of 5 cm under the slope surface; c and ϕ at depth of 3.5 cm represent a layer from 0 to 7 cm. Cohesion is a measure of forces which cement soil particles, while internal friction angle is a measure of the shear strength of soil due to friction. The variation of cohesion in depth at three dikes Thinh Long, Thai Tho and Yen Binh are graphically depicted in Figure 26, 27 and 28. The soil samples of Thinh Long and Yen Binh dikes show a light decrease of cohesion with increasing depth. However, soil cohesion is consistent over depth at Thai Tho dike for different grass species.

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Table 5: Coefficients of fitted curves of the relationship between root diameter and tensile

strength, τ

r

= a

τ

· d

b_bτ

.

Grass

a

τ

b

τ

SSE

Adj R-sq

Bermuda TL

13.960 -1.570

2856400

0.785 Ray TL

30.610 -0.243

8760

0.004 Carpet TT

25.410 -1.072

60508

0.689 Bermuda TT

17.070 -1.295

116490

0.718 Ray TT

10.540 -1.431

340020

0.757 Vetiver TT

17.220 -2.024

336270

0.867 Bermuda YB

26.290 -0.523

682170

0.081 Carpet YB

7.330 -1.020

121980

0.198 Table 6: Root tensile strength of four grass species.

Quantity

Bermuda TL

Bermuda TT

Bermuda YB

Vetiver

d

b

τ

b

d

b

τ

b

d

b

τ

b

d

b

τ

b

Average

0.35

169.328

0.28

110.147

0.21

63.247

0.52

115.582 Std.

0.15

408.954

0.11

77.342

0.08

44.554

0.21

159.102 Number of roots

80

70

375

101 Quantity

Carpet TT

Carpet YB

Ray Tl

Ray TT

Average

0.28

121.941

0.34

27.460

0.24

43.566

0.27

120.980 Std.

0.11

78.036

0.14

30.456

0.06

14.832

0.14

124.718 Number of roots

33

165

41

91

7 Root permeated soil material

This section is devoted to modelling the performance of a root permeated soil by relating root char-acteristics with soil cohesion variation over depth. The first subsection defines the concept of an artificial cohesion of roots and two models describing this parameter. The second subsection guides to calculate some characteristics of a root system in soil such as representative diameter, distribution over depth of roots and associated with total tensile strength...

7.1 Artificial root cohesion

The Mohr Coulomb theory describes soil failure in terms of shear stress and effective normal stress along an frictional sliding plane as [Lambe and Whitman, 1969]:

τ = cs+ (σ − pw) tan φ (12)

where cs is the effective cohesion, pw is the pore water pressure, σ is the soil normal stress, τ is

the shear strength and φ is the internal friction angle. Cohesion is the result of cementation, electrical bonding of clays and organic colloids and capillary tension, while φ represents the frictional interaction of individual particles and the interlocking of particles. The effective normal stress is caused by the soil weight and by the pore water pressure.

For root permeated soil like grass turf, the shear strength is enhanced by roots and can be modified by adding an artificial cohesion of roots cr [O’Loughlin and Ziemer, 1982].

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0 0.5 1 0 0.2 0.4 0.6 0.8 1

Intact root diameter [mm]

Broken root diameter [mm]

measurement d

rb = a*dri

(a) Bermuda, drb= 0.7998·driwith SSE = 0.8971

and AdjR-sq = 0.6643. 0 0.5 1 0 0.2 0.4 0.6 0.8 1

Intact root diameter [mm]

Broken root diameter [mm]

measurement d

rb = a*dri

(b) Carpet, drb= 0.8016 · dri with SSE = 1.3700

and AdjR-sq = 0.5914.

Figure 25: Comparison between diameter of intact roots d

ri

and broken roots d

rb

.

0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement

Figure 26: Cohesion in depth of soil with Bermuda grass roots at Thinh Long dike.

τ = cs+ cr+ (σ − pw) tan φ (13)

To determine the effects of root reinforcement on soil (i.e., grass turf), root cohesion values have been estimated using Wu et al. [1979] model in many studies. In which, the shear strength increment provided by roots is directly governed by the tensile force of roots developed per unit area of soil [Wu et al., 1979, Waldron, 1977, ?].

