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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">NHESSD</journal-id>
<journal-title-group>
<journal-title>Natural Hazards and Earth System Sciences Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">NHESSD</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci. Discuss.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2195-9269</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/nhessd-3-5777-2015</article-id><title-group><article-title>Effectiveness and efficiency of slot-check dam system on debris flow control</article-title>
      </title-group><?xmltex \runningtitle{Effectiveness and efficiency of slot-check dam system on debris flow control}?><?xmltex \runningauthor{Y.~H.~Zou and X.~Q.~Chen}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Zou</surname><given-names>Y. H.</given-names></name>
          <email>zyh@imde.ac.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Chen</surname><given-names>X. Q.</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>Key Laboratory of Mountain Hazards and Earth Surface Processes, Institute of Mountain Hazards and Environment, CAS, Chengdu, 610041, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Y. H. Zou (zyh@imde.ac.cn)</corresp></author-notes><pub-date><day>29</day><month>September</month><year>2015</year></pub-date>
      
      <volume>3</volume>
      <issue>9</issue>
      <fpage>5777</fpage><lpage>5804</lpage>
      <history>
        <date date-type="received"><day>24</day><month>July</month><year>2015</year></date>
           <date date-type="accepted"><day>31</day><month>August</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://nhess.copernicus.org/articles/.html">This article is available from https://nhess.copernicus.org/articles/.html</self-uri>
<self-uri xlink:href="https://nhess.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/articles/.pdf</self-uri>


