import pyproj
import math
import logging # 新增 logging 套件
import unicodedata
# 設定 logging，讓錯誤訊息能正確輸出到伺服器日誌
logging.basicConfig(level=logging.INFO)
logger = logging.getLogger(__name__)
# --- 計算 UTM Zone ---
def get_utm_zone(longitude):
return math.floor((longitude + 180) / 6) + 1
# --- 經緯度轉平面座標（根據不同 datum 判斷投影方式） ---
def latlon_to_projected(lat, lon, datum_key):
try:
if not (-90 <= lat <= 90):
raise ValueError("緯度必須在 -90 到 90 度之間")
if not (-180 <= lon <= 180):
raise ValueError("經度必須在 -180 到 180 度之間")
datum_epsg = DATUMS[datum_key]
source_crs = pyproj.CRS(datum_epsg)
if datum_key == 'TWD97':
target_crs = pyproj.CRS("EPSG:3826")
zone = "TM2-121"
is_south = False
else:
zone = get_utm_zone(lon)
is_south = lat < 0
utm_epsg = 32700 + zone if is_south else 32600 + zone
target_crs = pyproj.CRS.from_epsg(utm_epsg)
transformer = pyproj.Transformer.from_crs(source_crs, target_crs, always_xy=True)
x, y = transformer.transform(lon, lat)
return x, y, zone, is_south
except Exception as e:
# 將錯誤訊息輸出到日誌，方便伺服器維運
logger.error(f"轉換錯誤: {e}")
return None, None, None, None
# --- 平面座標轉經緯度 ---
def projected_to_latlon(x, y, zone, is_south, datum_key):
try:
datum_epsg = DATUMS[datum_key]
target_crs = pyproj.CRS(datum_epsg)
if datum_key == 'TWD97':
source_crs = pyproj.CRS("EPSG:3826")
elif datum_key == 'WGS 84':
if not isinstance(zone, int) or not (1 <= zone <= 60):
raise ValueError("UTM Zone 必須是 1 到 60 之間的整數")
utm_epsg = 32700 + zone if is_south else 32600 + zone
source_crs = pyproj.CRS.from_epsg(utm_epsg)
else:
raise ValueError(f"不支援的大地基準: {datum_key}")
transformer = pyproj.Transformer.from_crs(source_crs, target_crs, always_xy=True)
lon, lat = transformer.transform(x, y)
return lon, lat
except Exception as e:
# 將錯誤訊息輸出到日誌，方便伺服器維運
logger.error(f"反向轉換錯誤: {e}")
return None, None
# --- 定義常用大地基準 ---
DATUMS = {
"WGS 84": "EPSG:4326",
"TWD97": "EPSG:3824",
}
# --- 曼寧係數查詢（依據附件 ALL.md）---
MANNING_N_TABLE = {
"純細砂": 0.025,
"不緻密之細砂": 0.027,
"粗砂及細砂": 0.028,
"平常砂土": 0.030,
"砂質壤土": 0.032,
"堅壤土及黏質壤土": 0.035,
"平常礫土": 0.035,
"全面密草生": 0.040,
"粗礫、石礫及砂礫": 0.040,
"礫岩、硬頁岩、軟岩、水成岩": 0.045,
"硬岩": 0.050,
"混凝土": 0.012,
"鋼筋混凝土": 0.012,
}
def get_manning_materials_list():
"""
回傳所有支援的曼寧係數材料名稱清單。
"""
return list(MANNING_N_TABLE.keys())
# --- 最大容許流速表（僅取最大值）---
MAX_VELOCITY_TABLE = {
"純細砂": 0.30,
"不緻密之細砂": 0.46,
"粗砂及細砂": 0.61,
"平常砂土": 0.76,
"砂質壤土": 0.84,
"堅壤土及黏質壤土": 1.14,
"平常礫土": 1.52,
"全面密草生": 2.50,
"粗礫、石礫及砂礫": 1.83,
"礫岩、硬頁岩、軟岩、水成岩": 2.44,
"硬岩": 4.57,
"混凝土": 6.10,
"鋼筋混凝土": 12.0,
}
# --- 最小容許流速（僅混凝土/鋼筋混凝土）---
MIN_VELOCITY_CONCRETE = 0.8
def get_max_velocity_materials_list():
"""
回傳所有支援的最大容許流速材料名稱清單。
"""
return list(MAX_VELOCITY_TABLE.keys())
def normalize_material_name(material: str) -> str:
# 去除空白、全形轉半形、小寫
s = material.strip()
s = unicodedata.normalize('NFKC', s)
s = s.lower()
# 常見同義詞對應
if s in ["鋼筋混凝土", "rc", "reinforced concrete"]:
return "混凝土"
return s
def query_manning_n(material: str):
norm = normalize_material_name(material)
# 以標準化名稱查表
for k in MANNING_N_TABLE:
if normalize_material_name(k) == norm:
n = MANNING_N_TABLE[k]
v_range = MAX_VELOCITY_TABLE.get(k)
if n is not None and v_range is not None:
return k, n, v_range
elif n is not None:
return k, n, None
return None, None, None
def get_max_velocity(material: str):
return MAX_VELOCITY_TABLE.get(material)
# --- 土壓力係數計算 ---
def active_earth_pressure_coefficient(phi_deg: float):
"""主動土壓力係數 Ka (庫倫公式)"""
import math
phi = math.radians(phi_deg)
ka = round((1 - math.sin(phi)) / (1 + math.sin(phi)), 4)
formula = "Ka = (1 - sinφ) / (1 + sinφ)"
calculation_steps = f"Ka = (1 - sin{phi_deg:.2f}°) / (1 + sin{phi_deg:.2f}°) = {ka}"
regulation = "依據《水土保持技術規範》第117、118、164條"
explanation = "主動土壓力常用庫倫公式計算，設計時應依規範選用正確內摩擦角。"
input_params = {'phi': phi_deg}
return {
'Ka': ka,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
def passive_earth_pressure_coefficient(phi_deg: float):
"""被動土壓力係數 Kp (庫倫公式)"""
import math
phi = math.radians(phi_deg)
kp = round((1 + math.sin(phi)) / (1 - math.sin(phi)), 4)
formula = "Kp = (1 + sinφ) / (1 - sinφ)"
calculation_steps = f"Kp = (1 + sin{phi_deg:.2f}°) / (1 - sin{phi_deg:.2f}°) = {kp}"
regulation = "依據《水土保持技術規範》第117、118、164條"
explanation = "被動土壓力常用庫倫公式計算，設計時應依規範選用正確內摩擦角。"
input_params = {'phi': phi_deg}
return {
'Kp': kp,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
# --- 排水溝流速計算（曼寧公式，含流速檢核）---
def channel_flow_velocity(n: float, r: float, s: float, material: str = None):
import math
v = (1/n) * (r ** (2/3)) * (s ** 0.5)
warning = None
if material:
max_v = get_max_velocity(material)
min_v = None
if material in ["混凝土", "鋼筋混凝土"]:
min_v = MIN_VELOCITY_CONCRETE
if max_v and v > max_v:
warning = f"警告：計算流速 v = {v:.4f} m/s 已超過『{material}』最大容許流速 {max_v} m/s，應於適當位置設置消能設施。"
elif min_v and v < min_v:
warning = f"警告：計算流速 v = {v:.4f} m/s 低於『{material}』最小容許流速 {min_v} m/s，可能導致泥砂淤積。"
formula = "v = (1/n) × R^(2/3) × S^(1/2)"
calculation_steps = f"v = (1/{n:.3f}) × {r:.3f}^(2/3) × {s:.4f}^(1/2) = {v:.4f} m/s"
regulation = "依據《水土保持技術規範》第19、85條及附件曼寧公式、最大容許流速表"
explanation = "明渠流速常用曼寧公式計算，並應檢核材料最大容許流速以符合法規。"
input_params = {
'n': n,
'r': r,
's': s,
'material': material
}
return {
'velocity': v,
'warning': warning,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
def channel_flow_discharge(v: float, a: float) -> float:
"""流量 Q = v * A"""
return v * a
def slope_stability_safety_factor(slope: float, unit_weight: float = None, friction_angle: float = None, cohesion: float = None, water_table: float = 0, method: str = "簡化法", soil_type: str = None):
"""
邊坡穩定安全係數計算（簡化法，支援土壤參數查表）。
slope: 坡度（百分比）
unit_weight: 土壤單位重（kN/m3）
friction_angle: 摩擦角（°）
cohesion: 凝聚力（kPa）
water_table: 地下水位高（m）
method: 計算方法（預設簡化法）
soil_type: 土壤類型（可選，若有則自動查表）
"""
# 1. 若有土壤類型，查表自動補齊參數
if soil_type:
key, uw, coh, fa, _, _ = material_parameter_query(soil_type)
if unit_weight is None and uw: unit_weight = uw
if cohesion is None and coh is not None: cohesion = coh
if friction_angle is None and fa is not None: friction_angle = fa
# 預設值
if unit_weight is None: unit_weight = 18.0
if friction_angle is None: friction_angle = 30.0
if cohesion is None: cohesion = 0.0
# 2. 計算坡角
import math
beta = math.atan(slope / 100) # 坡度百分比轉坡角（弧度）
# 3. 簡化法（平面滑動）安全係數公式
# FS = (c + (γ * h * cosβ) * tanφ) / (γ * h * sinβ)
h = 5.0 # 假設滑動面深度5m（可擴充為參數）
γ = unit_weight
φ = math.radians(friction_angle)
c = cohesion
# 地下水位修正（若有，則有效單位重減半）
γ_eff = γ if water_table == 0 else γ * 0.5
numerator = c + (γ_eff * h * math.cos(beta)) * math.tan(φ)
denominator = γ_eff * h * math.sin(beta)
FS = numerator / denominator if denominator > 0 else float('inf')
is_pass = FS >= 1.5
formula = "FS = (c + γh cosβ tanφ) / (γh sinβ)"
calculation_steps = (
f"FS = ({c:.2f} + ({γ_eff:.2f} × {h:.2f} × cos{math.degrees(beta):.2f}° × tan{math.degrees(φ):.2f}°)) / "
f"({γ_eff:.2f} × {h:.2f} × sin{math.degrees(beta):.2f}°) = {FS:.2f}"
)
regulation = "依據《水土保持技術規範》第152、154條及附件最小安全係數表"
explanation = "坡地穩定設計須符合規範建議安全係數，常用簡化法計算平面滑動安全係數。"
input_params = {
'slope': slope,
'unit_weight': unit_weight,
'friction_angle': friction_angle,
'cohesion': cohesion,
'water_table': water_table,
'method': method,
'soil_type': soil_type
}
msg = (
f"簡化法FS={FS:.2f}（≧1.5 {'合格' if is_pass else '不合格'}）\n"
f"參數：坡度={slope}%，單位重={γ}kN/m3，摩擦角={math.degrees(φ):.1f}°，凝聚力={c}kPa，滑動面深度={h}m，地下水位={water_table}m\n"
f"公式：FS = (c + γh cosβ tanφ) / (γh sinβ)\n依據《水土保持技術規範》與常用設計手冊，建議安全係數FS≧1.5。"
)
return {
'fs': FS,
'is_pass': is_pass,
'slope': slope,
'unit_weight': γ,
'friction_angle': math.degrees(φ),
'cohesion': c,
'water_table': water_table,
'soil_type': soil_type,
'method': method,
'h': h,
'message': msg,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
# --- USLE 參數查表 ---
R_TABLE = {
'台北市': 350, '新北市': 340, '桃園市': 320, '台中市': 370, '南投縣': 400, '高雄市': 300, '屏東縣': 320, '花蓮縣': 420, '台東縣': 410,
}
K_TABLE = {
'黏土': 0.20, '砂土': 0.30, '壤土': 0.25, '礫石': 0.15, '一般黏土': 0.20, '砂壤土': 0.28,
}
C_TABLE = {
'裸地': 1.0, '草地': 0.05, '農地': 0.3, '林地': 0.01, '水田': 0.02,
}
P_TABLE = {
'無措施': 1.0, '等高耕作': 0.5, '梯田': 0.2, '覆蓋作物': 0.3,
}
def get_supported_regions():
"""
回傳所有支援的地區名稱清單（R 因子/降雨/IDF/年雨量等）。
"""
return list(R_TABLE.keys())
def get_supported_soil_types():
"""
回傳所有支援的土壤類型清單（K 因子/土壤參數/滲透係數等）。
"""
return list(K_TABLE.keys())
def get_supported_land_uses():
"""
回傳所有支援的土地利用型態清單（C 因子/逕流係數等）。
"""
return list(C_TABLE.keys())
def get_supported_practices():
"""
回傳所有支援的水保措施清單（P 因子）。
"""
return list(P_TABLE.keys())
def query_r_factor(region: str = None, rainfall: float = None):
"""
查詢降雨沖蝕指數 R 值
參數：
- region: 地區名稱（如「台北市」、「新北市」等）
- rainfall: 年平均降雨量（mm）
回傳：dict，含 R 值、來源說明、單位等
"""
r_value, r_src = get_r_factor(region, rainfall)
if region and region in R_TABLE:
return {
'success': True,
'data': {
'region': region,
'r_value': r_value,
'unit': '百萬焦耳·公釐/公頃·小時·年',
'source': r_src
},
'message': f"地區 {region} 的降雨沖蝕指數 R = {r_value}，單位：百萬焦耳·公釐/公頃·小時·年"
}
elif rainfall:
return {
'success': True,
'data': {
'rainfall': rainfall,
'r_value': r_value,
'unit': '百萬焦耳·公釐/公頃·小時·年',
'source': r_src
},
'message': f"年平均降雨量 {rainfall} mm 推估的降雨沖蝕指數 R = {r_value}，單位：百萬焦耳·公釐/公頃·小時·年"
}
else:
supported = list(R_TABLE.keys())
return {
'success': False,
'data': supported,
'message': f"請提供地區名稱或年平均降雨量，支援查詢的地區有：{', '.join(supported)}"
}
def query_k_factor(soil_type: str = None, soil_factor: float = None):
"""
查詢土壤沖蝕指數 K 值
參數：
- soil_type: 土壤類型（如「黏土」、「砂土」等）
- soil_factor: 直接指定的 K 值
回傳：dict，含 K 值、來源說明、單位等
"""
k_value, k_src = get_k_factor(soil_type, soil_factor)
if soil_type and soil_type in K_TABLE:
return {
'success': True,
'data': {
'soil_type': soil_type,
'k_value': k_value,
'unit': '公噸·公頃·年/公頃·百萬焦耳·公釐',
'source': k_src
},
'message': f"土壤類型 {soil_type} 的沖蝕指數 K = {k_value}，單位：公噸·公頃·年/公頃·百萬焦耳·公釐"
}
elif soil_factor is not None:
return {
'success': True,
'data': {
'soil_factor': soil_factor,
'k_value': k_value,
'unit': '公噸·公頃·年/公頃·百萬焦耳·公釐',
'source': k_src
},
'message': f"使用者指定的土壤沖蝕指數 K = {k_value}，單位：公噸·公頃·年/公頃·百萬焦耳·公釐"
}
else:
supported = list(K_TABLE.keys())
return {
'success': False,
'data': supported,
'message': f"請提供土壤類型或直接指定 K 值，支援查詢的土壤類型有：{', '.join(supported)}"
}
def query_c_factor(land_use: str = None, cover_factor: float = None):
"""
查詢覆蓋與管理因子 C 值
參數：
- land_use: 土地利用類型（如「裸地」、「草地」等）
- cover_factor: 直接指定的 C 值
回傳：dict，含 C 值、來源說明、單位等
"""
c_value, c_src = get_c_factor(land_use, cover_factor)
if land_use and land_use in C_TABLE:
return {
'success': True,
'data': {
'land_use': land_use,
'c_value': c_value,
'unit': '無因次',
'source': c_src
},
'message': f"土地利用類型 {land_use} 的覆蓋與管理因子 C = {c_value}，單位：無因次"
}