First, when all roots are assumed to be oriented initially perpendicular to the shear plane, the artificial root cohesion can be written as:

cr= τr

Ar

A(cos θ tan φ + sin θ) (14)

with Tr= τrsin θ is the parallel component and σr= τrcos θ is the perpendicular component of

the root tensile stress τrwith regard to the shear zone. The root area ratio (RAR) is defined as Ar/A

and θ is the angle of shear rotation. Some studies on root permeated soil indicated that the internal friction angle was likely to be affected little by roots [Gray, 1974]. Based on field observations of conifers, Wu et al. [1979] estimated the shear rotation angle θ to vary between 45o _{and 70}o_{and cause}

negligible effect on term (cos θ tan φ + sin θ). This term is roughly 1.2 for a large range of θ values, the artificial root cohesion is therefore simplified as follow:

(20)

0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (a) Bermuda 0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (b) Carpet 0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (c) Ray 0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (d) Vetiver

Figure 27: Cohesion in depth of soil with Bermuda, Carpet, Ray and Vetiver grass roots at

Thai Tho dike.

0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (a) Bermuda 0 0.5 1 0 10 20 30 Cohesion [kG/cm2] Depth [cm] measurement (b) Carpet

Figure 28: Cohesion in depth of soil with Bermuda and Carpet grass roots at Yen Binh dike.

cr= 1.2 · τr·

Ar

A (15)

Besides, all roots are assumed to break simultaneously in Wu’s static root model. Prototype and laboratory experiments have indicated that roots break progressively (...). Deviation of the relationship between shear strength increment and tensile force generated by roots per unit area of soil was also established in study of Fan and Chen [2010]. Pollen and Simon [2005] described the breaking progress of roots using a fiber bundle model.

(21)

Second, ? estimated the shear strength increase from fiber reinforcement in a sand ∆SR by the

following expression:

∆SR= tR[sin(90 − ψ) + cos(90 − ψ) tan φ] (16)

with

ψ = tan−1[ 1

k + (tan i)−1] (17)

in which tRis the mobilised tensile strength of fibers per unit area of soil; φ is the internal friction

of sand; i is the initial orientation angle of fiber with respect to shear surface; x is the horizontal of shear displacement; z is the thickness of the shear zone; and k is the shear distortion ratio (k = x/z). The shear strength increment reaches maximum value when root inclination is about (450_{+ φ).}

7.2 Root tensile strength

In this part, the equations developed in sections 2 to 5 are used to determine several parameters characterising a grass root system developing in soil. A sequence of steps is proposed as follows:

• determine (by counting) the number of roots nr0 at the reference depth d0 in a cylinder soil

sample, which is for example 3 cm in diameter and some 30 cm of length;

• determine the average root diameter dr and its contribution P er [%] to the total number of

roots using Equation 1, dr= ad· P erbd;

• determine root tensile stress τrassociated with root diameter drusing Equation 11, τr= aτ·dbrτ.

Note that, here dr replaces the diameter at breaking point db for the sake of simplicity;

• determine Root Number Ratio RNR at a given depth d within the grass turf, which is about 20 to 30 cm thick, using Equation 7, RN R = eaR·(d−d0)_;

The tensile strength created by a root depends on its diameter dr and tensile stress τr as follow:

tr=

π 4 · d

2

r· τr= ar· τr (18)

in which, ar is the cross-section area of the root:

ar=

π 4 · d

2

r (19)

As discussed in previous section, Root Number Ratio RN R represents the root distribution in depth more directly than RAR does because RN R can be more simply determined with less uncer-tainty. Number of roots nr decreases with increasing depth d under the slope surface and can be

expressed using the function of RN R:

nr= nr0· RN R(d) (20)

where, nr0 is the number of roots representing in a sample area asat the reference depth d0 and

RN R(d) is the Root Number Ratio at depth d. If all roots are assumed to work simultaneously, the tensile strength generated by a number of roots nr at depth d under the slope surface is now

calculated as: X tr= nr· tr· 1 as (21) where as = (pi/4) · d2s is the sample area with a diameter ds. In our measurement, a cylinder

with diameter of 3 cm was used to take samples at Yen Binh dike. As aforementioned, roots with diameter dr occupy P er [%] of the total amount of roots. If this ratio remains the same over depth,

the number of roots that really work is P er [%] of nr. Replacing nr from Equation 20 and tr from

18 into 23 leads to the long form of the total tensile strength: X tr= nr· P er 10 · ar as · τr (22)

(22)

Table 7: Several parameters characterising a single root.

Grass root

n

r0

at d

0

Percentage

Diameter

Tensile stress

RNR

n

r0

Per [%]

d

r

[mm]

τ

r

[10

6

N/m

2

]

[-]

Bermuda

44

60

0.214

58.882 RN R = e

0.117·(d−1.5)

Carpet

80

60

0.108

70.960 RN R = e

0.1507·(d−1.5) or X tr= nr0· P er 10 · RN R(d) · ( dr ds )2· τr (23)

As expressed in the above equation, the root tensile strength is proportional to root number ratio RN R which exponentially decreases over depth. In the coming subsection, the tensile strength is related to the soil cohesion values obtained from the direct shear tests in Yen Binh.