      <abstract>
    <p>Slot-check dam system is commonly used to control sediment transport
associated with debris flows and mitigate debris flow hazards. This
paper aims to estimate the performance of the slot-check dam system in
the field and set up a verification to evaluate the efficiency of
a slot-check dam system and each subsystem in debris flow sediment
control. Field survey on a group of a series of slot-check dams at
Shengou Basin in Yunnan, China reveals that the conserving sediment
volume of each dam is related to its relative location in the group,
gradually decreasing from upstream to downstream. The cumulative
sediment volume within a subsystem of slot-check dams closely related
to the characteristics of the catchment controlled by the
subsystem. It increases with the controlled catchment area of the most
downstream dam in subsystem and the distance from the dam to the
upstream most. Evaluation models for the conserving efficiency of
a slot-check dam system on debris flow control in a river basin and
each subsystem within the group associate to the controlled catchment
characteristics have been proposed. The layout principle of
a slot-check dam system in a river basin has been developed based on
the conserving efficiency of a subsystem of slot-check dams which
would allow the slot-check dam system to be designed in a more
scientific way.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Debris flows are widely recognized as one of the dominant geomorphic
processes in steep mountainous terrain (Remaître and Malet,
2010). Debris flows occur when masses of poorly sorted sediment,
agitated and saturated with water, surge down slopes in response to
gravitational attraction. They can travel long distances in channels
with modest slopes and to inundate vast areas. Large debris flows can
exceed 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> in volume and release more that
10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>16</mml:mn></mml:msup></mml:math></inline-formula> J of potential energy, but even commonplace flow of <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> can denude vegetation, clog drainage-ways,
damage structures and endanger humans (Iverson, 1997).</p>
      <p>One of the most effective techniques to manage debris-flow hazards is
to construct series of check dams (Takahashi, 1981; Remaître and
Malet, 2010; Chen et al., 2013; Fiebiger, 1997; Heumader, 2000; Huebl
and Fiebiger, 2005; Hungr et al., 1987; Mizuyama, 2008). They play an
important role in the management and development of a river basin
(Busnelli et al., 2001). One of their most common functions is to
enhance sediment deposition, reducing the bed gradient and flow
velocity in order to check soil erosion within a stream, such as
a gully (Castillo et al., 2014).</p>
      <p>Two kinds of check dams can be distinguished: closed and open
(Busnelli et al., 2001; Li, 1997; Catella et al., 2005). Conventional
closed check dams are overflowed by the water discharge and intercept
all but the fine particles of the solid material. Hence they are
rapidly filled up by the sediment transport. Conversely, open check
dams are constructed with suitable openings in the body of the
structure, thus part of the sediment is allowed to pass through
(Busnelli et al., 2001). Slot-check dam, an open-type check dam with
slot shaped openings, has been shown to be efficient in reducing
debris flow run-out (Remaître et al., 2008; Jia et al.,
2011). If the opening slots of the check dam are large enough,
deposition upstream the check dam during ordinary events is
negligible, its storage capacity is left available for the very large
debris flows (Busnelli et al., 2001; Chen et al., 2013; Li, 1997).</p>
      <p>Considerable theoretical and numerical works have been performed on
the size, shape and structure of torrential check dams, allowing the
definition of general design criteria (Remaître and Malet,
2010; Armanini and Larcher, 2001; Han and Ou, 2004; Jia et al., 2011;
Johnson and McCuen, 1989; Lien, 2003; Li, 1997; Catella et al., 2005;
Shrestha et al., 2008). Some researchers studied the river bed
variations after check dam system construction
(Conesa-García et al., 2007; Xu et al., 2004; Zimmermann and
Church, 2001). Less research has focused on the optimal number and
location of these dams along the debris-flow track (Osti and Egashira,
2008; Hassanli et al., 2009; Remaître and Malet, 2010) as well
as the quantitative evaluation on slot-check dam system efficiency in
sediment control in the field (Remaître and Malet,
2010). Preliminary study on the efficiency of the subsystem in
a slot-check dam group has been proposed (Zou et al., 2014). In the
study, a new way for the analysis on the efficiency of a slot-check
dam group was provided. The conserving efficiency of the subsystem
within a slot-dam group was associated with catchment shape
characteristics. But it was only focused on the contribution of
a subsystem to the whole slot-check dam group. The efficiency of the
single slot-check dam and the efficiency of the whole slot-check dam
system and its subsystem on the sediment control in a river basin were
not evaluated. And it is important that more related catchment
characteristics associated with sediment erosion and dam parameters
should be considered in the efficiency evaluation. Principle on the
layout of a slot-check dam system in a debris flow river basin is also
needed to be proposed for the mitigation of debris flow hazards.</p>
      <p>This paper is aimed at evaluating the efficiency of the slot-check dam
system and its subsystem in sediment control for the river basin.
A quantitative method is proposed for estimating the efficiency of
slot-check dam system in debris flow hazards mitigation. The layout
principle of a slot-check dam system in a river basin is analyzed
based on the efficiency of a subsystem of slot-check dams on sediment
control.</p>
</sec>
<sec id="Ch1.S2">
  <title>Study area</title>
      <p>The study area is Shengou Basin in Dongchuan district, Kunming in
China. Shengou Basin is a tributary of the right bank of Xiaojiang
River, and a typical debris-flow gully in the mountainous regions of
southwestern China (Fig. 1). It covers an area of about
32 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and is located in the northeastern Dongchuan
district, extending
103<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>09<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>07<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>–103<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:msup><mml:mn>15</mml:mn><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>00<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E and
26<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>04<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>47<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>–26<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:msup><mml:mn>09</mml:mn><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>03<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> N. The basic parameters
of Shengou Basin are listed in Table 1.</p>
      <p>Shengou Basin pertains to a subtropical monsoon climate zone with
distinct dry and wet seasons, vertical zoning and regional heavy
rainstorm. It has an annual rainfall 600–1200 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in the river
valley and 700 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in the alpine region. The precipitation in
the rainy season from May to October accounts for 88 % of total
annual precipitation. Rainstorm and rain shower accounted for above
half of the total annual precipitation. The centers of rainstorms
mainly occurred at the zone from 2500 to 3000 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> in the river
basin. The annual rate of rainstorm is 0.8–1.5 times per year,
maximum rainfall intensity reached 123.6 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in 24 h,
63.4 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in 1 h and 20.8 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in 10 min.</p>
      <p>The water discharge in the river trench is about
0.5 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Water level would suddenly arise if
rainstorm occurs and the flow discharge could be large than
100 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The peak discharge of flood with return
year of 50 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">years</mml:mi></mml:math></inline-formula> is 169.2 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Debris flows
would properly occur in the rivers under the rainstorm with return
year of 10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">years</mml:mi></mml:math></inline-formula>.</p>
      <p>Debris flows threaten the safety of more than 12 000 people living in
Shengou Basin. The outburst of debris flow may damage the highway and
railway at the downstream area and block Dabai river which Shengou
river flows into. In order to control sediment transport and mitigate
debris flow hazards, a slot-check dam group with a series of five dams
had been built in 2010 at the upper region of Shengou Basin (Figs. 1
and 2). The main characteristics of the slot-check dams are listed in
Table 2.</p>
</sec>
<sec id="Ch1.S3">
  <title>Methodology</title>
      <p>This research aims to assess the effectiveness of the chain of
check-dams and a individual check dam through field survey and
analytical study. Field survey had been conducted to investigate the
performance of the slot-check dams. The effectiveness of the series of
slot-check dams in sediment control has been verified from its
stability resistant to the impact of debris flows, soil conservation
function and downstream erosion prevention. The efficiency to assess
the function of the mitigation project has been represented by several
quantitative evaluation parameters. And the methodology of the
derivation of efficiency has been given in the follows.</p>
<sec id="Ch1.S3.SS1">
  <title>Efficiency of the slot-check dam system in sediment control</title>
      <p>The efficiency of an individual check dam in the entire chain of check
dams <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>:

                <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          The efficiency of subsystem in the slot-check dam system
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mtext>subs</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is to be established to assess the role of a dam
and the subsystem in the whole dam system. It can be represented by
the ratio of the accumulated volume of deposit stored within the
subsystem <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to the total sediment volume stored within
the dam group <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:

                <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          The efficiency of a slot-check dam system in mitigating debris flow
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mtext>sys</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is to be established to assess the role of the dam
system in mitigating debris flow and sediment control at the river
basin. It can be represented by the ratio of the volume of sediment
stored within the storage of the dam group <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to the
possible surface erosion volume of the region <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>:

                <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Since the sediment volume in the river basin is related to the
characteristics of the catchment area and the rainfall factor in the
area, the possible surface erosion volume of the region can be
calculated as:

                <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the rainfall factor of debris flow in the river
basin,

                <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the critical rainstorm intensity per 24 h that
induced debris flow in the river basin, <inline-formula><mml:math display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is the frequency of the
related rainstorm, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the average annual rainfall
intensity per 24 h, and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the sediment volume base according to the
characteristics of the catchment area,

                <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is the shape factor, that is associated with the
erosion ability of debris flows in the river basin,

                <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E7"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E8"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> is the volume coefficient, that is a dimensionless
parameter. Substitute Eq. (7) into Eq. (8) then,

                <disp-formula id="Ch1.E9" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Intuitively, the cumulative sediment volume stored upstream each dam
is related to the characteristics of the catchment area, the rainfall
factor in the area <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the geometry of the opening
slots of dam <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:

                <disp-formula id="Ch1.E10" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>

          where

                <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E11"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E12"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the shape coefficient,

                <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E13"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E14"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            Substitute Eq. (13) into Eq. (14), then accumulate deposit volume in
a subsystem is:

                <disp-formula id="Ch1.E15" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is catchment area controlled by slot-check dam;
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is distance from the dam to the most upstream point of
the region; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the open rate of the dam;
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the coefficient of transport capacity of the
slot-check dam, related to the opening size of the slot of check dam
to the representative particle size of debris flow, <inline-formula><mml:math display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>.</p>
      <p>Ikeya and Uehara (1980), Mizuyama et al. (1988) and Itoh et al. (2011)
studied various types of open-type dams and pointed out that the
debris flow will be trapped when the ratio of representative particle
size of debris flow to the post spacing is larger than its closure
threshold. Here from the experimental tests, we introduce <inline-formula><mml:math display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> (Eq. 16)
as the closure coefficient of openings in slot-check dam. When <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, sediments of debris flow would filled the small opening slots in
the check dam and gradually deposit within the slot-check dam
storage. In this condition, almost no discharge through openings of
the dam occurs. On the other hand, debris flow discharge from the
large slots.

                <disp-formula id="Ch1.E16" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>2.5</mml:mn><mml:msqrt><mml:mfrac><mml:mi mathvariant="italic">γ</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:msqrt><mml:mfrac><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>90</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> is the density of debris flow; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>90</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is the
90 % particle size of the debris flow; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> is the minimum
width of the opening size.</p>
      <p>(i) for small slot (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>):

                <disp-formula id="Ch1.E17" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.</mml:mn></mml:mrow></mml:math></disp-formula>

          Substitute Eqs. (17) and (15) into Eq. (2), then the conservation
efficiency of a subsystem of dams in the whole system can be
calculated as:

                <disp-formula id="Ch1.E18" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>i</mml:mi></mml:munderover><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Substitute Eqs. (17), (9) and (15) into Eq. (3), then the efficiency
of the subsystem on erosion control at a river basin:

                <disp-formula id="Ch1.E19" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>∑</mml:mo><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p>(ii) for large slot (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>):

                <disp-formula id="Ch1.E20" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>≠</mml:mo><mml:mn>0.</mml:mn></mml:mrow></mml:math></disp-formula>