elif cover_factor is not None:
return {
'success': True,
'data': {
'cover_factor': cover_factor,
'c_value': c_value,
'unit': '無因次',
'source': c_src
},
'message': f"使用者指定的覆蓋與管理因子 C = {c_value}，單位：無因次"
}
else:
supported = list(C_TABLE.keys())
return {
'success': False,
'data': supported,
'message': f"請提供土地利用類型或直接指定 C 值，支援查詢的土地利用類型有：{', '.join(supported)}"
}
def query_p_factor(practice: str = None, practice_factor: float = None):
"""
查詢水土保持處理因子 P 值
參數：
- practice: 水土保持措施（如「無措施」、「等高耕作」等）
- practice_factor: 直接指定的 P 值
回傳：dict，含 P 值、來源說明、單位等
"""
p_value, p_src = get_p_factor(practice, practice_factor)
if practice and practice in P_TABLE:
return {
'success': True,
'data': {
'practice': practice,
'p_value': p_value,
'unit': '無因次',
'source': p_src
},
'message': f"水土保持措施 {practice} 的處理因子 P = {p_value}，單位：無因次"
}
elif practice_factor is not None:
return {
'success': True,
'data': {
'practice_factor': practice_factor,
'p_value': p_value,
'unit': '無因次',
'source': p_src
},
'message': f"使用者指定的水土保持處理因子 P = {p_value}，單位：無因次"
}
else:
supported = list(P_TABLE.keys())
return {
'success': False,
'data': supported,
'message': f"請提供水土保持措施或直接指定 P 值，支援查詢的水土保持措施有：{', '.join(supported)}"
}
def get_r_factor(region, rainfall=None):
if region and region in R_TABLE:
return R_TABLE[region], f"依據地區查表({region})"
elif rainfall:
return rainfall * 0.3, "依據年降雨量簡化推估"
else:
return 300, "預設值"
def get_k_factor(soil_type, soil_factor=None):
if soil_type and soil_type in K_TABLE:
return K_TABLE[soil_type], f"依據土壤類型查表({soil_type})"
elif soil_factor is not None:
return soil_factor, "由使用者輸入"
else:
return 0.25, "預設值"
def get_c_factor(land_use, cover_factor=None):
if land_use and land_use in C_TABLE:
return C_TABLE[land_use], f"依據土地利用查表({land_use})"
elif cover_factor is not None:
return cover_factor, "由使用者輸入"
else:
return 0.05, "預設值"
def get_p_factor(practice, practice_factor=None):
if practice and practice in P_TABLE:
return P_TABLE[practice], f"依據措施查表({practice})"
elif practice_factor is not None:
return practice_factor, "由使用者輸入"
else:
return 0.5, "預設值"
def soil_erosion_modulus(length, slope, rainfall, region=None, soil_type=None, land_use=None, practice=None, soil_factor=None, cover_factor=None, practice_factor=None, method='USLE'):
"""
土壤侵蝕模數/流失量計算（USLE公式，支援地區、土壤、土地利用、措施查表）。
"""
# 1. R 因子
R, R_src = get_r_factor(region, rainfall)
# 2. K 因子
K, K_src = get_k_factor(soil_type, soil_factor)
# 3. L 因子
m = 0.5 if slope >= 5 else 0.2
L = (length / 22.13) ** m
# 4. S 因子
import math
theta = math.atan(slope / 100)
S = 10.8 * math.sin(theta) + 0.03
# 5. C 因子
C, C_src = get_c_factor(land_use, cover_factor)
# 6. P 因子
P, P_src = get_p_factor(practice, practice_factor)
# 7. USLE 計算
A = R * K * L * S * C * P
formula = "A = R × K × L × S × C × P"
calculation_steps = (
f"A = {R:.2f} × {K:.3f} × {L:.3f} × {S:.3f} × {C:.3f} × {P:.3f} = {A:.2f}"
)
regulation = "依據《水土保持技術規範》第35、92條及附件USLE公式、參數表"
explanation = "USLE公式為國際通用土壤流失量推估方法，台灣水保規範明定可用於坡地土壤侵蝕評估。"
input_params = {
'length': length,
'slope': slope,
'rainfall': rainfall,
'region': region,
'soil_type': soil_type,
'land_use': land_use,
'practice': practice,
'soil_factor': soil_factor,
'cover_factor': cover_factor,
'practice_factor': practice_factor,
'method': method
}
msg = (
f"USLE公式：A = R*K*L*S*C*P\n"
f"R(降雨侵蝕力)={R:.2f}（{R_src}），K(土壤可蝕性)={K:.3f}（{K_src}），L(坡長)={L:.3f}，S(坡度)={S:.3f}，C(覆蓋)={C:.3f}（{C_src}），P(水保)={P:.3f}（{P_src}）\n"
f"依據美國USDA/NRCS與台灣水保局公開資料，參數可依地區/作物/措施調整。"
)
# 回傳所有參數明細
return {
'erosion_modulus': A,
'soil_loss': A,
'method': method,
'region': region,
'soil_type': soil_type,
'land_use': land_use,
'practice': practice,
'R': R, 'R_src': R_src,
'K': K, 'K_src': K_src,
'L': L,
'S': S,
'C': C, 'C_src': C_src,
'P': P, 'P_src': P_src,
'message': msg,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
# 逕流係數表（依據水土保持技術規範第18條）
RUNOFF_COEFF_TABLE = {
'陡峻山地': {
'min': 0.75,
'max': 0.90,
'開發中': 0.95
},
'山麓區': {
'min': 0.70,
'max': 0.80,
'開發中': 0.90
},
'丘陵地或森林': {
'min': 0.50,
'max': 0.75,
'開發中': 0.90
},
'平坦耕地': {
'min': 0.45,
'max': 0.60,
'開發中': 0.85
},
'非農業使用': {
'min': 0.75,
'max': 0.95,
'開發中': 1.00
},
'農業區': {
'min': 0.45,
'max': 0.60,
'開發中': 0.85
}
}
def get_runoff_coeff(land_use, runoff_coeff=None, is_developing=False):
"""
查詢逕流係數C值
land_use: 土地利用類型或集水區狀況，必須是以下之一：
- 陡峻山地
- 山麓區
- 丘陵地或森林
- 平坦耕地
- 非農業使用
runoff_coeff: 直接指定的逕流係數值
is_developing: 是否為開發中狀態
"""
# 驗證land_use是否為有效值
valid_land_uses = ['陡峻山地', '山麓區', '丘陵地或森林', '平坦耕地', '非農業使用', '農業區']
if land_use not in valid_land_uses:
return None, f"土地利用類型必須是以下之一：{', '.join(valid_land_uses)}"
# 如果直接指定逕流係數，直接返回
if runoff_coeff is not None:
return runoff_coeff, "由使用者輸入"
# 開發中狀態直接返回1.0
if is_developing:
return 1.0, "開發中狀態，逕流係數以1.0計算"
# 查表並計算平均值
if land_use in RUNOFF_COEFF_TABLE:
if is_developing:
return RUNOFF_COEFF_TABLE[land_use]['開發中'], f"開發中狀態，{land_use}"
else:
# 計算範圍內的平均值
min_val = RUNOFF_COEFF_TABLE[land_use]['min']
max_val = RUNOFF_COEFF_TABLE[land_use]['max']
avg = (min_val + max_val) / 2
return avg, f"{land_use}逕流係數範圍：{min_val}~{max_val}，採用平均值{avg:.2f}"
return None, f"找不到土地利用類型：{land_use}"
def calc_idf_coeffs(P):
"""
依據規範公式，計算A、B、C、G、H係數
"""
A = (P / (189.96 + 0.31 * P)) ** 2
B = 55
C = (P / (381.71 + 1.45 * P)) ** 2
G = (P / (42.89 + 1.33 * P)) ** 2
H = (P / (65.33 + 1.836 * P)) ** 2