7.3 Root reinforcement in soil

Data of diameter, distribution of root over depth and soil cohesion are more sufficient at Yen Binh dike than at Thinh Long and Thai Tho. Therefore, further calculation and analysis will make use of the data set obtained from Yen Binh. The values of diameter, root number ratio and tensile stress are computed for a single root according to the above sequences and given in Table 7. Roots of level 4 are assumed to contribute 60 [%] of the total number of roots for Bermuda and Carpet grass root samples taken from Yen Binh dike.

At an arbitrary depth d, all roots are assumed to be parallel to each other and work simultaneously. Leave out the effect of the angle of shear distortion and the initial orientation angle of root with respect to shear surface, the total tensile strength is simply the sum of the tensile strength induced by each single root. The decay of the total tensile strength of Bermuda and Carpet roots over depth are displayed in Figures 29 and 30, respectively, for different values of nr0. The total tensile strength is

the sum of the tensile strength induced by every single root. Therefore, the total strength apparently increases with larger numbers of roots acting at an arbitrary depth.

To investigate the effect of Bermuda and Carpet roots on soil cohesion, the values of P tr and

corresponding cohesion c at the same depth are plotted together in Figure 31. In which, P tr is

calculated with the number of roots nr0 44 and 80 (averaged out all samples) for Bermuda and

Carpet grass, respectively. The values of cohesion c are obtained from section 6, where results of the direct shear tests at Yen Binh dike show that soil cohesion slightly decreases with increasing depth under the slope surface.

Data plotted in Figures 31 are scattering; and a clear tendency is hardly recognised. Average values of cohesion are computed at depths of 3.5, 11 and 18 cm and plotted together with corresponding root tensile strengths in Figure 32. In general, the decrease of soil cohesion c over depth is likely to be proportional to the decrease of the total root tensile strength. In a fictitious grass turf, cohesion of soil only cs is considered the same over the entire turf thickness. The cohesion of root permeated

soil is influenced by the root density distribution and associated tensile strength. In the other words, the cohesion of root permeated soil is the total of the soil cohesion cs and the artificial root cohesion

cr induced by the total tensile strengthP tras follow:

c = cs+ cr (24)

As shown in Figure 32, the relationship between cohesion c (response variable y) and total root tensile strengthP tr(predictor variable x) can be simply expressed as an linear function:

(23)

0 0.5 1 0

10

20

30

Total tensile strength [MN/m2]

Depth [cm]

(a) Number of root nr0= 18

0 0.5 1

0

10

20

30

Depth [cm] (b) Number of root nr0= 32 0 0.5 1 0 10 20 30

Depth [cm] (c) Number of root nr0= 50 0 0.5 1 0 10 20 30

Depth [cm]

(d) Number of root nr0= 70

Figure 29: Decay of Bermuda root tensile strength over depth with different number of roots

n

r0

at reference depth d

0

.

in which a1 is a constant and a2 is the line slope. The constant (a1) is the cohesion value of soil

only cs when there is no root in soil (no tensile strength). The slope a2 indicates the magnitude of

effect on y (cohesion) due to changing of x (total root trenstile strength). Equation 25 is then written as:

c = cs+ a2·

X

tr (26)

Coefficients of fitted curves relating total tensile strength and cohesion of root permeated soil are given in Table 8.

The cohesion of soil cs within the grass turf can be different from the cohesion of the dike core

soil underneath because the two layers are often compacted differently in construction phase. For example, cohesion of soil taken from Yen Binh dike body is 0.344 kG/cm2_{while cohesion varies from}

less than 0.1 to more than 0.4 kG/cm2_{within the grass turf of about 30 cm thick. In principle, the dike}

Table 8: Coefficients of fitted curves of the relationship between total root tensile strength

and cohesion, c = c

s

+ a

2

· σt

r

.

Grass

c

s

a

2

SSE

Adj R-sq

Bermuda YB

0.01827

0.02668

-

0.8022

(24)

0 0.5 1 0

10

20

30

Depth [cm]

(a) Number of root nr0= 18

0 0.5 1

0

10

20

30

Depth [cm] (b) Number of root nr0= 32 0 0.5 1 0 10 20 30

Depth [cm] (c) Number of root nr0= 50 0 0.5 1 0 10 20 30

Depth [cm]

(d) Number of root nr0= 70

Figure 30: Decay of Carpet root tensile strength over depth with different number of roots

n

r0

at reference depth d

0

.