          For a stony debris flow,

                <disp-formula id="Ch1.E21" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.11</mml:mn><mml:msup><mml:mfenced close=")" open="("><mml:mfrac><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>95</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mfenced><mml:mn>0.36</mml:mn></mml:msup><mml:msubsup><mml:mi>C</mml:mi><mml:mi>a</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.93</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> is the minimum space of slots, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
sediment concentration at the peak discharge occurring at the front
part of the debris flow and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>95</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is 95 % grain size (Mizuyama
et al., 1995).</p>
      <p>Substitute Eqs. (21) and (15) into Eq. (2), then the conservation
efficiency of a subsystem of dams in the whole system can be
calculated as:

                <disp-formula id="Ch1.E22" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>i</mml:mi></mml:munderover><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Substitute Eqs. (21), (9) and (15) into Eq. (3), then the efficiency
of the slot-check dam system on erosion control at a river basin:

                <disp-formula id="Ch1.E23" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>∑</mml:mo><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Optimal design of the layout of a slot-check dam system</title>
      <p>The optimal layout of the slot-check dam system is essential in the
dam system design. Figure 7 shows the outline of slot-check dam system
design for debris flow hazard mitigation. The layout could be
developed based on the characteristics of the controlled catchment
area of the subsystem, storage capacity of a single dam, required
total reservation of sediments and the appropriate dam sites. Based on
the efficiency evaluation model, the efficiency of the whole designed
dam system in sediment control in the basin and a subsystem in the
group can be estimated. That can provide a quantitative base for
counter calculation and comparison the optimal layouts. Actually, the
dam system to be designed in a river basin is not closed but an open
system which is just a subsystem for a more extended system. As shown
in Fig. 8, after the design or plan of a layout of a system, a new dam
system can also be added or inserted into the existed old system
without breaking the original arrangement. And the controlled
catchment area as well as the distant to upstream most of a subsystem
can be calculated as:
<?xmltex \hack{\allowdisplaybreaks}?>

                <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E24"><mml:mtd/><mml:mtd/><mml:mtd><mml:mfenced open="{" close=""><mml:mtable rowspacing="0.2ex" columnspacing="1em" class="cases" columnalign="left" framespacing="0em"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">⋯</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">⋯</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E25"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>adesign</mml:mtext></mml:msub><mml:mo>∑</mml:mo><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:msubsup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>adesign</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the rainfall factor with the designed
return year of debris flow.

