STRUCTURAL DESIGN OF OPEN CHANNEL

INPUTS

curve

Fig. Trapezoidal section of channel

GEOMETRY

Wall thickness \(t_w\) \(m\)
Bottom width \(b\) \(m\)
Thickness of bottom slab \(t_s\) \(m\)
Height of wall \(H\) \(m\)
Side slope \(S_s\)

GEOTECHNICAL DATA

Angle of internal friction of foundation material \(\phi_f\) \(°\)
Bearing capacity of foundation material \(\sigma_f\) \(kN/m^2\)
Cohesion of foundation material \(C_f\) \(kN/m^2\)
Angle of internal friction of backfill material \(\phi_b\) \(°\)
Inclination of backfill material \(i_b\) \(°\)
Dry density of backfill material \(\gamma_d\) \(kN/m^3\)
Saturated density of backfill material \(\gamma_{sat}\) \(kN/m^3\)

OTHERS

Flow depth \(h_w\) \(m\)
Density of concrete \(\gamma_{c}\) \(kN/m^3\)
Horizontal seismic coefficient \(A_h\) \(-\)
Backfill depth \(h_s\) \(m\)
Depth of silt in the canal \(h_{sil}\) \(m\)
Ground water depth considered during saturation IN (%) \(w_w\) \(%\)
Uplift considered(%) \(P_s\) \(%\)

CALCULATIONS

Earth pressure at rest

\(K_r=(1-\sin\phi_b)\)

Slope of wall

\(\theta=\frac{180}{\pi}\cot(S_s)\)

If \(\theta\) is less than \(\phi_b\) then no soil pressure shall act on the structure otherwise the earth pressure shall be considered.

CALCULATION OF DIMENSION OF THE CHANNEL

Total height of channel, \(H_T\)

\(H_T=t_s+H\)

Flow top width, \(T_w\)

\(T_w=2h_wS_s+b\)

Top width of silt, \(T_s\)

\(T_s=2h_{sil}S_s+b\)

Inner top width, \(T_i\)

\(T_i=b+2S_sH\)

Outer top width, \(T_o\)

\(T_o=T_i+2H_TS_s\)

Bottom width of slab, \(b_o\)

\(b_o=2t_stan(\theta/2)+b\)

CENTROID OF THE SECTION

Area of channel, \(A\)

\(A=\frac{1}{2}(b_o+T_o)H_T-\frac{1}{2}(b+T_i)H\)

Centroid x

\(\bar{x}=\frac{b_o}{2}\)

Centroid y

\(y_1=\frac{H}{3}\frac{2T_i+b}{T_i+b}+t_s\)


\(A_1=\frac{1}{2}(b+T_i)H\)


\(y_2=\frac{H_T}{3}\frac{2T_o+b_o}{T_o+b_o}\)

\(A_2=\frac{1}{2}(b_o+T_o)H_T\)

\(\bar{y}=\frac{A_1y_1-A_2y_2}{A_1-A_2}\)

Silt area, \(A_s\)

\(A_s=\frac{1}{2}h_w(b+T_s)\)

Flow area, \(A_f\)

\(A_f=\frac{1}{2}h_w(b+T_w)\)