0 0.5 1 0 0.01 0.02 0.03 0.04 0.05

Soil cohesion [MN/m

2 ]

(a) Bermuda grass, number of root nr0= 44

0 0.5 1 0 0.01 0.02 0.03 0.04 0.05

Soil cohesion [MN/m

2 ]

(b) Carpet grass, number of root nr0= 80

Figure 31: Root tensile strength

P t

_r

vs. measured soil cohesion c.

core soil is compacted more intensively than the top layer where grass roots develop, thus resulting in a larger value of cohesion of the dike core. Although, Bermuda and Carpet grass were planted on the same dike slope, soil cohesion csis not necessary to be the same within grass turf of these species.

Recall the distribution of root number over depth in subsection 3.3, Carpet root system contains a larger number and penetrates more deeply than Bermuda, thus resulting in different cohesion of soil within the two grass turfs and their thickness as well. Therefore, it is not surprising when csis 0.01827

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0 0.5 1 1.5 2 0 0.02 0.04 0.06 0.08 0.1

Cohesion [MN/m

2 ]

measured y = a + bx

(a) Bermuda root

0 0.5 1 1.5 2 0 0.02 0.04 0.06 0.08 0.1

Cohesion [MN/m

2 ]

measured y = a + bx

(b) Carpet root

Figure 32: Effect of root tensile strength on soil cohesion.

smaller than cohesion measured at 18 cm under the slope surface as shown in Figure 28.

Using the newly developed equations 26 calculates the decay of cohesion c over increasing depth d for Bermuda and Carpet grass from Yen Binh dike. The computed results reproduce relatively well the measurements presented in section 6 as depicted in figure 33. Cohesion values calculated below 18 cm illustrate the decreasing effect of root tensile strength on cohesion with increasing depth. In reality, roots concentrate within the top layer of about 25 to 30 cm (grass turf); below that might possibly be the dike core with different shear strength as discussed above.

0 0.05 0.1 0 10 20 30 40 Total cohesion [MN/m2] Depth [cm] computed measured

(a) Bermuda root

0 0.05 0.1 0 10 20 30 40 Total cohesion [MN/m2] Depth [cm] computed measured (b) Carpet root

Figure 33: Effect of root tensile strength on soil cohesion.

8 Summary

This section is concerned with expressing main characteristics of four grass species on some dike slopes in the north of Viet Nam including root diameter, root distribution over depth, root tensile stress. Roots are classified into four levels 1, 2, 3 and 4. Level 4 roots contribute about 70 to 80 % of the total amount of roots. In general, root diameter dr can be expressed as a power function of the associated

percentage P er as follow:

dr= ad· P erbr (27)

The distribution of number, volume and weight of roots over depth are principally identical. At an arbitrary depth, the volume and weight of roots are proportional to the number of roots despite of level and size. About 60 to 90 % of root amount (i.e., number, volume and weight) presents in the top layer of 10 cm thick. There is less than 10 % acting under 20 cm from the slope surface. To

(26)

represent the distribution of roots in depth, a parameter Root Number Ratio (RNR) is proposed as the ratio of number of roots nr at a certain depth d to the number of root nr0 at a reference depth

d0:

RN R = nr nr0

(28) Pulling tests were mainly performed with roots of levels 1 and 2 using a digital force gauge to determine root tensile stress. The inverse relationship between tensile stress and root diameter established in some earlier works is confirmed again, one can read:

τr= aτ· dbbτ (29)

Combination of some relevant parameters leads to the total tensile strengthP tr generated by a

number of roots nrat an arbitrary depth d. The term can be expressed as follow:

X tr= nr0· P er 10 · RN R(d) · ( dr ds )2· τr (30)

Finally, cohesion c of a root permeated soil at an arbitrary depth d can be simply expressed as an linear function of total root tensile strengthP tr as follow:

c = cs+ a2·

X

tr (31)

The equation relatively well model the effect of tensile strength generated by roots on shear strength of a root permeated soil or the top layer where roots focus.

(27)

References

C.-C. Fan and Y.-W. Chen. Effect of root architecture on the shearing resistance of root-permeated soils. Ecological Engineering, Elsevier, 36:813–826, 2010. doi: 10.1016/j.ecoleng.2010.03.003. D.H. Gray. Reinforcement and stabilization of soil by vegetation. Journal of the Geotechnical

Engi-neering Division, ASCE, 100(6):695–699, June 1974.

T.W. Lambe and R.V. Whitman. Soil Mechanics. John Wiley & Sons, Inc., United States of America, 1969.

C. O’Loughlin and R.B. Ziemer. The importance of root strenth and deterioration rates upon edaphic stability in steepland forest. In Proc. of I.U.F.R.O. Workshop P.1.07-00 Ecology of Subalpine Ecosystems as a Key to Management, pages 70–78, Oregon State University, Corvallis, Oregon, 1982.