                <disp-formula id="Ch1.E26" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo movablelimits="false">∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mo movablelimits="false">∑</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the storage capacity of the single dam with the
number <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> in the dam system.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>Results and discussion</title>
      <p>Field survey had been conducted to investigate the performance of the
slot-check dams. The effectiveness of the series of slot-check dams in
sediment control has been verified from its stability resistant to the
impact of debris flows, soil conservation function and downstream
erosion prevention (Fig. 2). Figure 2 shows the performance of the
five slot-check dams with a continuous layout from the upstream
(Fig. 1) in Shengou Basin. Each slot-check dam had played an effective
role in erosion conservation as a certain amount volume of sediments
deposited within the storage of each dam. The dams successfully
resisted to the impact of debris flows since they were running in good
condition without damage in dam body or dam foundation.</p>
      <p>The construction of check dams in a gully reach causes a flow
perturbation upstream and downstream of each structure. It creates
a backwater effect by increasing the water depth immediately upstream
of the structure (Castillo et al., 2014). An equilibrium regime of
sediment deposit formed upstream each dam after encountering
a transient subcritical state due to dam block (Fig. 3).</p>
      <p>For dam-filling conditions, a hydraulic jump habitually occurs and
a flow drop downstream of the check dam also produces (Castillo
et al., 2014). Except for the upstream source, the sediments stored
within each couple of check dams mainly come from the bank and the
lateral slope on both sides of the gully, rather than from the
bed. From the field investigation, the base of each check dam is not
exposed. No apparent downstream bed erosion has been observed expect
the partial erosion in the preventing rib downstream the first dam
(Fig. 4).</p>
      <p>Figure 5 shows the sketch of equilibrium deposit within the slot-check
dam system. Equilibrium deposits had been blocked and formed upstream
each dam. Debris flow sediments with different volume were blocked by
the dam at each step and deposited within the dam group. It shows that
the sediment conserving function of a dam largely depends on its
relative location in the group.</p>
      <p>Characteristics of deposits upstream the dams were measured on
29 November 2012 and the efficiency of each dam was estimated
(Table 3). From the comparison of the effective height of dam and the
deposit height, all five dams are not completely used up with
remaining capacity for subsequent sediment conservation. Although the
dams have blocked a great amount of sediments, the largest dam
efficiency is not more than sixty percent. Since the slope of deposit
is slower than the original channel slope (Fig. 3), storage per height
at upper layer is larger than that at lower layer in the dam
reservior.</p>
      <p>The volume of deposit stored within each slot-check dam storage and
the accumulated volume of deposits upstream each dam are related to
the control catchment area at that point and the distance from the dam
to the most upstream point in the catchment (Fig. 6). The volume
within the dam storage initially increases with the increase of its
controlled catchment area (Fig. 6a). But after the volume increases to
a maximum value at a dam located at the midstream, it decreases with
the controlled catchment area. However, the accumulated volume
upstream the slot check dam always increases with the controlled area,
initially it increases sharply, then slightly and gradually approaches
to a stable value. About 60 % of sediment has been blocked
upstream the third dam in the dam system.</p>
      <p>The relationship between the sediment deposit volume upstream the
slot-check dam and the distance from the dam to the first dam is
similar (Fig. 6b). The accumulated deposit volume upstream the slot
check dam approaches to a stable value when the dam sits far away from
the first dam in the group.</p>
      <p>The efficiency of slot-check dam system associated with the
characteristics of the catchment mountain is listed in Table 4. The
conserving efficiency of a slot-check dam system on debris flow
control in a river basin and each subsystem within the group are
associated with the related catchment characteristics. Since the
movable sediments volume in Shengou Basin is about <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>6.017</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, the efficiency of the whole dam system in
sediment control in the basin is calculated and compared with the
results of the evaluation model.</p>
      <p>According to Table 4, the efficiency of each individual dam in the
group is different. For an optimal design, (1) the individual dam
height or the storage capacity should be determined according to its
efficiency in the group <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. (2) To make sure the
difference between two connected subsystems efficiency
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is more or less the same. (3) Since the
system efficiency in the basin is about 20 %, more mitigation
projects or methods should be added in order to prevent debris flow
hazards to greater extent.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Conclusions</title>
      <p>Slot-check dam system, an interconnected defense system, shows its
significant effectiveness in sediment transport control associated
with debris flows.
<list list-type="order"><list-item>
      <p>Field survey had been conducted to investigate the performance of
the slot-check dams in Shengou Basin. The dams successfully resisted
to the impact of debris flows since they were running in good
condition without damage in dam body or dam foundation. Each
slot-check dam had played an effective role in erosion conservation as
a certain amount volume of sediments deposited within the storage of
each dam.</p></list-item><list-item>
      <p>The conserving efficiency of a slot-check dam system on debris
flow control in a river basin and each subsystem within the group are
associated with their related catchment parameters. The conserving
sediment volume of each dam is related to its relative location and
catchment area in the group, gradually decreasing from upstream to
downstream.</p></list-item><list-item>
      <p>Quantitative method were proposed for estimating the efficiency of
slot-check dam system based on the rainfall factor, shape factor and
related dam parameters. The data obtained in the Shengou Basin has
been come up with a quantitative example of optimal design of the
slot-check dam system. The dam height and location in the basin can be
better determined based on the evaluation of dam system efficiency, so
that they works at maximum efficiency.</p></list-item></list>
Further study and more field data in different river basins are needed
to promote the application of the efficiency evaluation model.</p>
</sec>

      
      </body>
    <back><ack><title>Acknowledgements</title><p>This research was substantially supported by Knowledge Innovation
Project of Chinese Academy of Sciences (Approval No. KZZD-EW-05-01)
and the National Science and Technology Support Program of China
(No. 2014BAL05B01). The great help of K. H. Hu and W. Zhong is also
gratefully acknowledged.</p></ack><ref-list>
    <title>References</title>

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  </ref-list><app-group content-type="float"><app><title/>

<?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.T1"><caption><p>Main characteristics of Shengou Basin.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.85}[.85]?><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="59.750787pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="36.988583pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="36.988583pt"/>
     <oasis:colspec colnum="6" colname="col6" align="justify" colwidth="36.988583pt"/>
     <oasis:colspec colnum="7" colname="col7" align="justify" colwidth="36.988583pt"/>
     <oasis:colspec colnum="8" colname="col8" align="justify" colwidth="36.988583pt"/>
     <oasis:colspec colnum="9" colname="col9" align="justify" colwidth="36.988583pt"/>
     <oasis:thead>
       <oasis:row>

         <?xmltex \mrwidth{17mm}?><oasis:entry colname="col1" morerows="1">River basin</oasis:entry>

         <?xmltex \mrwidth{17mm}?><oasis:entry rowsep="1" colname="col2" morerows="2">Catchment<?xmltex \hack{\break}?> area<?xmltex \hack{\break}?> <inline-formula><mml:math display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>