LOAD CALCULATION

1. NORMAL CONDITION

Loads Load intensity(kN/m) Force (kN) Moment arm (m) Resisting moment(kNm) Overturning moment(kNm)
1. Self-weight \(=\gamma_{c}A\) \(P_1=F_1\) \(x_1=\frac{b_o}{2}\) \(M_1=F_1×x_1\) -
2. Weight of water \(F_2=\gamma_{w}A_f\) \(P_2=F_2\) \(x_2=\frac{b_o}{2}\) \(M_2=F_2×x_2\) -
3. Weight of silt \(F_3=\gamma_{w}A_s\) \(P_3=F_3\) \(x_3=\frac{b_o}{2}\) \(M_3=F_3×x_3\) -
4. Hydrostatic force at both sides \(F_4=\gamma_{w}h_w\) \(P_4=\frac{1}{2}F_4h_w\) \(x_4=\frac{h_w}{3}\) \(M_4=F_4×x_4\) \(M_4=F_4×x_3\)
5. Lateral load due to silt \(F_5=(\gamma_{sat}-\gamma_{w})k_rh_{sil}\) \(P_5=\frac{1}{2}F_5h_{sil}\) \(x_5=\frac{h_{sil}}{3}\) \(M_5=F_5×x_5\) \(M_5=F_5×x_5\)
6. Earth pressure at both sides \(F_6=k_r\gamma_{d}h_s\) \(P_6=\frac{1}{2}F_4h_s\) \(x_6=\frac{h_s}{3}\) \(M_6=F_4×x_6\) \(M_6=F_4×x_6\)
7. Hydrostatic pressure at both sides (Water table) \(F_7=k_r\gamma_{w}h_wt (=0)\) \(P_7=\frac{1}{2}F_7h_wt\) \(x_7=\frac{h_wt}{3}\) \(M_7=F_7×x_7\) \(M_7=F_7×x_7\)
8. Seismic load \(F_8=A_h\gamma_cA\) \(P_8=F_8\) \(x_8=\bar{y}\) - \(M_8=F_8×x_8\)

STABILITY ANALYSIS

Factor of safety against sliding

\(FS_s=\frac{(C_fL+Ntan(\phi_f))}{T}\)

Factor of safety against overturning

\(F_o=\frac{RM}{RO}\)

Eccentricity

\(e=\frac{L}{2}-\frac{M}{V}\)

Minimum bearing pressure

\(\sigma_{min}=\frac{V}{L}(1-\frac{6e}{L})\)

Maximum bearing pressure

\(\sigma_{max}=\frac{V}{L}(1+\frac{6e}{L})\)

STABILITY ANALYSIS OF OPEN CANAL

Load combination Horizontal force (kN) Vertical force (kN) Total resisting moment (kNm) Total overturning moment (kNm) Resultant moment (kNm)
1.Without seismic load_Empty case \(H_1=P_6-P_6+P_7-P_7\) \(V_1=P1\) \(RM_1=M_1+M_7\) \(RO_1=M_7\) \(M_2=RM_1-RO_1\)
2.Without seismic load_Full case \(H_2=P_4-P_4+P_5-P_5+P_6-P6+P_7-P_7\) \(V_2=P_1+P_2+P_3\) \(RM_2=M_1+M_2+M_3+M_4+M_5+M_6+M_7\) \(RO_2=M_4+M_5+M_6+M_7\) \(M_2=RM_2-RO_2\)
3.With seismic load_Empty case \(H_3=P_6-P6+P_7-P_7+P_8\) \(V_3=P_1\) \(RM_3=M_1+M_7\) \(RO_3=M_7+M_8\) \(M_3=RM_3-RO_3\)
4.With seismic load_Full case \(H_4=P_4-P_4+P_5-P_5+P_6-P6+P_7-P_7+P_8\) \(V_4=P_1+P_2+P_3\) \(RM_4=M_1+M_2+M_3+M_4+M_5+M_6+M_7\) \(RO_4=M_4+M_5+M_6+M_7+M_8\) \(M_4=RM_2-RO_2\)
IN CASE OF SATURATED LOAD, UPLIFT LOAD SHALL BE INCLUDED AND CAN BE CALCULATED AS GIVEN BELOW

Depth of water, \(h_{wt}\)

\(h_{wt}=w_wh_{WT}\)

Where, \(h_{WT}\) = Ground water table depth during saturated condition

At walls

Width of wall where uplift acts

\(b_u=S_sh_{wt}\)

Uplift force at walls

\(F_{9w}=\gamma_{w}h_{wt}b_u\)

Centroid at one side

\(x_{9w1}=\frac{b_u}{3}\)

Centroid at other side

\(x_{9w1}=\frac{b_u}{3}+b_o\)

Uplift at base slab

\(F_{9s}=\gamma_{w}h_{wt}b_o\)

Centroid

\(x_{9s}=\frac{b_o}{2}\)