return A, B, C, G, H
def calc_rainfall_intensity_by_spec(P, T, t):
"""
依據規範公式，計算降雨強度I值
P: 年平均降雨量(mm)
T: 重現期(年)
t: 集流時間/降雨延時(分鐘)
"""
import math
A, B, C, G, H = calc_idf_coeffs(P)
I = (G + H * math.log(T)) ** (A / ((t + B) ** C))
return I, {'A': A, 'B': B, 'C': C, 'G': G, 'H': H}
def get_rainfall_intensity(region=None, rainfall_intensity=None, return_period=None, duration=None, P=None):
"""
若有P值，優先依規範公式推估I值，否則查表或用經驗公式。
"""
if P is not None and return_period is not None and duration is not None:
I, coeffs = calc_rainfall_intensity_by_spec(P, return_period, duration)
src = f"依據規範公式(P={P}, T={return_period}, t={duration})，A={coeffs['A']:.3f},B={coeffs['B']},C={coeffs['C']:.3f},G={coeffs['G']:.3f},H={coeffs['H']:.3f}"
return I, src
elif rainfall_intensity is not None:
return rainfall_intensity, "由使用者輸入"
elif region and hasattr(globals(), 'RAINFALL_INTENSITY_TABLE') and region in globals()['RAINFALL_INTENSITY_TABLE']:
return globals()['RAINFALL_INTENSITY_TABLE'][region], f"依據地區查表({region})"
elif duration is not None:
# 使用經驗公式 I = a/(t+b)^n
coeff = IDF_COEFF.get(region, IDF_COEFF['default'])
a, b, n = coeff['a'], coeff['b'], coeff['n']
I = a / ((duration + b) ** n)
src = f"依據經驗公式I=a/(t+b)^n，a={a},b={b},n={n}"
return I, src
else:
# 如果沒有足夠的參數，使用預設值
return 100.0, "預設值（未指定降雨強度或相關參數）"
def catchment_peak_runoff(area, rainfall_intensity=None, runoff_coeff=None, land_use=None, region=None, return_period=None, duration=None, method="Rational", P=None):
"""
集水區最大逕流量計算（Rational公式，支援土地利用、地區查表，並可依P自動推估I值）。
"""
# 1. 逕流係數 C
if runoff_coeff is not None:
C, C_src = runoff_coeff, "由使用者輸入"
elif land_use is not None:
C, C_src = get_runoff_coeff(land_use, runoff_coeff)
if C is None:
# 如果查詢失敗，使用預設值
C, C_src = 0.6, "預設值（無法查詢土地利用類型）"
else:
# 如果沒有提供 runoff_coeff 和 land_use，使用預設值
C, C_src = 0.6, "預設值（未指定逕流係數或土地利用類型）"
# 2. 降雨強度 I
if rainfall_intensity is not None:
I, I_src = rainfall_intensity, "由使用者輸入"
else:
I, I_src = get_rainfall_intensity(region, rainfall_intensity, return_period, duration, P)
# 3. 面積 A
A = area # ha
# 4. Rational 公式 Q = C * I * A / 360
Q = C * I * A / 360
formula = "Q = C × I × A / 360"
calculation_steps = f"Q = {C:.2f} × {I:.1f} × {A:.2f} / 360 = {Q:.4f} cms"
regulation = "依據《水土保持技術規範》第16、17、18條及附件降雨強度、逕流係數表"
explanation = "集水區面積小於1000公頃時，無實測資料可採Rational公式計算洪峰流量。"
input_params = {
'area': area,
'rainfall_intensity': rainfall_intensity,
'runoff_coeff': runoff_coeff,
'land_use': land_use,
'region': region,
'return_period': return_period,
'duration': duration,
'method': method,
'P': P
}
msg = (
f"Rational公式：Q = C * I * A / 360\n"
f"C(逕流係數)={C:.2f}（{C_src}），I(降雨強度)={I:.1f}mm/hr（{I_src}），A(面積)={A:.2f}ha\n"
f"依據《水土保持技術規範》第17條與附件公式，參數可依土地利用、地區、重現期、歷時、年雨量調整。"
)
return {
'peak_runoff': Q,
'runoff_coeff': C,
'runoff_coeff_src': C_src,
'rainfall_intensity': I,
'rainfall_intensity_src': I_src,
'area': A,
'method': method,
'message': msg,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
def retaining_wall_stability_check(height: float, thickness: float = None, unit_weight: float = None, friction_angle: float = None, cohesion: float = None, backfill_slope: float = 0, water_table: float = 0, soil_type: str = None, seismic_coef: float = 0.15, foundation_type: str = "土層", top_width: float = None, bottom_width: float = None, wall_unit_weight: float = 24.0):
"""
護岸/擋土牆穩定檢核（滑動、傾倒、承載力，支援土壤參數查表，含地震情況檢核）。
height: 牆高(m)
thickness: 牆底厚度(m)，矩形斷面用
unit_weight: 回填土單位重(kN/m3)
friction_angle: 回填土摩擦角(°)
cohesion: 回填土凝聚力(kPa)
backfill_slope: 回填坡度(°)
water_table: 地下水位高(m)
soil_type: 土壤類型（可選，若有則自動查表）
seismic_coef: 水平地震係數（預設0.15，依據台灣地震區域）
foundation_type: 基礎類型（"岩盤"或"土層"，預設"土層"）
top_width: 牆頂寬度(m)，梯形斷面用
bottom_width: 牆底寬度(m)，梯形斷面用
wall_unit_weight: 牆體單位重(kN/m3)，預設24.0（混凝土）
"""
# 1. 若有土壤類型，查表自動補齊參數
if soil_type:
key, uw, coh, fa, _, _ = material_parameter_query(soil_type)
if unit_weight is None and uw: unit_weight = uw
if cohesion is None and coh is not None: cohesion = coh
if friction_angle is None and fa is not None: friction_angle = fa
# 預設值
if unit_weight is None: unit_weight = 18.0
if friction_angle is None: friction_angle = 30.0
if cohesion is None: cohesion = 0.0
# 幾何參數
H = height
γ = unit_weight
φ = friction_angle
c = cohesion
β = backfill_slope
h_w = water_table
kh = seismic_coef # 水平地震係數
γ_wall = wall_unit_weight # 牆體單位重
# 判斷是矩形還是梯形斷面
is_trapezoidal = (top_width is not None and bottom_width is not None)
if is_trapezoidal:
# 梯形斷面
B = bottom_width # 底寬
T = top_width # 頂寬
else:
# 矩形斷面
if thickness is None:
raise ValueError("矩形斷面必須提供牆底厚度(thickness)參數")
B = thickness
T = thickness
# 2. 土壓力計算（簡化庫倫法，假設無黏聚力）
import math
φ_rad = math.radians(φ)
β_rad = math.radians(β)
# 2.1 常時土壓力係數
K_a = (math.cos(β_rad) - math.sqrt(math.cos(β_rad)**2 - math.cos(φ_rad)**2)) / (math.cos(β_rad) + math.sqrt(math.cos(β_rad)**2 - math.cos(φ_rad)**2)) if β > 0 else (1 - math.sin(φ_rad)) / (1 + math.sin(φ_rad))
# 2.2 地震時土壓力係數（Mononobe-Okabe法）
θ = math.atan(kh) # 地震角
K_ae = (math.cos(φ_rad - θ)**2) / (math.cos(θ) * math.cos(β_rad + θ) * (1 + math.sqrt(math.sin(φ_rad + β_rad) * math.sin(φ_rad - θ) / (math.cos(β_rad + θ) * math.cos(β_rad))))**2) if β > 0 else (math.cos(φ_rad - θ)**2) / (math.cos(θ)**2 * (1 + math.sqrt(math.sin(φ_rad) * math.sin(φ_rad - θ) / math.cos(θ)))**2)