         <?xmltex \mrwidth{21mm}?><oasis:entry rowsep="1" colname="col3" morerows="2">Main stream<?xmltex \hack{\break}?> length<?xmltex \hack{\break}?> <inline-formula><mml:math display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> (km)</oasis:entry>

         <?xmltex \mrwidth{13mm}?><oasis:entry rowsep="1" colname="col4" morerows="2">Average<?xmltex \hack{\break}?> width<?xmltex \hack{\break}?> <inline-formula><mml:math display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> (m)</oasis:entry>

         <?xmltex \mrwidth{13mm}?><oasis:entry rowsep="1" colname="col5" morerows="2">Relative<?xmltex \hack{\break}?> altitude<?xmltex \hack{\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (m)</oasis:entry>

         <?xmltex \mrwidth{13mm}?><oasis:entry rowsep="1" colname="col6" morerows="2">Average<?xmltex \hack{\break}?> slope<?xmltex \hack{\break}?> <inline-formula><mml:math display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> (%)</oasis:entry>

         <oasis:entry namest="col7" nameend="col9" align="center">Debris flow </oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col7"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>

         <oasis:entry colname="col8"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>

         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col7"/>

         <oasis:entry colname="col8"/>

         <oasis:entry colname="col9"/>

       <?xmltex \interline{[-12pt]}?></oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry colname="col1">Shengou</oasis:entry>