N. Pollen and A. Simon. Estimating the mechanical effects of riparian vegetation on stream bank stability using a fiber bundle model. Water Resources Research, 41, 2005. doi: 10.1029/2004WR003801.

B. Reubens, J. Poesen, F. Danjon, G. Geudens, and B. Muys. The role of fine and coarse roots in shallow slope stability and soil erosion control with a focus on root system architecture: a review. Trees, 21:385–402, 2007.

J.T.C.M. Sprangers. Vegetation dynamics and erosion resistance of seadyke grassland. PhD thesis, Wageningen Agriculture University, Wageningen, The Netherlands, 1999.

L.H. Trung. Destructive tests with the wave overtopping simulator. Comm. on hydraulic and geotech-nical eng, 2011-01, Delft University of Technology, Delft, The Netherlands, July 2011.

L.H. Trung, H.J. Verhagen, J.W. van der Meer, and V.M. Cat. Strength of the landward slopes of sea dikes in vietnam. In 8th International Conference on Coastal and Port Engineering in Developing Countries, Chennai, India, 2012.

T.Q. Tuan. Characteristics of bermuda grass and carpet grass. Technical report, Water Resources University, Ha Noi, Viet Nam, August 2012.

L.J. Waldron. The shear resistance of root-permeated homogeneous and stratified soil. Soil Science Society of America Journal, 41(5):843–849, September 1977.

T.H. Wu, W.P. III McKinnell, and D.N. Swanston. Strength of tree roots and landslides on prince of wales island, alaska. Canadian Journal of Geotechnical Research, 16(1):19–33, 1979.

M.J. Young. Wave overtopping and grass cover layer failure on the inner slope of dikes. Master thesis, UNESCO - IHE Institute for Water Education, Delft, the Netherlands, 2005.

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Data measured to determine root characteristics of some popular grass species on Vietnamese sea dikes are given in the following Appendices. The first section presents data of root diameters associated with root levels and numbers of every level. Roots of level 4 occupy about up to 80 % of the total amount of roots. The volume and weight of root slices (a sample is divided into a number of shorter slices) with regard to depths are given in the second section. Based on the value of volume and weight, density of root is derived. The third and forth sections show how the number of roots and weight of roots vary with increasing depth under the slope surface, samples were taken from the Yen Binh dike. The fifth section presents the data obtained from the tensile strength measurement of single roots. The shear strength of soil containing grass roots (cohesion and angle of internal friction) are given in the sixth section.

A

Root diameter

Average diameters of four root level are presented with corresponding percentages which the levels contribute to the total amount of roots. In the following tables, for each root sample, the first line gives the root diameters of four levels and the second line introduces their percentages of the total number of roots.

Table 9: Root diameter of Bermuda and Ray grass on the Thinh Long dike.

Sample

Root level

Sum of 3 levels

Sum of 4 levels

1

2

3

4 (1, 2, 3) [%]

(1, 2, 3, 4) [%]

Bermuda grass

1

1.10

0.66

0.35

0.16

0.35

1.02

5.17

93.45

6.55

100

2

0.82

0.53

0.24

0.13

1.07

3.73

13.33

81.87

18.13

100

3

0.96

0.63

0.41

0.13

0.32

2.25

7.80

89.63

10.37

100

4

0.99

0.65

0.36

0.17

0.25

1.33

6.32

92.10

7.90

100

5

0.92

0.57

0.29

0.14

0.36

4.16

9.03

86.45

13.55

100

6

1.01

0.56

0.29

0.14

0.32

1.35

3.82

94.50

5.50

100

7

0.67

0.36

0.20

0.11

0.27

1.32

5.41

93.00

7.00

100

8

1.06

0.57

0.38

0.17

2.35

11.76

22.35

63.53

36.47

100

9

1.06

0.48

0.23

0.13

1.96

2.11

3.02

92.91

7.09

100 Ray grass

1

1.04

0.62

0.38

0.17

0.15

1.09

1.73

97.03

2.97

100

2

1.03

0.52

0.32

0.12

0.24

2.50

4.63

92.63

7.37

100

3

1.13

0.71

0.33

0.15

0.64

2.26

3.87

93.23

6.77

100

(29)

Table 10: Root diameter of Vetiver, Carpet, Bermuda and Ray grass on the Thai Thuy dike.