# 2.3 計算土壓力
P_a = 0.5 * γ * H**2 * K_a # 常時主動土壓力
P_ae = 0.5 * γ * H**2 * K_ae # 地震時主動土壓力
# 3. 牆體重量與地震力
if is_trapezoidal:
# 梯形斷面牆體重量
A_wall = (B + T) * H / 2 # 梯形面積
W = γ_wall * A_wall # 牆重（單位長度）
# 重心位置（距離牆趾）
x_g = B/3 * (2*B + T) / (B + T)
else:
# 矩形斷面牆體重量
W = γ_wall * B * H # 牆重（單位長度）
# 重心位置（距離牆趾）
x_g = B/2
W_h = kh * W # 牆體水平地震力
# 4. 滑動檢核
# 4.1 常時滑動安全係數
F_slide = (W * math.tan(φ_rad) + c * B) / P_a if P_a > 0 else float('inf')
# 4.2 地震時滑動安全係數
F_slide_eq = (W * math.tan(φ_rad) + c * B) / (P_ae + W_h) if (P_ae + W_h) > 0 else float('inf')
# 5. 傾倒檢核
# 5.1 常時傾倒安全係數
M_r = W * x_g # 牆重對趾部的抗傾倒力矩
M_o = P_a * H/3 # 主動土壓力對趾部的傾倒力矩
F_overturn = M_r / M_o if M_o > 0 else float('inf')
# 5.2 地震時傾倒安全係數
M_r_eq = M_r # 地震時抗傾倒力矩（不變）
M_o_eq = P_ae * H/3 + W_h * H/2 # 地震時傾倒力矩
F_overturn_eq = M_r_eq / M_o_eq if M_o_eq > 0 else float('inf')
# 6. 合力作用點位置檢核
# 6.1 常時合力作用點
e = B/2 - (M_r - M_o) / W # 偏心距
x = B/2 - e # 合力作用點距離牆趾的距離
# 6.2 地震時合力作用點
e_eq = B/2 - (M_r_eq - M_o_eq) / W # 地震時偏心距
x_eq = B/2 - e_eq # 地震時合力作用點距離牆趾的距離
# 6.3 合力作用點位置檢核
if foundation_type == "岩盤":
# 岩盤基礎：合力作用點必須在基礎底寬之二分之一中段內
pass_force_location = x >= B/4 and x <= 3*B/4
pass_force_location_eq = x_eq >= B/4 and x_eq <= 3*B/4
else:
# 土層基礎：合力作用點必須在基礎底寬之三分之一中段內
pass_force_location = x >= B/3 and x <= 2*B/3
pass_force_location_eq = x_eq >= B/3 and x_eq <= 2*B/3
# 7. 承載力檢核
q_max = W / B + (W * e * 6) / (B**2) # 牆趾最大壓力
q_allow = 200.0 # 假設基礎承載力標準值（kPa），可查表
F_bearing = q_allow / q_max if q_max > 0 else float('inf')
# 8. 合格判斷
# 8.1 常時情況
pass_slide = F_slide >= 1.5
pass_overturn = F_overturn >= 2.0
pass_bearing = F_bearing >= 3.0 # 修正為3.0，符合規範要求
pass_normal = pass_slide and pass_overturn and pass_bearing and pass_force_location
# 8.2 地震時情況
pass_slide_eq = F_slide_eq >= 1.2
pass_overturn_eq = F_overturn_eq >= 1.5
pass_earthquake = pass_slide_eq and pass_overturn_eq and pass_force_location_eq
# 8.3 總體合格判斷
is_pass = pass_normal and pass_earthquake
# 9. 說明
msg = (
f"【常時情況】\n"
f"滑動SF={F_slide:.2f}（≧1.5 {'合格' if pass_slide else '不合格'}），"
f"傾倒SF={F_overturn:.2f}（≧2.0 {'合格' if pass_overturn else '不合格'}），"
f"承載SF={F_bearing:.2f}（≧3.0 {'合格' if pass_bearing else '不合格'}），"
f"合力作用點位置{'合格' if pass_force_location else '不合格'}\n"
f"【地震情況】\n"
f"滑動SF={F_slide_eq:.2f}（≧1.2 {'合格' if pass_slide_eq else '不合格'}），"
f"傾倒SF={F_overturn_eq:.2f}（≧1.5 {'合格' if pass_overturn_eq else '不合格'}），"
f"合力作用點位置{'合格' if pass_force_location_eq else '不合格'}\n"
f"土壤參數：單位重={γ}kN/m3，摩擦角={φ}°，凝聚力={c}kPa，Kₐ={K_a:.3f}，Kₐₑ={K_ae:.3f}\n"
f"依據《水土保持技術規範》第120條，安全係數要求：常時滑動≧1.5，常時傾倒≧2.0，常時承載≧3.0，地震時滑動≧1.2，地震時傾倒≧1.5。"
)
formula = (
"【常時情況】\n"
"滑動: SF = (W tanφ + cB) / Pa\n"
"傾倒: SF = Mr / Mo\n"
"承載: SF = q_allow / q_max\n"
"【地震情況】\n"
"滑動: SF = (W tanφ + cB) / (Pae + Wh)\n"
"傾倒: SF = Mr / (Moe + Wh×H/2)"
)
# 根據斷面類型準備計算步驟輸出
if is_trapezoidal:
wall_info = f"梯形斷面：高度 = {H:.2f} m，頂寬 = {T:.2f} m，底寬 = {B:.2f} m，牆體單位重 = {γ_wall:.2f} kN/m³\n"
wall_weight_calc = f"牆體重量 W = {γ_wall:.2f} × ({B:.2f} + {T:.2f}) × {H:.2f} / 2 = {W:.2f} kN/m\n"
wall_centroid = f"重心位置 x_g = {B:.2f}/3 × (2×{B:.2f} + {T:.2f}) / ({B:.2f} + {T:.2f}) = {x_g:.2f} m\n"
else:
wall_info = f"矩形斷面：高度 = {H:.2f} m，厚度 = {B:.2f} m，牆體單位重 = {γ_wall:.2f} kN/m³\n"
wall_weight_calc = f"牆體重量 W = {γ_wall:.2f} × {B:.2f} × {H:.2f} = {W:.2f} kN/m\n"
wall_centroid = f"重心位置 x_g = {B:.2f}/2 = {x_g:.2f} m\n"
calculation_steps = (
f"【牆體幾何與重量】\n"
f"{wall_info}"
f"{wall_weight_calc}"
f"{wall_centroid}"
f"【常時情況】\n"
f"土壓力係數 Ka = {K_a:.4f}\n"
f"主動土壓力 Pa = 0.5 × {γ:.2f} × {H:.2f}² × {K_a:.4f} = {P_a:.2f} kN/m\n"
f"滑動: SF = ({W:.2f} × tan{φ:.2f}° + {c:.2f} × {B:.2f}) / {P_a:.2f} = {F_slide:.2f}\n"
f"傾倒: SF = {M_r:.2f} / {M_o:.2f} = {F_overturn:.2f}\n"
f"承載: SF = {q_allow:.2f} / {q_max:.2f} = {F_bearing:.2f}\n"
f"合力作用點位置: x = {x:.2f} m（{foundation_type}基礎，{'合格' if pass_force_location else '不合格'}）\n"
f"【地震情況】\n"
f"地震係數 kh = {kh:.2f}\n"
f"地震時土壓力係數 Kae = {K_ae:.4f}\n"
f"地震時主動土壓力 Pae = 0.5 × {γ:.2f} × {H:.2f}² × {K_ae:.4f} = {P_ae:.2f} kN/m\n"
f"牆體水平地震力 Wh = {kh:.2f} × {W:.2f} = {W_h:.2f} kN/m\n"
f"地震時滑動: SF = ({W:.2f} × tan{φ:.2f}° + {c:.2f} × {B:.2f}) / ({P_ae:.2f} + {W_h:.2f}) = {F_slide_eq:.2f}\n"
f"地震時傾倒: SF = {M_r_eq:.2f} / ({P_ae:.2f} × {H/3:.2f} + {W_h:.2f} × {H/2:.2f}) = {F_overturn_eq:.2f}\n"
f"地震時合力作用點位置: x = {x_eq:.2f} m（{foundation_type}基礎，{'合格' if pass_force_location_eq else '不合格'}）"
)
regulation = "依據《水土保持技術規範》第117、118、120、164條及附件最小安全係數表"
explanation = "擋土牆設計須同時檢核常時與地震情況下的滑動、傾倒安全係數及合力作用點位置，並符合規範建議標準。"
# 根據斷面類型準備輸入參數
if is_trapezoidal:
input_params = {
'height': height,
'top_width': top_width,
'bottom_width': bottom_width,
'unit_weight': unit_weight,
'friction_angle': friction_angle,
'cohesion': cohesion,
'backfill_slope': backfill_slope,
'water_table': water_table,
'soil_type': soil_type,
'seismic_coef': seismic_coef,
'foundation_type': foundation_type,
'wall_unit_weight': wall_unit_weight
}
else:
input_params = {
'height': height,
'thickness': thickness,
'unit_weight': unit_weight,
'friction_angle': friction_angle,
'cohesion': cohesion,
'backfill_slope': backfill_slope,
'water_table': water_table,
'soil_type': soil_type,
'seismic_coef': seismic_coef,
'foundation_type': foundation_type,
'wall_unit_weight': wall_unit_weight
}
return {
# 常時情況
'sf_slide': F_slide,
'sf_overturn': F_overturn,