         <oasis:entry colname="col2">31.77</oasis:entry>

         <oasis:entry colname="col3">13.55</oasis:entry>

         <oasis:entry colname="col4">51.20</oasis:entry>

         <oasis:entry colname="col5">2520.00</oasis:entry>

         <oasis:entry colname="col6">20.30</oasis:entry>

         <oasis:entry colname="col7">318.22</oasis:entry>

         <oasis:entry colname="col8">282.86</oasis:entry>

         <oasis:entry colname="col9">247.51</oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.T2"><caption><p>Basic parameters of the slot-check dams.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.87}[.87]?><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="65.441339pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="65.441339pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="82.512992pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="82.512992pt"/>
     <oasis:colspec colnum="6" colname="col6" align="justify" colwidth="82.512992pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Dam</oasis:entry>  
         <oasis:entry colname="col2">Length of dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col3">Effective height of dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col4">Height of drainage hole in dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col5">Width of drainage hole in dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col6">Design discharge<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mtext>proj</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">a</oasis:entry>  
         <oasis:entry colname="col2">63.9</oasis:entry>  
         <oasis:entry colname="col3">8.0</oasis:entry>  
         <oasis:entry colname="col4">0.50</oasis:entry>  
         <oasis:entry colname="col5">0.40</oasis:entry>  
         <oasis:entry colname="col6">96.55</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">b</oasis:entry>  
         <oasis:entry colname="col2">79.0</oasis:entry>  
         <oasis:entry colname="col3">12.0</oasis:entry>  
         <oasis:entry colname="col4">0.40</oasis:entry>  
         <oasis:entry colname="col5">0.40</oasis:entry>  
         <oasis:entry colname="col6">96.55</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">c</oasis:entry>  
         <oasis:entry colname="col2">65.5</oasis:entry>  
         <oasis:entry colname="col3">10.0</oasis:entry>  
         <oasis:entry colname="col4">0.40</oasis:entry>  
         <oasis:entry colname="col5">0.40</oasis:entry>  
         <oasis:entry colname="col6">96.55</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">d</oasis:entry>  
         <oasis:entry colname="col2">100.0</oasis:entry>  
         <oasis:entry colname="col3">10.5</oasis:entry>  
         <oasis:entry colname="col4">0.50</oasis:entry>  
         <oasis:entry colname="col5">0.40</oasis:entry>  
         <oasis:entry colname="col6">96.55</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">e</oasis:entry>  
         <oasis:entry colname="col2">62.0</oasis:entry>  
         <oasis:entry colname="col3">6.0</oasis:entry>  
         <oasis:entry colname="col4">0.50</oasis:entry>  
         <oasis:entry colname="col5">0.40</oasis:entry>  
         <oasis:entry colname="col6">96.55</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.T3"><caption><p>Deposits upstream each slot-check dam measured on 29 November 2012.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.87}[.87]?><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="85.358268pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="85.358268pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="79.667717pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="79.667717pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Dam</oasis:entry>  
         <oasis:entry colname="col2">Height of deposit<?xmltex \hack{\hfill\break}?>upstream the dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col3">Volume of deposit<?xmltex \hack{\hfill\break}?>upstream the dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col4">Effective height of<?xmltex \hack{\hfill\break}?>dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (m)</oasis:entry>  
         <oasis:entry colname="col5">Efficiency of each<?xmltex \hack{\hfill\break}?>dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>self</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mover accent="true"><mml:mo>=</mml:mo><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:msubsup><mml:mi>H</mml:mi><mml:mi>s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mi>H</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">a</oasis:entry>  
         <oasis:entry colname="col2">2.90</oasis:entry>  
         <oasis:entry colname="col3">7.20</oasis:entry>  
         <oasis:entry colname="col4">8.00</oasis:entry>  
         <oasis:entry colname="col5">0.13</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">b</oasis:entry>  
         <oasis:entry colname="col2">6.20</oasis:entry>  
         <oasis:entry colname="col3">26.40</oasis:entry>  
         <oasis:entry colname="col4">12.00</oasis:entry>  
         <oasis:entry colname="col5">0.27</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">c</oasis:entry>  
         <oasis:entry colname="col2">7.40</oasis:entry>  
         <oasis:entry colname="col3">32.80</oasis:entry>  
         <oasis:entry colname="col4">10.00</oasis:entry>  
         <oasis:entry colname="col5">0.55</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">d</oasis:entry>  
         <oasis:entry colname="col2">6.10</oasis:entry>  
         <oasis:entry colname="col3">29.00</oasis:entry>  
         <oasis:entry colname="col4">10.50</oasis:entry>  
         <oasis:entry colname="col5">0.34</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">e</oasis:entry>  
         <oasis:entry colname="col2">4.60</oasis:entry>  
         <oasis:entry colname="col3">14.50</oasis:entry>  
         <oasis:entry colname="col4">6.00</oasis:entry>  
         <oasis:entry colname="col5">0.59</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.T4"><caption><p>The efficiency and associated catchment parameters of each slot-check dam system.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.7}[.7]?><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="54.060236pt"/>
     <oasis:colspec colnum="6" colname="col6" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="7" colname="col7" align="justify" colwidth="54.060236pt"/>
     <oasis:colspec colnum="8" colname="col8" align="justify" colwidth="54.060236pt"/>
     <oasis:colspec colnum="9" colname="col9" align="justify" colwidth="48.369685pt"/>
     <oasis:colspec colnum="10" colname="col10" align="justify" colwidth="48.369685pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Dam</oasis:entry>  
         <oasis:entry colname="col2">Controlled<?xmltex \hack{\hfill\break}?>catchment<?xmltex \hack{\hfill\break}?>area<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (km<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">Distance<?xmltex \hack{\hfill\break}?>to most<?xmltex \hack{\hfill\break}?>upstream<?xmltex \hack{\hfill\break}?>point<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (km)</oasis:entry>  
         <oasis:entry colname="col4">Deposit<?xmltex \hack{\hfill\break}?>volume<?xmltex \hack{\hfill\break}?>upstream<?xmltex \hack{\hfill\break}?>a dam<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Cumulative<?xmltex \hack{\hfill\break}?>deposit<?xmltex \hack{\hfill\break}?>volume<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>subsystem<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col6">Individual<?xmltex \hack{\hfill\break}?>dam<?xmltex \hack{\hfill\break}?>efficiency<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>group<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col7">Subsystem<?xmltex \hack{\hfill\break}?>efficiency<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>group<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col8">Subsystem<?xmltex \hack{\hfill\break}?>efficiency<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>group<?xmltex \hack{\hfill\break}?>(model)<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">η</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mrow><mml:mtext>subs</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col9">System<?xmltex \hack{\hfill\break}?>efficiency<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>basin<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">System<?xmltex \hack{\hfill\break}?>efficiency<?xmltex \hack{\hfill\break}?>in the<?xmltex \hack{\hfill\break}?>basin<?xmltex \hack{\hfill\break}?>(model)<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">η</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mrow><mml:mtext>sys</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">a</oasis:entry>  
         <oasis:entry colname="col2">4.24</oasis:entry>  
         <oasis:entry colname="col3">1.97</oasis:entry>  
         <oasis:entry colname="col4">7.20</oasis:entry>  
         <oasis:entry colname="col5">7.20</oasis:entry>  
         <oasis:entry colname="col6">0.07</oasis:entry>  
         <oasis:entry colname="col7">0.07</oasis:entry>  
         <oasis:entry colname="col8">0.16</oasis:entry>  
         <oasis:entry colname="col9">0.01</oasis:entry>  
         <oasis:entry colname="col10">0.03</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">b</oasis:entry>  
         <oasis:entry colname="col2">5.60</oasis:entry>  
         <oasis:entry colname="col3">2.46</oasis:entry>  
         <oasis:entry colname="col4">26.40</oasis:entry>  
         <oasis:entry colname="col5">33.60</oasis:entry>  
         <oasis:entry colname="col6">0.24</oasis:entry>  
         <oasis:entry colname="col7">0.31</oasis:entry>  
         <oasis:entry colname="col8">0.42</oasis:entry>  
         <oasis:entry colname="col9">0.06</oasis:entry>  
         <oasis:entry colname="col10">0.08</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">c</oasis:entry>  
         <oasis:entry colname="col2">7.41</oasis:entry>  
         <oasis:entry colname="col3">3.06</oasis:entry>  
         <oasis:entry colname="col4">32.80</oasis:entry>  
         <oasis:entry colname="col5">66.40</oasis:entry>  
         <oasis:entry colname="col6">0.30</oasis:entry>  
         <oasis:entry colname="col7">0.60</oasis:entry>  
         <oasis:entry colname="col8">0.53</oasis:entry>  
         <oasis:entry colname="col9">0.11</oasis:entry>  
         <oasis:entry colname="col10">0.10</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">d</oasis:entry>  
         <oasis:entry colname="col2">10.32</oasis:entry>  
         <oasis:entry colname="col3">3.80</oasis:entry>  
         <oasis:entry colname="col4">29.00</oasis:entry>  
         <oasis:entry colname="col5">95.40</oasis:entry>  
         <oasis:entry colname="col6">0.26</oasis:entry>  
         <oasis:entry colname="col7">0.87</oasis:entry>  
         <oasis:entry colname="col8">0.74</oasis:entry>  
         <oasis:entry colname="col9">0.16</oasis:entry>  
         <oasis:entry colname="col10">0.14</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">e</oasis:entry>  
         <oasis:entry colname="col2">15.26</oasis:entry>  
         <oasis:entry colname="col3">4.91</oasis:entry>  
         <oasis:entry colname="col4">14.50</oasis:entry>  
         <oasis:entry colname="col5">109.90</oasis:entry>  
         <oasis:entry colname="col6">0.13</oasis:entry>  
         <oasis:entry colname="col7">1.00</oasis:entry>  
         <oasis:entry colname="col8">1.00</oasis:entry>  
         <oasis:entry colname="col9">0.18</oasis:entry>  
         <oasis:entry colname="col10">0.19</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <fig id="App1.Ch1.F1"><caption><p>The slot-check dam system in Shengou Basin.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f01.pdf"/>