Sample

Root level

Sum of 3 levels

Sum of 4 levels

1

2

3

4 (1, 2, 3) [%]

(1, 2, 3, 4) [%]

Vetiver grass

1

1.46

0.94

0.50

0.25

19.83

9.91

12.15

58.10

41.90

100

2

1.56

0.96

0.50

0.24

24.62

12.56

9.52

53.30

46.70

100 Carpet grass

1

0.91

0.57

0.37

0.19

1.46

4.13

11.79

82.62

17.38

100

2

0.85

0.57

0.30

0.19

2.90

7.05

4.01

86.03

13.97

100 Bermuda grass

1

0.93

0.43

0.27

0.12

2.00

4.51

9.51

83.98

16.02

100

2

0.66

0.34

0.23

0.14

1.47

3.89

8.85

85.79

14.21

100 Ray grass

1

1.48

0.94

0.59

0.21

1.34

2.39

6.90

89.37

10.63

100

2

1.56

0.96

0.50

0.24

0.96

1.49

4.25

93.30

6.70

100 Table 11: Root diameter of Bermuda and Carpet grass on the Yen Binh dike.

Sample

Root level

Sum of 3 levels

Sum of 4 levels

1

2

3

4 (1, 2, 3) [%]

(1, 2, 3, 4) [%]

Bermuda grass

1

1.01

0.67

0.36

0.21

2.95

7.86

18.18

71.01

28.99

100

2

0.90

0.63

0.37

0.20

3.74

10.16

12.30

73.80

26.20

100 Carpet grass

1

1.12

0.62

0.43

0.20

3.82

7.03

12.23

76.91

23.09

100

2

1.19

0.60

0.36

0.18

3.81

7.24

13.14

75.81

24.19

100

(30)

B

Distribution of root volume and root weight in depth

A soil sample was about 30 cm long and divided into 3 slices, each of 10 cm long. The volume and weight of root in every slice were measured. Obtained values are given in the present section. Based on the value of volume and weight, density of root is derived.

Table 12: Volume and weight of root in depth of Bermuda and Ray grass on the Thinh Long

dike.

Sample

Volume of root [ml]

P V

i

[ml]

Weight of root [gr]

P m

i

[gr]

0-10cm

10-20cm

20-30cm

0-30cm

0-10cm

10-20cm

20-30cm

0-30cm

Bermuda grass

1

30.0

7.0

0.2

37.2

7.90

0.80

0.08

8.78

2

5.0

2.0

0.5

7.5

0.40

0.20

0.10

0.70

3

8.0

2.0

0.2

10.2

2.60

0.80

0.10

3.50

4

15.0

5.0

0.5

20.5

6.50

1.40

0.20

8.10

5

17.0

3.0

0.7

20.7

2.90

0.70

0.30

3.90

6

20.0

2.0

0.7

22.7

10.50

0.60

0.20

11.30

7

8.0

2.0

0.2

10.2

1.10

0.70

0.10

1.90

8

7.0

1.0

0.2

8.2

1.60

0.10

1.70

9

7.0

1.0

0.1

8.1

1.60

0.30

0.07

1.97 Ray grass

1

37.0

7.0

1.4

45.4

13.50

1.10

0.20

14.80

2

26.0

5.0

1.0

32.0

13.70

3.00

0.50

17.20

3

35.0

8.0

2.3

45.3

17.80

1.60

0.90

20.30

(31)

Table 13: Volume and weight of root in depth of Vetiver, Carpet, Bermuda and Ray grass

on the Thai Thuy dike.

Sample

Volume of root [ml]

P V

i

[ml]

Weight of root [gr]

P m

i

[gr]

0-10cm

10-20cm

20-30cm

0-30cm

0-10cm

10-20cm

20-30cm

0-30cm

Vetiver grass

1

60.0

5.0

0.4

65.4

43.20

2.20

0.20

45.60

2

70.0

4.0

0.0

74.0

59.10

0.80

59.90 Carpet grass

1

4.0

3.0

2.0

9.0

2.60

0.90

0.80

4.30

2

9.0

5.0

0.3

14.3

4.00

3.50

0.30

7.80 Bermuda grass

1

6.0

1.0

0.1

7.1

5.90

0.70

0.10

6.70

2

1.0

0.2

0.0

1.2

1.20

1.20 Ray grass

1

10.0

9.0

0.8

19.8

3.70

6.00

3.50

13.20

2

40.0

5.0

2.0

47.0

19.60

3.50

2.30

25.40 Table 14: Volume and weight of root in depth of Bermuda and Carpet grass on the Yen Binh

dike.

Sample

Volume of root [ml]

P V

i

[ml]

Weight of root [gr]

P m

i

[gr]

0-10cm

10-20cm

20-30cm

0-30cm

0-10cm

10-20cm

20-30cm

0-30cm

Bermuda

7.0

0.4

0.0

7.4

5.70

0.20

5.90

(32)

C

Distribution of root number in depth, Yen Binh dike

Soil samples were taken with a 3-cm-in-diameter hollow steel cylinder. The extracted soil samples were then divided into slices of 3 cm long. The number of roots in each slice was counted manually giving data in the table below.