'sf_bearing': F_bearing,
'force_location': x,
'pass_force_location': pass_force_location,
'pass_slide': pass_slide,
'pass_overturn': pass_overturn,
'pass_bearing': pass_bearing,
'pass_normal': pass_normal,
# 地震情況
'sf_slide_eq': F_slide_eq,
'sf_overturn_eq': F_overturn_eq,
'force_location_eq': x_eq,
'pass_force_location_eq': pass_force_location_eq,
'pass_slide_eq': pass_slide_eq,
'pass_overturn_eq': pass_overturn_eq,
'pass_earthquake': pass_earthquake,
# 總體合格判斷
'is_pass': is_pass,
# 其他參數
'unit_weight': γ,
'friction_angle': φ,
'cohesion': c,
'soil_type': soil_type,
'height': H,
'thickness': B,
'backfill_slope': β,
'water_table': h_w,
'seismic_coef': kh,
'foundation_type': foundation_type,
# 輸出信息
'message': msg,
'regulation': regulation,
'explanation': explanation,
'input_params': input_params,
'formula': formula,
'calculation_steps': calculation_steps
}
def vegetation_slope_suggestion(slope: float, soil_type: str, climate: str):
"""
植生護坡設計建議。
依據《水土保持技術規範》及附件，依坡度、土壤、氣候自動查表建議。
"""
# 坡度分級
if slope <= 5:
grade = 1
elif slope <= 15:
grade = 2
elif slope <= 30:
grade = 3
elif slope <= 40:
grade = 4
elif slope <= 55:
grade = 5
elif slope <= 100:
grade = 6
else:
grade = 7
# 建議工法與草種
if grade <= 3:
method = "噴播草皮或直接播種，分區分期施工"
species = "百慕達草、狗牙根、地毯草等耐旱耐沖蝕草種"
coverage = 90.0
extra = ""
elif grade <= 5:
method = "噴播草皮+格框或土工網，分區分期施工"
species = "百慕達草、狗牙根、地毯草等耐旱耐沖蝕草種"
coverage = 90.0
extra = "坡度較大時應加強排水設施與坡面穩定措施"
else:
method = "格框+噴播草皮或植生袋，分區分期施工"
species = "百慕達草、狗牙根、地毯草等耐旱耐沖蝕草種，並可輔以灌木或喬木"
coverage = 90.0
extra = "坡度極大時須加強排水、坡面穩定與緩衝帶設置"
# 註明依據條文
regulation = (
"依據《水土保持技術規範》第8、167、172條及附件坡度分級、樣區面積、覆蓋率等規定，"
"建議坡面植生覆蓋率達90%，草種以百慕達草、狗牙根等耐旱耐沖蝕草種為主，"
"坡度大於30%時應加強排水與坡面穩定措施，並分區分期施工以減少裸露面積。"
)
msg = f"{extra}\n{regulation}"
return slope, soil_type, climate, method, species, coverage, msg
def material_parameter_query(material: str):
"""
常用材料設計參數查詢。
"""
MATERIAL_PARAMETER_TABLE = {
# 土壤類
"一般黏土": {"unit_weight": 18.0, "cohesion": 20.0, "friction_angle": 25.0, "strength": 200.0, "message": "依據常用土壤工程手冊"},
"砂土": {"unit_weight": 17.5, "cohesion": 0.0, "friction_angle": 32.0, "strength": 150.0, "message": "依據常用土壤工程手冊"},
"礫石": {"unit_weight": 20.0, "cohesion": 0.0, "friction_angle": 38.0, "strength": 250.0, "message": "依據常用土壤工程手冊"},
# 混凝土類
"混凝土": {"unit_weight": 24.0, "cohesion": None, "friction_angle": None, "strength": 21000.0, "message": "f'c=210kg/cm²，依據混凝土設計規範"},
# 石材類
"花崗岩": {"unit_weight": 26.0, "cohesion": None, "friction_angle": None, "strength": 100000.0, "message": "依據岩石工程手冊"},
"石灰岩": {"unit_weight": 25.0, "cohesion": None, "friction_angle": None, "strength": 80000.0, "message": "依據岩石工程手冊"},
# 其他常見材料
"頁岩": {"unit_weight": 23.0, "cohesion": None, "friction_angle": None, "strength": 40000.0, "message": "依據岩石工程手冊"},
"砂岩": {"unit_weight": 22.0, "cohesion": None, "friction_angle": None, "strength": 35000.0, "message": "依據岩石工程手冊"},
}
# 支援模糊查詢
key = None
for k in MATERIAL_PARAMETER_TABLE.keys():
if k in material or material in k:
key = k
break
if key:
param = MATERIAL_PARAMETER_TABLE[key]
return (key, param["unit_weight"], param["cohesion"], param["friction_angle"], param["strength"], param["message"])
else:
return (material, None, None, None, None, f"查無此材料，支援查詢的材料有：{', '.join(MATERIAL_PARAMETER_TABLE.keys())}")
def get_supported_materials():
"""
回傳所有支援的常用材料設計參數材料名稱清單。
"""
# 使用與 material_parameter_query 函數中相同的材料參數表
MATERIAL_PARAMETER_TABLE = {
# 土壤類
"一般黏土": {"unit_weight": 18.0, "cohesion": 20.0, "friction_angle": 25.0, "strength": 200.0, "message": "依據常用土壤工程手冊"},
"砂土": {"unit_weight": 17.5, "cohesion": 0.0, "friction_angle": 32.0, "strength": 150.0, "message": "依據常用土壤工程手冊"},
"礫石": {"unit_weight": 20.0, "cohesion": 0.0, "friction_angle": 38.0, "strength": 250.0, "message": "依據常用土壤工程手冊"},
# 混凝土類
"混凝土": {"unit_weight": 24.0, "cohesion": None, "friction_angle": None, "strength": 21000.0, "message": "f'c=210kg/cm²，依據混凝土設計規範"},
# 石材類
"花崗岩": {"unit_weight": 26.0, "cohesion": None, "friction_angle": None, "strength": 100000.0, "message": "依據岩石工程手冊"},
"石灰岩": {"unit_weight": 25.0, "cohesion": None, "friction_angle": None, "strength": 80000.0, "message": "依據岩石工程手冊"},
# 其他常見材料
"頁岩": {"unit_weight": 23.0, "cohesion": None, "friction_angle": None, "strength": 40000.0, "message": "依據岩石工程手冊"},
"砂岩": {"unit_weight": 22.0, "cohesion": None, "friction_angle": None, "strength": 35000.0, "message": "依據岩石工程手冊"},
}
return list(MATERIAL_PARAMETER_TABLE.keys())
# 坡面保護工法建議查表
SLOPE_PROTECTION_TABLE = [
# (坡度上限, 建議工法, 適用說明)
(5, "草皮或直接播種", "坡度平緩，適合草皮、噴播或直接播種。"),
(15, "噴播草皮+分區施工", "坡度較緩，建議分區分期噴播草皮，必要時加覆蓋物。"),
(30, "噴播草皮+格框/土工網", "坡度中等，建議噴播草皮並加格框或土工網。"),
(40, "格框+噴播草皮/土工網", "坡度較大，建議格框、土工網加強，並輔以噴播草皮。"),
(55, "格框+混凝土/石籠+草皮", "坡度陡峭，建議格框、混凝土或石籠加草皮，並加強排水。"),
(100, "混凝土/石籠+格框+植生袋", "坡度極大，建議混凝土、石籠、格框與植生袋組合，並設緩衝帶。"),
(999, "結構型護坡（混凝土、石籠）", "超陡坡，需採結構型護坡並加強排水與穩定。"),
]
def get_supported_slope_protection_methods():
"""
回傳所有支援的坡面保護工法建議清單。
"""
return list(set([row[1] for row in SLOPE_PROTECTION_TABLE]))
# 土壤滲透係數查表（m/hr）
SOIL_K_TABLE = {
'砂土': 1.0,
'壤土': 0.2,
'黏土': 0.01,
'礫石': 5.0,
'砂壤土': 0.5,
'一般黏土': 0.01,
}
def get_supported_soil_k_types():
"""
回傳所有支援的土壤滲透係數土壤類型清單。
"""
return list(SOIL_K_TABLE.keys())
# IDF曲線查表（部分地區、重現期、歷時，mm/hr）
IDF_TABLE = {
'台北市': {
10: {10: 200, 30: 140, 60: 110, 120: 80, 180: 60},