    </fig>

      <fig id="App1.Ch1.F2"><caption><p>Performance of slot-check dams in Shengou Basin on 29 November 2012.
<bold>(a<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="bold">1</mml:mn></mml:msub></mml:math></inline-formula>–e<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="bold">1</mml:mn></mml:msub></mml:math></inline-formula>)</bold> View from the downstream, and <bold>(a<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="bold">2</mml:mn></mml:msub></mml:math></inline-formula>–e<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="bold">2</mml:mn></mml:msub></mml:math></inline-formula>)</bold> view from the upstream of the five check dams.</p></caption>
      <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f02.pdf"/>

    </fig>

      <fig id="App1.Ch1.F3"><caption><p>Debris flow sediment deposit upstream a slot-check dam.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f03.pdf"/>

    </fig>

      <fig id="App1.Ch1.F4"><caption><p>Downstream erosion at the toe of the first slot-check dam.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f04.pdf"/>

    </fig>

      <fig id="App1.Ch1.F5"><caption><p>Sketch of equilibrium deposit within the slot-check dam system.</p></caption>
      <?xmltex \igopts{width=\textwidth}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f05.pdf"/>

    </fig>

      <fig id="App1.Ch1.F6"><caption><p>Relationship between the volumes of sediment stored upstream the slot-check dam. <bold>(a)</bold> The drained catchment area; <bold>(b)</bold> the position of the check dam along the river.</p></caption>
      <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f06.pdf"/>

    </fig>

      <fig id="App1.Ch1.F7"><caption><p>Design procedure of slot-check dam system for debris flow hazard mitigation.</p></caption>
      <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f07.pdf"/>

    </fig>

      <fig id="App1.Ch1.F8"><caption><p>Controlled catchment area of each subsystem.</p></caption>
      <?xmltex \igopts{width=284.527559pt}?><graphic xlink:href="https://nhess.copernicus.org/preprints/3/5777/2015/nhessd-3-5777-2015-f08.pdf"/>

    </fig>

    </app></app-group></back>
    </article>