Table 15: Distribution of root number in depth of Bermuda and Carpet grass on the Yen

Binh dike.

Layer

Representative depth

Sample

cm - cm

cm

s0

s4

s8

s12

s16

s20

Bermuda grass

0 to 3

1.5

23

30

26

55

40

92 3 to 6

4.5

11

39

31

15

47

54 6 to 9

7.5

8

19

9

25

4

13 9 to 12

10.5

7

21

2

5

17

11 12 to 15

13.5

4

20

3

13

24

11 15 to 18

16.5

6

15

3

9

7 18 to 21

19.5

4

11

2

0

5

5 21 to 24

22.5

6

7

3

0

3 Total number of roots

69

162

79

116

146

196 Carpet grass

0 to 3

1.5

79

98

69

72

98

65 3 to 6

4.5

28

46

71

30

18

51 6 to 9

7.5

59

72

58

25

10

31 9 to 12

10.5

35

15

4

8

9

8 12 to 15

13.5

36

7

6

4

5 15 to 18

16.5

19

12

2

5

3

7 18 to 21

19.5

13

4

2

3

16 21 to 24

22.5

1

7

10

9 24 to 27

25.5

1

(33)

D

Distribution of root weight in depth, Yen Binh dike

The hollow steel cylinders are 5 cm in diameter. Soil samples were sliced into pieces of 5 cm long each. Weight of roots contained in every slice was measured by a digital scale and obtained values are tabulated in this section.

Table 16: Distribution of root weight [gram] in depth [cm] of Bermuda and Carpet grass on

the Yen Binh dike.

Layer

Representative depth

Sample

cm - cm

cm

i

ii

iii

iv

v

Bermuda grass

0 to 5

2.5 0.4612

2.1008

0.5 0.2174

0.4188

5 to 10

7.5 0.1408

0.1216

0.0598

0.0274

0.1025

10 to 15

12.5 0.0532

0.0509

0.0113

0.0378

0.0289

15 to 20

17.5

0.027 0.0464

0.0211

0.0375

0.0211

20 to 25

22.5 0.0568

0.0584

0.0383

0.0154

25 to 30

27.5

0.007 0.0111

Total root weight

P m

i

[gr]

0.6822

2.3765

0.6576

0.3584

0.5978

Carpet grass

0 to 5

2.5 0.1465

0.5252

0.2024

1.6449

0.1786

5 to 10

7.5 0.0202

0.2279

0.0858

0.2368

0.0514

10 to 15

12.5 0.0943

0.06 0.1019

0.0211

15 to 20

17.5 0.0525

0.0137

0.1027

0.0264

20 to 25

22.5 0.0268

0.0485

0.0207

25 to 30

27.5

0.019 0.0294

30 to 35

32.5 0.0165

(34)

E

Root tensile strength

For grass samples taken on the Thinh Long and Thai Thuy dikes, diameter of root db was measured

at breaking point. Therefore, root cross-section area Aband root tensile strength τbwere derived with

this diameter value.

E.1 Thinh Long dike

Table 18: Root tensile strength of Bermuda grass on the Thinh Long dike.

No. Diameter Pull force Area Tensile

db [mm] Fp [N] Ab [mm2] τb [106N/m2] 1 0.44 6.00 0.152 39.460 2 0.42 8.10 0.139 58.465 3 0.43 8.00 0.145 55.089 4 0.36 2.90 0.102 28.491 5 0.47 6.70 0.173 38.618 6 0.27 1.80 0.057 31.438 7 0.47 9.30 0.173 53.604 8 0.19 1.20 0.028 42.324 9 0.30 2.50 0.071 35.368 10 0.22 1.00 0.038 26.307 11 0.38 1.00 0.113 8.817 12 0.47 9.50 0.173 54.757 13 0.36 4.70 0.102 46.175 14 0.32 4.50 0.080 55.953 15 0.21 2.30 0.035 66.405 16 0.26 3.30 0.053 62.155 17 0.56 10.40 0.246 42.225 18 0.46 11.60 0.166 69.800 19 0.49 6.90 0.189 36.590 20 0.43 10.30 0.145 70.927 21 0.46 12.10 0.166 72.808 22 0.44 12.70 0.152 83.523 23 0.44 9.00 0.153 58.655 24 0.37 2.50 0.108 23.251 25 0.44 8.80 0.152 57.875 26 0.47 11.60 0.173 66.861 27 0.60 4.60 0.283 16.269 28 0.56 15.70 0.246 63.743 29 0.44 11.90 0.152 78.262 30 0.60 19.30 0.283 68.260 31 0.70 19.30 0.385 50.150 32 0.56 11.60 0.246 47.097 33 0.35 11.20 0.096 116.410 34 0.55 9.30 0.238 39.144 35 0.48 5.50 0.181 30.394 36 0.50 6.80 0.196 34.632 37 0.30 5.00 0.071 70.736 38 0.28 8.50 0.062 138.043 39 0.27 5.60 0.057 97.807

(35)

Table 17: Root tensile strength of Ray grass on the Thinh Long dike.