25: {10: 240, 30: 160, 60: 130, 120: 95, 180: 70},
50: {10: 270, 30: 180, 60: 150, 120: 110, 180: 80},
},
'新北市': {
10: {10: 190, 30: 135, 60: 105, 120: 75, 180: 55},
25: {10: 230, 30: 155, 60: 125, 120: 90, 180: 65},
50: {10: 260, 30: 170, 60: 140, 120: 105, 180: 75},
},
'台中市': {
10: {10: 170, 30: 120, 60: 95, 120: 70, 180: 50},
25: {10: 210, 30: 140, 60: 120, 120: 85, 180: 60},
50: {10: 240, 30: 160, 60: 135, 120: 100, 180: 70},
},
}
def get_supported_idf_locations():
"""
回傳所有支援的IDF曲線地點清單。
"""
return list(IDF_TABLE.keys())
# 若無查表資料，採經驗公式 I = a/(t+b)^n
IDF_COEFF = {
'default': {'a': 800, 'b': 15, 'n': 0.7},
'台北市': {'a': 900, 'b': 12, 'n': 0.72},
'新北市': {'a': 850, 'b': 13, 'n': 0.71},
'台中市': {'a': 700, 'b': 15, 'n': 0.68},
}
def idf_curve_query(location: str, return_period: float, duration: float, P: float = None):
"""
降雨強度-歷時-頻率（IDF）曲線查詢（支援地區/重現期/歷時查表與推估，並可依P自動推估A、B、C、G、H）。
location: 地區名稱
return_period: 重現期（年）
duration: 歷時（分鐘）
P: 年平均降雨量（mm，可選，若有則依規範公式自動推估I值）
"""
loc = location
rp = int(round(return_period))
dur = int(round(duration))
# 1. 查表
intensity = None
src = ""
detail = ""
if loc in IDF_TABLE and rp in IDF_TABLE[loc]:
# 找最接近的歷時
durations = sorted(IDF_TABLE[loc][rp].keys())
closest = min(durations, key=lambda x: abs(x-dur))
intensity = IDF_TABLE[loc][rp][closest]
src = f"依據IDF查表({loc}, {rp}年, {closest}分)"
# 2. 若無查表，優先依P用規範公式
if intensity is None and P is not None:
I, coeffs = calc_rainfall_intensity_by_spec(P, return_period, duration)
intensity = I
src = f"依據規範公式(P={P}, T={return_period}, t={duration})"
detail = (
f"A={coeffs['A']:.3f}, B={coeffs['B']}, C={coeffs['C']:.3f}, G={coeffs['G']:.3f}, H={coeffs['H']:.3f}\n"
f"I = (G + H * ln(T)) ^ (A / (t + B)^C)"
)
# 3. 若無P則用經驗公式
if intensity is None:
coeff = IDF_COEFF.get(loc, IDF_COEFF['default'])
a, b, n = coeff['a'], coeff['b'], coeff['n']
intensity = a / ((dur + b) ** n)
src = f"依據經驗公式I=a/(t+b)^n，a={a},b={b},n={n}"
detail = "I = a / (t + b)^n\nt 為歷時（分鐘）"
msg = (
f"IDF曲線查詢：地區={loc}，重現期={rp}年，歷時={dur}分鐘\n"
f"降雨強度={intensity:.1f} mm/hr（{src}）\n"
f"{detail}"
f"依據《水土保持技術規範》與各地IDF曲線，若無查表資料則採規範公式或經驗公式推估。"
)
return {
'location': loc,
'return_period': rp,
'duration': dur,
'rainfall_intensity': intensity,
'source': src,
'message': msg
}
def slope_protection_suggestion(slope: float, soil_type: str = None, rainfall: float = None, region: str = None):
"""
坡面保護工法建議查詢（依坡度分級、土壤、降雨/地區自動查表）。
參數：坡度、土壤、降雨、地區
回傳：建議工法、說明
"""
# 根據坡度查表
method = ""
for limit, m, desc in SLOPE_PROTECTION_TABLE:
if slope <= limit:
method = m
break
if not method:
method = "結構型護坡（混凝土、石籠）"
desc = "超陡坡，需採結構型護坡並加強排水與穩定。"
# 組合說明
msg = f"坡度={slope}%，土壤={soil_type or '-'}，降雨={rainfall or '-'}mm，建議工法：{method}。{desc}"
regulation = "依據《水土保持技術規範》第8、167、172條及附件坡度分級、樣區面積、覆蓋率等規定"
return slope, soil_type, rainfall, method, f"{msg}\n{regulation}"
def gabion_stability_check(
height: float,
width: float,
wall_weight: float,
phi: float,
delta: float,
theta: float,
i: float,
gamma: float,
friction_coef: float,
pressure_mode: str = "active"
) -> dict:
"""
土石籠擋土牆穩定分析（主動/被動土壓力）。
參數：
- height: 土石籠高度 (m)
- width: 土石籠寬度 (m)
- wall_weight: 擋土牆總重 (kN/m)
- phi: 土壤內摩擦角 (°)
- delta: 牆背摩擦角 (°)
- theta: 牆背傾斜角 (°)
- i: 地表傾斜角 (°)
- gamma: 土壤飽和單位重 (kN/m³)
- friction_coef: 摩擦係數
- pressure_mode: 土壓力模式 ("active" 或 "passive")
回傳：dict，含 success, data, message, report（繁體中文完整報告書）
"""
import math
from datetime import datetime
try:
# 1. 計算土壓力係數
phi_rad = math.radians(phi)
theta_rad = math.radians(theta)
delta_rad = math.radians(delta)
i_rad = math.radians(i)
if i == 0:
# 簡化公式 (當地表水平時)
if pressure_mode == "active":
k = (1 - math.sin(phi_rad)) / (1 + math.sin(phi_rad))
formula = "Ka = (1 - sinφ) / (1 + sinφ)"
else:
k = (1 + math.sin(phi_rad)) / (1 - math.sin(phi_rad))
formula = "Kp = (1 + sinφ) / (1 - sinφ)"
else:
# 完整庫倫公式
if pressure_mode == "active":
numerator = math.cos(phi_rad - theta_rad)**2
denominator = math.cos(theta_rad)**2 * math.cos(delta_rad + theta_rad)
sqrt_part = math.sqrt(
(math.sin(phi_rad + delta_rad) * math.sin(phi_rad - i_rad)) /
(math.cos(delta_rad + theta_rad) * math.cos(theta_rad - i_rad))
)
k = numerator / (denominator * (1 + sqrt_part)**2)
formula = "Ka = cos²(φ-θ) / [cos²θ·cos(δ+θ)·(1+√Q)²], Q = [sin(φ+δ)·sin(φ-i)] / [cos(δ+θ)·cos(θ-i)]"
else:
numerator = math.cos(phi_rad + theta_rad)**2
denominator = math.cos(theta_rad)**2 * math.cos(delta_rad - theta_rad)
sqrt_part = math.sqrt(
(math.sin(phi_rad + delta_rad) * math.sin(phi_rad + i_rad)) /
(math.cos(delta_rad - theta_rad) * math.cos(theta_rad - i_rad))
)
k = numerator / (denominator * (1 - sqrt_part)**2)
formula = "Kp = cos²(φ+θ) / [cos²θ·cos(δ-θ)·(1-√Q)²], Q = [sin(φ+δ)·sin(φ+i)] / [cos(δ-θ)·cos(θ-i)]"
# 2. 計算土壓力總和
pa = 0.5 * gamma * height**2 * k
# 3. 計算分力
pv = pa * math.sin(delta_rad + theta_rad)
ph = pa * math.cos(delta_rad + theta_rad)
# 4. 計算力矩
mr = wall_weight * width / 2
mf = ph * height / 3
# 5. 計算安全係數
fs_overturning = mr / mf if mf != 0 else float('inf')
fs_sliding = ((wall_weight + pv) * friction_coef) / ph if ph != 0 else float('inf')
# 穩定性評估
assessment = []
if fs_overturning >= 1.5:
assessment.append("抗傾覆: 安全")
else:
assessment.append("抗傾覆: 不安全!")
if fs_sliding >= 1.5:
assessment.append("抗滑動: 安全")
else:
assessment.append("抗滑動: 不安全!")
# 報告書
report = (
f"【土石籠擋土牆{pressure_mode}土壓力分析計算書】\n"
f"生成時間: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}\n\n"
f"## 輸入參數\n"
f"- 分析模式: {pressure_mode}土壓力分析\n"
f"- 土壤內摩擦角 φ = {phi}°\n"
f"- 牆背摩擦角 δ = {delta}°\n"
f"- 牆背傾斜角 θ = {theta}°\n"
f"- 地表傾斜角 i = {i}°\n"
f"- 土壤飽和單位重 γ = {gamma} kN/m³\n"
f"- 擋土牆總重 W = {wall_weight} kN/m\n"
f"- 土石籠高度 H = {height} m\n"
f"- 土石籠寬度 B = {width} m\n"
f"- 摩擦係數 μ = {friction_coef}\n\n"
f"## 計算公式\n{formula}\n\n"
f"## 計算結果\n"
f"- 土壓力係數 K{'a' if pressure_mode == 'active' else 'p'} = {k:.4f}\n"
f"- 土壓力總和 P{'a' if pressure_mode == 'active' else 'p'} = {pa:.2f} kN/m\n"
f"- 垂直分力 Pv = {pv:.2f} kN/m\n"
f"- 水平分力 Ph = {ph:.2f} kN/m\n"
f"- 扶正力矩 Mr = {mr:.2f} kN·m/m\n"
f"- 傾倒力矩 Mf = {mf:.2f} kN·m/m\n"
f"- **穩定性評估**: {' | '.join(assessment)}\n"
)
msg = f"土壓力係數: {k:.4f}, 土壓力總和: {pa:.2f} kN/m, 安全係數: 抗傾覆={fs_overturning:.2f}, 抗滑動={fs_sliding:.2f}"
return {
"success": True,
"data": {
"pressure_coef": k,
"total_pressure": pa,
"vertical_force": pv,
"horizontal_force": ph,
"restoring_moment": mr,
"overturning_moment": mf,
"fs_overturning": fs_overturning,
"fs_sliding": fs_sliding,
"assessment": assessment
},
"message": msg,
"report": report
}
except Exception as e:
return {
"success": False,
"message": f"計算錯誤: {str(e)}",
"report": ""
}
def u_channel_rebar_calculation(
height: float,
wall_slope: float,
soil_slope: float,
soil_angle: float,
effective_depth: float,
soil_weight: float = 18.0
) -> dict:
"""
U型溝鋼筋量計算
參數：
- height: 溝高 (m)
- wall_slope: 溝壁傾角 (m)
- soil_slope: 土方傾角 (°)
- soil_angle: 安息角 (°)
- effective_depth: 有效厚度 (m)
- soil_weight: 土重 (kN/m³)，預設 18.0
回傳：dict，含計算結果與報告書
"""
import math
# 角度轉換
wall_slope_rad = math.atan(wall_slope)
soil_slope_rad = math.radians(soil_slope)
soil_angle_rad = math.radians(soil_angle)
# 計算土壓力係數 Ka
numerator = math.sin(soil_angle_rad) * math.sin(soil_angle_rad - soil_slope_rad)
denominator = math.cos(wall_slope_rad + soil_slope_rad) * math.cos(wall_slope_rad)
if numerator / denominator < 0:
return {
"success": False,
"message": "根據公式此資料不能計算",
"report": "【U型溝鋼筋量計算報告】\n\n輸入參數：\n- 溝高 H = {:.3f} m\n- 溝壁傾角 m = {:.3f}\n- 土方傾角 i = {:.2f}°\n- 安息角 ψ = {:.2f}°\n- 有效厚度 d = {:.3f} m\n- 土重 γ = {:.1f} kN/m³\n\n計算結果：\n根據公式此資料不能計算，請檢查輸入參數是否合理。"
}
ka = (math.cos(soil_angle_rad + wall_slope_rad))**2 / (
(math.cos(wall_slope_rad))**2 *
(1 + math.sqrt(numerator / denominator))**2
)
# 計算土壓力 P
p = soil_weight * height**2 * ka / (2 * math.cos(wall_slope_rad))
# 計算彎矩 M
m = soil_weight * height**3 * ka / (6 * math.cos(wall_slope_rad))
# 計算鋼筋量 As (使用容許應力 1400 kgf/cm² * 0.875)
jfs = 1400 * 0.875 # kgf/cm²
as_rebar = m / (jfs * effective_depth) * 1000000 / 1000 # cm²
# 生成報告書
report = (
"【U型溝鋼筋量計算報告】\n\n"
"輸入參數：\n"
f"- 溝高 H = {height:.3f} m\n"
f"- 溝壁傾角 m = {wall_slope:.3f}\n"
f"- 土方傾角 i = {soil_slope:.2f}°\n"
f"- 安息角 ψ = {soil_angle:.2f}°\n"
f"- 有效厚度 d = {effective_depth:.3f} m\n"
f"- 土重 γ = {soil_weight:.1f} kN/m³\n\n"
"計算公式：\n"
"1. 土壓力係數 Ka = cos²(ψ+m) / [cos²m·(1+√Q)²]\n"
" 其中 Q = [sinψ·sin(ψ-i)] / [cos(m+i)·cosm]\n"
"2. 土壓力 P = γ·H²·Ka / (2·cosm)\n"
"3. 彎矩 M = γ·H³·Ka / (6·cosm)\n"
"4. 鋼筋量 As = M / (fs·d) × 10⁶ / 1000\n\n"
"計算結果：\n"
f"- 土壓力係數 Ka = {ka:.4f}\n"
f"- 土壓力 P = {p:.3f} kN/m\n"
f"- 彎矩 M = {m:.3f} kN·m/m\n"
f"- 鋼筋量 As = {as_rebar:.3f} cm²/m"
)
return {
"success": True,
"data": {
"earth_pressure_coef": ka,
"earth_pressure": p,
"moment": m,
"rebar_area": as_rebar
},
"message": f"土壓力係數 Ka = {ka:.4f}, 土壓力 P = {p:.3f} kN/m, 彎矩 M = {m:.3f} kN·m/m, 鋼筋量 As = {as_rebar:.3f} cm²/m",
"report": report
}
# 鋼筋規格資料表
REBAR_TABLE = {
"#3": {"diameter": 9.53, "area": 0.71, "weight": 0.559, "perimeter": 29.9, "name": "10"},
"#4": {"diameter": 12.7, "area": 1.27, "weight": 0.994, "perimeter": 39.9, "name": "13"},
"#5": {"diameter": 15.9, "area": 1.98, "weight": 1.55, "perimeter": 49.9, "name": "16"},
"#6": {"diameter": 19.1, "area": 2.85, "weight": 2.24, "perimeter": 60.0, "name": "19"},
"#7": {"diameter": 22.2, "area": 3.88, "weight": 3.05, "perimeter": 69.7, "name": "22"},
"#8": {"diameter": 25.4, "area": 5.07, "weight": 3.98, "perimeter": 79.8, "name": "25"},
"#9": {"diameter": 28.7, "area": 6.45, "weight": 5.06, "perimeter": 90.2, "name": "29"},
"#10": {"diameter": 32.2, "area": 8.17, "weight": 6.41, "perimeter": 101.2, "name": "32"},
"#11": {"diameter": 35.8, "area": 10.08, "weight": 7.91, "perimeter": 112.5, "name": "36"},
"#14": {"diameter": 43.0, "area": 14.52, "weight": 11.4, "perimeter": 135.1, "name": "43"},
"#18": {"diameter": 57.3, "area": 25.81, "weight": 20.3, "perimeter": 180.0, "name": "57"}
}
def get_rebar_info(rebar_number: str) -> dict:
"""
查詢鋼筋規格資料
參數：
- rebar_number: 鋼筋編號（如 "#3"）
回傳：dict，含直徑、截面積、單位重量、周長
"""
return REBAR_TABLE.get(rebar_number)
def get_all_rebar_numbers() -> list:
"""
回傳所有可用的鋼筋編號
"""
return list(REBAR_TABLE.keys())
def calculate_rebar_weight(rebar_number: str, length: float) -> float:
"""
計算鋼筋重量
參數：
- rebar_number: 鋼筋編號（如 "#3"）
- length: 長度（m）
回傳：重量（kg）
"""
rebar_info = get_rebar_info(rebar_number)
if rebar_info:
return rebar_info["weight"] * length
return None