No.

Diameter

Pull force

Area

Tensile

d

b

[mm]

F

p

[N]

A

b

[mm

2

]

τ

b

[10

6

N/m

2

]

1

0.20

2.70

0.031

85.944

2

0.26

2.30

0.053

43.320

3

0.21

1.30

0.035

37.533

4

0.20

1.10

0.031

35.014

5

0.22

2.70

0.038

71.028

6

0.18

1.20

0.025

47.157

7

0.25

2.60

0.049

52.967

8

0.19

1.30

0.028

45.851

9

0.31

2.30

0.075

30.473

10

0.22

2.50

0.038

65.767

11

0.26

1.80

0.053

33.903

12

0.34

3.40

0.091

37.448

13

0.26

3.30

0.053

62.155

14

0.29

1.60

0.066

24.223

15

0.28

1.70

0.062

27.609

16

0.24

2.10

0.045

46.420

17

0.18

1.10

0.025

43.227

18

0.30

5.10

0.071

72.150

19

0.25

1.60

0.049

32.595

20

0.46

5.30

0.166

31.891

21

0.27

2.60

0.057

45.410

22

0.21

1.80

0.035

51.969

23

0.18

1.00

0.025

39.298

24

0.21

1.30

0.035

37.533

25

0.15

0.60

0.018

33.953

26

0.16

0.70

0.020

34.815

27

0.17

1.40

0.023

61.679

28

0.17

0.90

0.023

39.651

29

0.21

2.20

0.035

63.518

30

0.26

0.80

0.053

15.068

31

0.23

1.90

0.042

45.731

32

0.30

3.10

0.071

43.856

33

0.28

2.10

0.062

34.105

34

0.25

1.80

0.049

36.669

35

0.21

1.40

0.035

40.420

36

0.34

3.50

0.091

38.550

37

0.27

4.00

0.057

69.862

38

0.24

1.20

0.045

26.526

39

0.28

1.60

0.062

25.984

40

0.18

0.90

0.025

35.368

41

0.26

2.10

0.053

39.553

(36)

continued from previous page

No. Diameter Pull force Area Tensile db [mm] Fp [N] Ab [mm2] τb [106N/m2] 40 0.49 2.00 0.189 10.606 41 0.26 2.80 0.053 52.738 42 0.19 4.00 0.028 141.079 43 0.36 6.10 0.102 59.929 44 0.34 5.60 0.091 61.679 45 0.27 4.00 0.057 69.862 46 0.32 5.30 0.080 65.900 47 0.38 6.70 0.113 59.077 48 0.18 3.40 0.025 133.612 49 0.13 9.40 0.012 765.981 50 0.20 10.30 0.031 327.859 51 0.12 3.90 0.011 344.836 52 0.06 3.20 0.003 1131.768 53 0.05 2.90 0.002 1476.958 54 0.25 6.70 0.049 136.491 55 0.08 3.60 0.005 716.197 56 0.12 4.50 0.011 397.887 57 0.04 1.80 0.001 1363.374 58 0.10 2.10 0.008 267.380 59 0.05 5.70 0.002 2902.986 60 0.25 1.20 0.049 24.446 61 0.10 2.80 0.008 356.507 62 0.20 0.60 0.031 19.099 63 0.57 7.10 0.255 27.824 64 0.33 4.20 0.086 49.106 65 0.45 2.80 0.159 17.605 66 0.46 7.60 0.166 45.731 67 0.32 0.90 0.080 11.191 68 0.27 1.90 0.057 33.185 69 0.35 2.20 0.096 22.866 70 0.34 6.00 0.091 66.085 71 0.48 1.80 0.181 9.947 72 0.55 9.30 0.238 39.144 73 0.56 7.10 0.246 28.827 74 0.40 3.10 0.126 24.669 75 0.37 3.00 0.108 27.902 76 0.23 0.50 0.042 12.034 77 0.32 0.90 0.080 11.191 78 0.40 4.80 0.126 38.197 79 0.28 1.10 0.062 17.864 80 0.31 3.00 0.075 39.747

Root characteristics of some grass species on the sea dikes in Viet Nam